Mucopolysaccharidosis type III (MPS III) or Sanfilippo syndrome is a neurodegenerative disease caused by the accumulation of mucopolysaccharides in the body. As the symptoms are wide ranging, it is a challenge to provide a diagnosis and psychological treatment for affected children.The main objective of this study was to describe a form of music therapy treatment applied to three children diagnosed with MPS III. The psychological variables were evaluated by an ad hoc observation recording template, and the physiological variables were measured with a digital meter before and after each session. The perception of the parents was also considered through a semi-structured interview.An improvement in the psychological variables was shown in all cases. Changes in the physiological variables were also noted, although they varied according to each child. The parents report some benefit of music therapy and they share difficulty in assessing the extent of benefits of the music therapy.Findings indicate that music therapy can be a useful form of treatment with multiple benefits for children with conditions such as MPS III or similar conditions. However, further research is needed in this area and in the development of specific ways of evaluating music therapy. Among the approximately 7000 existing rare diseases , mucopolThe MPS group is classified into several subgroups, namely: (1) MPS I or Hurler syndrome; (2) MPS II or Hunter syndrome; (3) MPS III or Sanfilippo syndrome ; 4) MPS IV or Morquio syndrome (variants A and B); 5) MPS VI or Marotaux-Lamy; (6); and (7) MPS IX or Natowicz syndrome .M = 8; SD = 1) diagnosed with Sanfilippo syndrome and residing near the study site participated in this study. The participants were two siblings with MPS III type A (a girl and a boy), and a girl diagnosed with MPS III type B. Non-probabilistic, convenience sampling was used as Sanfilippo is a rare disease and the number of patients in a concentrated location is limited. The inclusion criteria to participate in this study was being a child diagnosed with Sanfilippo who attended the Music Therapy Research Centre in Biscay, Spain.Three children aged between 7 and 9 , diastolic blood pressure (DBP) and heart rate (HR).An additional instrument used was the ad hoc semi-structured interview. This was applied to the participating children’s parents to discover the children's general clinical history, as well as the differences observed after participating in music therapy sessions. Interviews used in similar studies were considered to create the interview –51.Barthel Index was also included [Kappa indices of between 0.84 and 0.97. In terms of validity, Wade and Hewer [The included . This meincluded  was usedincluded  obtainednd Hewer  obtainedFour different instruments were used for data collection:This is a study of three cases with mixed methodology. A qualitative descriptive analysis was used by employing an arbitrary observation code and a semi-structured interview. A quantitative analysis was also used by quantifying observation and taking physiological data using the digital meter. Specifically, data were taken in a prospective and longitudinal manner, since the information was collected at different times along three months, and it was a study with an intra-subject repeated measures design.Children attended 45-min weekly one-to-one sessions at Music Therapy Research Centre in Biscay, Spain. To carry out this study, a total of 20 sessions were observed over three months. All participants obtained permission from their parents through passive consent, after being informed about the study. Before beginning the observational period, the music therapist (MT) provided to the observer the basic sociodemographic data of each case, with the consent of their parents.The patients went to the Music Therapy Research Centre accompanied by their parents or caregivers. Only the music therapist (MT), the co-therapist  and the study's observer were present. The profile of the MT is a pianist who has played in different countries since he was 4 years old, and worked in different fields, including special education and health; he was a university lecturer and held a master's degree in music therapy. The observer was a psychologist specialised in healthcare, with experience with children and adolescents.The MT welcomed each child when they arrived and took them to the room where the sessions were held, which was located at Music Therapy Research Centre. The room was large and had natural light. It was empty except for an acoustic piano tuned to 432 Hz, a Spanish guitar tuned to 440 Hz, a marimba and a cabinet with instruments in another room. Due to the degree of hyperactivity and impulsivity of the patients, an attempt was made before starting the session to eliminate, cover or block any elements that could hinder the course of the session. There were also some instruments that had been previously selected for each session according to the patient and the pre-established objectives.The sessions were structured into three parts: The session started with the child listening to the so-called ‘welcome song’ or ‘welcome passage’. This consisted of a few seconds of silence, followed by an improvised passage played by the MT (who was located near and in front of the child) on the classical guitar. The performance was based on the patient’s needs and lasted about two minutes. After this, there were again a few seconds of silence. In this case, the child's role was receptive.The second part further developed the session by using a more active method, involving vocal or instrumental participation. The patient was invited to sing in an improvised and creative way using their name, the name(s) of siblings, parents, etc. promoting emotional expression, memory and speech. When instruments were used, the patient was offered contact with the instrument  and the patient's musical production began. The MT accompanied the sounds made by the child, trying to harmonise with their creation to communicate and encourage integration between child, MT and co-therapist. The rhythms and tones emitted by the patient were not always the same, which required great attention on the part of the MT to adapt to the different pitches and rhythmic context. According to how the patient was seen to respond in terms of their emotions and movement, the therapeutic relationship was aimed at fostering different aspects; for example, percussion instruments were used to work on gross motor control.The last part of the session used a receptive method, as the first part did. At the end of the session, after asking the patient to take a seat, the MT played a musical passage on the classical guitar for approximately two minutes. Although the passage was improvised, it could be based on the musical passages used during this same session.Information was collected at the beginning and the end of each session. Both psychological and physiological variables were taken in the room before starting, prior to any musical stimulus. The subsequent measurement was taken at the end of the session, in the same conditions as the initial one, although the psychological measurements were collected within (at the most) 5 min after finishing the session. An audio-visual recording of each session was also made with prior written consent in order to complete the assessment in case the scores were lost.A semi-structured interview was conducted by the researcher with the parents to expand the information relating to each case, and to gain a qualitative insight into the possible benefits of the therapy. This interview was carried out after completing the observation process three months afterwards, in order to assess the long-term impact of the intervention and to consider the consolidation of the effects of the sessions. The interview was held in a quiet, private place at Music Therapy Research Centre, and it was audio recorded to prevent any loss of information. The parents had previously signed an informed consent form describing the objective of the interview and the study, and indicating that the interview would be recorded. Interviews lasted almost one hour and were performed by the researcher who was a health psychologist.Barthel Index, he has a moderate dependency. The most notable symptoms are walking on tiptoes and intestinal problems leading to poor sleep quality. He has never been hospitalised and only takes nutritional and vitamin supplements. He has received treatment for deworming, and once a month the mother refers that he goes to energy-based therapies, like energetic kinesiology which focuses on the energetic processes in the body.A. is a 7-year-old boy who suffers from MPS IIIA. He was diagnosed when he was 1 year old, although his symptoms were not recognized until he was 4 years old. There are seven people in the household and he is the youngest of three siblings who all suffer from MPS IIIA. He currently remains in his school year and follows an adapted curriculum. He has a therapeutic teacher that helps him outside the standard school lessons and he also receives speech therapy sessions. According to the This section analyses the calculations related to the variables observed in A.’s seven sessions through the registration template. This was later converted into means and deviations, resulting in the findings shown in Fig. The researcher’s qualitative observations for the physical, communicative, emotional and cognitive dimensions are described below. A. walked on tiptoes and tried to leave the room and turn off the lights during the sessions. The physical and communication dimensions were particularly remarkable. At the physical level, it was generally difficult to measure his vital signs due to hyperactivity and movements, and it was not possible to carry out measurements in session three. When he listened to the guitar, he moved his legs, although he looked calm (because of his position in the chair), and his breathing was calm and relaxed. However, when he participated actively and played the drum, for example, he did not move his legs. Both verbal and non-verbal communication (sounds) increased when he was stimulated through songs and sounds. At the social-emotional level, positive emotions were strongly expressed and he smiled when he played. Cognitively, his attention was focused on each instrument, and when the MT stopped playing or changed instruments, he also focused on what the MT asked him to do and did himself. He was able to remember as he could repeat his MT’s name and play the instruments; if he could not play a given instrument, he had the capacity to learn. Creative behaviour was observed. For example, if he dropped the drumstick, he continued playing with his hand.His mother said that she had seen a great change in her son A. since he had started going to the Music Therapy Research Centre to receive music therapy sessions. At first, he did not like them; he cried and was upset when he had to go; however, she reported that now he is happy and compared with other children suffering from Sanfilippo, she considered that her son’s level of development had improved. For instance, she explained that hyperactivity was less marked and that he smiled a lot and was more obedient, as he paid attention to the instructions received, although she did not attribute it to anything specific. She was happy with her son's general development and said that he was happy when he arrived home after his music therapy sessions.These variables were analysed by finding the means and standard deviations of diastolic blood pressure, systolic blood pressure and heart rate that were collected before and after the sessions. The results are shown in Fig. Barthel Index, she has a severe dependency level. The most characteristic symptoms are coarse facial features, hyperactivity and impulsivity. She was hospitalised in 2012 for an operation on her adenoids, and in 2014 to remove her tonsils, as it was causing sleep apnoea. She has septal hypertrophy and had many high fevers and ear infections as a child. She has recurrent respiratory infections, so she takes Flixotide daily, and Ventolin on an occasional basis. She also takes risperidone and diazepam to decrease hyperactivity. She has visited an osteopath and physiotherapist for four years.R. is a 9-year-old girl who was diagnosed with MPS III-B when she was 4 years old, although the onset of symptoms was observed at 2 years old, when she stopped talking. She lives with her parents and has had special educational arrangements at school for three years. According to the This section analyses the calculation of the variables observed in the five sessions of R.’s case through the registration template. This was later converted into means and deviations, resulting in the findings shown in Fig. The researcher’s qualitative observations relating the physical, communicative, emotional and cognitive dimensions are described below. Before starting the sessions, rigidity in the muscle tone of R.’s extremities could be seen. Her breathing was unsteady and she was crying when she arrived. In this case, the most remarkable changes were found at the physical social and emotional level. During the sessions she showed hyperactivity, as she constantly wandered around the room; however, when listening to the guitar, she was able to concentrate on the music being played at that moment and to sit in the chair properly without moving, with slower breathing and a greater level of relaxation. At the communicational level, it is important to highlight her non-verbal responses, as she made a large number of sounds as a response to the MT. The greatest social and emotional change was evidenced by the fact that the crying at the beginning of the sessions disappeared when listening to the guitar. She also became involved with the other people in the room, which fostered group integration. Despite R.’s cognitive deterioration, she paid attention to the music therapist while he played during the sessions.The parents highlighted the difficulty in observing changes in their daughter due to the deterioration characteristic of the disease. When she started to attend the sessions, they saw more changes, since they noticed more active participation, more verbal and musical communication, as well as more calmness. Over the past year, they said she had been calm during the session, but when they left, hyperactivity and behaviour problems returned. They also emphasised that it was difficult to see changes due to the subjective nature of the treatment, comparing it with medicine.The means and standard deviations of the systolic, diastolic and heart rate presented by R. both before and after the sessions were used to analyse these variables Fig. .Fig. 4PrBarthel Index, she has a severe level of dependency. The most notable symptoms are motor clumsiness and reduced mobility. She had convulsions once and has poor circulation and intestinal disorders that result in poor sleep quality. She also has three crushed vertebrae and scoliosis. She was hospitalised when she was 5 years old to have her adenoids removed due to apneas at night and otitis. She takes natural enzymatic and vitamin supplements. She usually has intestinal parasites and receives treatment for deworming, and the mother mentions that once a month she goes to energy-based therapies like energetic kinesiology which focuses on the energetic processes in the body.X. is a 9-year-old girl who suffers from MPS IIIA. She was diagnosed when she was 3 years old, at the same age when the symptoms started due to a gait anomaly. There are seven people in the household. She is the middle child, and her two siblings also suffer from MPS III-A. She has special educational arrangements at school and attends speech therapy sessions. According to the This section analyses the calculation of the variables observed in the eight sessions of X.’s case through the registration template. This was later converted into means and deviations, resulting in the findings shown in Fig. The researcher’s qualitative observations relating to the physical, communicative, emotional and cognitive dimensions are described below. Before beginning the sessions, there was restlessness in X.’s legs and strong emotions, notably anguish and general restlessness. Restlessness in her legs diminished with music, and her level of relaxation increased. She communicated by repeating the sounds made by the MT, or creating her own singing, and playing the instrument played by the MT. At the gestural and body level, she frequently held the MT’s hand and maintained visual contact with him. The social and emotional aspects were also intensified, with positive or neutral emotions predominating. X. smiled at the MT and approached the people who were present, showing group integration. At the cognitive level, the most remarkable thing was her ability to pay attention when the MT played an instrument, and her creativity, as she created new harmonies by singing.X.’s mother considered the role of music in people's lives to be fundamental. She mentioned the difficulty in terms of being able to observe changes, and of assessing what remained after leaving the sessions, given the neurodegenerative disease suffered by her daughter. X. really likes music, and she sings and dances daily. This is a way of communicating with her that her mother has used since childhood. X.’s mother reported that, in general, X. was relaxed when she went home after the sessions. For example, there were days that she cried when she went to the session due to back pain. However, when she came out of the session, she felt more relaxed. Her mother stated that X. clearly enjoyed the sessions.These variables were analysed by finding the means and standard deviations of X.'s diastolic blood pressure, systolic blood pressure and heart rate that were collected before and after the sessions. The results are shown in Fig. This study uses a mixed methods approach to describe the effects of music therapy on three patients with Sanfilippo syndrome. This was done by measuring which psychological  and physiological (measured quantitatively) variables in these children increased or decreased after the music therapy intervention.There were higher scores after music therapy sessions in the four psychological variables included in the present study in all cases. This showed an improvement in terms of physical, communication, social, emotional and cognitive levels after participating in music therapy sessions. Some variations were found in the dimensions according to each child’s specific needs and limitations, which were shown in the measurements prior to the sessions. In the case of A., the physical and communication dimensions prevailed since the extent of his disability in these areas was less marked than in the other cases. He was the only one that maintained his verbal abilities and used them in the sessions. In the case of R., the changes at the physical level stood out because hyperactivity was particularly marked initially although it decreased considerably during the sessions. Besides, in R.’s case, an improvement was particularly noticeable in the social and emotional aspects, since she cried before starting the sessions and but this decreased as the session progressed. X. experienced improvements especially on a physical level, due to the general restlessness shown before the sessions and the relaxation during the therapy.These results can be compared with those obtained from children with ASD. García  observedOn a different note, the assessments made by the parents varied considerably. However, in all cases, the parents stated that, to a greater or lesser extent, they had seen that music therapy had benefited their children, especially at a social-emotional level. Furthermore, the common point of all the cases was the difficulty in making long-term evaluations of music therapy, due to the degenerative character of the disease. This information highlighted the importance of working with families in this type of study. Parents’ views were essential because their involvement provided a source of external feedback for the researcher that went beyond what was observed in the sessions. In other studies, in which parents have been interviewed, in addition to finding positive opinions about the use of music therapy, researchers also stressed the importance of their collaboration , 36, 38.The physiological variables showed greater variability in the results. This could be due to each child’s varying needs and baseline activation level. In the cases in which it tended to increase, the pre-treatment measurement was low whereas, in those where it tended to decrease, the pre-treatment measurement was in the normal average range or slightly above, so it was adjusted to what each individual needed at the time. To a greater or lesser extent, systolic blood pressure decreased in all cases. The heart rate was found to have increased in the siblings, which may have to do with the level of activation that the sessions produced on them, as a way of preparing the body for the action required. In the case of R., the pre-treatment measurement was higher in all measures, which may be due to the fact that her activation level was higher, especially due to crying and hyperactivity. After the sessions, all the indicators decreased to a normal range level, and a balance was achieved between the sympathetic and parasympathetic nervous systems , 45.Although no studies have been conducted on the measurement of physiological variables in children with MPS III or similar diseases when participating in a music therapy treatment, these results can be compared with research carried out on dimensions that are affected in these children, such as pain, stress and anxiety. In these studies, there was a decrease in the relevant indicators, with increased relaxation and reduced pain, anxiety and stress, as in the case of R. and in all cases in systolic blood pressure –43.This study has some limitations that should be considered for future research. Mainly, it should be noted that, since it is a rare disease and it is difficult to put together a sample, the number of the selected sample is small, with only three participants. Given the small sample size, the results were not compared between the cases, as it was considered that the results would not be relevant and would not be an appropriate representation of reality.Another limitation was the measure used to collect psychological variables. This was an ad hoc template on the direct observation of these variables by the researcher. It could lead to the impression of being subjective judgment, in which the observer’s perspectives and wishes may have influenced observation, although an attempt was made to overcome this limitation by recording the sessions. For future studies, it would be important to introduce different observers and calculate the interjudge agreement as a measurement of reliability. In addition, as it is a non-standardised instrument, despite relying on validated measures, some studies would be needed to determine its reliability and validity.Continuing with the assessment, another limitation is that due to the degree of affectation of the children and their ages, a standardised evaluation of the variables studied was not carried out. As the sample was small, a qualitative descriptive approach was chosen in order to obtain information of clinical and scientific interest. However, it would be interesting, for future studies and for international comparisons, to use standardised instruments, especially through a standardised parental report.A final limitation to note is the lack of previous research on the subject, which makes it very difficult to compare or comment on the results found in this study. Although it has been based on research on music therapy and other diseases that have similarities with Sanfilippo, there are no previous studies on this disease in particular or any type of non-medical treatment. However, this type of limitation can serve as an opportunity to identify new gaps in the literature and consequently stimulate new research.Regarding the implications of this preliminary clinical report, the results could be useful to encourage the development of a music therapy programme not only for children with MPS III but for anyone suffering from a rare disease or a neurodegenerative disorder of this nature that involves verbal and cognitive impairment. It can also influence the creation of a validated test to reliably and validly evaluate music therapy sessions, which could lead to a more quantitative study to determine if the differences are significant. It is also important to highlight the importance of this type of studies where the purpose is to gain a better understanding about the effectiveness of this intervention among this group of patients since it could be applied at an earlier age when the deterioration is not so marked.The results of this study provide preliminary information and indicate positive changes in both psychological and physiological variables after having received music therapy sessions. This leads to the conclusion that this treatment is a promising practice for improving quality of life. The study provides information that has not been published to date and can be of great social importance, as it can be very helpful for professionals and family members of those affected. These data could serve as a basis for future research that has greater resources available, such as a larger sample, rigorous design and a standardised assessment and treatment. Also, further research should be done both on this rare disease and music therapy so that more can be learnt about them and to clarify whether this treatment is effective.


It is well known that a small number of graphene nanoparticles embedded in polymers enhance the electrical conductivity; the polymer changes from being an insulator to a conductor. The graphene nanoparticles induce several quantum effects, non-covalent interactions, so the percolation threshold is accelerated. We studied five of the most widely used polymers embedded with graphene nanoparticles: polystyrene, polyethylene-terephthalate, polyether-ketone, polypropylene, and polyurethane. The polymers with aromatic rings are affected mainly by the graphene nanoparticles due to the π-π stacking, and the long-range terms of the dispersion corrections are predominant. The polymers with linear structure have a CH-π stacking, and the short-range terms of the dispersion corrections are the important ones. We used the action radius as a measuring tool to quantify the non-covalent interactions. This action radius was the main parameter used in the Monte-Carlo simulation to obtain the conductivity at room temperature (300 K). The action radius was the key tool to describe how the percolation transition works from the fundamental quantum levels and connect the microscopic study with macroscopic properties. In the Monte-Carlo simulation, it was observed that the non-covalent interactions affect the electronic transmission, inducing a higher mean-free path that promotes the efficiency in the transmission. The science of polymeric materials has revolutionized today’s science and technology. Today, almost every industrial component has a polymer in it ; there iExperimental and computational studies of conductivity in nanocomposite polymer-graphene present a change in the electrical behavior according to a sigmoid curve ,32,33. IThe percolation threshold for carbon nanotubes embedded in polypropylene is around 5% ,39, wherOur group has proved that quantum effects are the main reason for the percolation threshold occurring so rapidly, and we are developing a methodology to calculate the conductivity of these nano-compounds theoretically. In this work, we simulated the nanocomposites at the microscopic level using an ab-initio computational framework to characterize the quantum effects correctly. Then, we approached the macroscopical level with a Monte-Carlo simulation, which has been proven to give accurate results ,42,43,44The ab-initio calculations were made to characterize the systems’ quantum effects appropriately and then to incorporate them in the macroscopic simulation and phase conductivity analysis.The DFT calculations were carried out using the Perdew–Burke–Ernzerhof (PBE) functional , Grimme More details of the ab-initio calculations are presented in the Deposition Process. The random deposition of the graphene nanoparticles over the polymer matrix within a specific percentage is achieved using a Metropolis Monte-Carlo model. The implementation of this model consists of three subparts: a first-neighbors function, the introduction of a training period, and a condition to generate the random deposition of graphene. The details are in the The graphene-clustering Process. It is well known that the deposition process may produce clustered particles over the substrate. In particular, the graphene nanoparticles in a polymer tend to make clusters or fragments that fit together, forming a two-dimensional coverage. In the previous procedure, we could obtain a small concentration of graphene particles or isolate them. Thus, we establish a minimum number of connected graphene particles to be considered a cluster. The detailed algorithm is presented in the i-th to the j-th cluster. Then we defined the transition rate matrix or the intensity matrix (M) as a function of the Euclidean distance between clusters and each nanocomposite potential. The interaction potential (iju) between the i-th and the j-th clusters was expressed as an expansion of the van der Walls interaction potential proposed by Hamaker [R−6, R−8, and R−12) [dist is the minimal distance between clusters, the parameter R is entirely determined by the nanocomposite and represents the action radius obtained in the ab-initio simulation. The M matrix is defined using Equation (2) and is given by the last-passenger model. The inversion of the M matrix is almost the Green matrix of the system [Transmission probabilities. The transmission probability is measured using stochastic theory. The transition rate is defined as the probability to pass from the  Hamaker . The intnd R−12) . In partnd R−12)  form thee system  and alloThe stochastic simulation is made to emulate the experimental situation as accurately as possible. The simulation is made in three parts: the deposition process of the graphene nanoparticles on the polymer; the accumulation process; and, finally, the electronic transport in the nanocomposite modeling. A summary of the details is:M matrix is called the transmission matrix. In particular, in phase-type distribution theory, the M matrix is defined i,ju and U = (−T)−1, where U is the expected value in state j prior to absorption given initiation in the state i [U. We repeat this procedure 50,000 times and the output data are the saturation of the simulated polymer. In the In electronic transport theory, the  state i . Then, wG =σA/L, in which A and L are in nanometric dimensions 100 nm2 and 10 nm, respectively.To prove our model, we compared the simulation with experimental results, in which the graphene nanoparticles are obtained from graphene oxide nanoparticles and added to the polymer matrix. The simulations made with PS-graphene nanocomposites were compared with the experimental results obtained by Qi et al. , in whicThe systems were optimized to obtain the most stable geometries by performing a systematic search, as was mentioned in the methodology section. These geometries are shown in The adsorption energies and the HOMO-LUMO gap are shown in A monomer of polystyrene in gas phase presents a gap around 2.37 eV, and polystyrene’s monomers in the presence of graphene have a gap of 0.599 eV. The PET monomer has a HOMO-LUMO gap of 3.58 eV in gas phase and 0.20 eV with graphene interaction. The PEK monomer has a gap of 2.82 eV alone and 0.19 eV with graphene. The linear polymers present the same HOMO-LUMO gap of 0.9 eV representing a huge diminishment from the pristine form of the polymer, which is 3.66 eV for the PP and 5.83 eV for PU. The gas-phase polymers have a big HOMO-LUMO gap in agreement with the insulator properties of the polymer. As soon as graphene nanoparticles are incorporated into the systems, the HOMO-LUMO gap diminished drastically, according to a semiconductor material.With the optimized structures, adsorption energies, and HOMO-LUMO gap, it was noticed that there is an increasing tendency to improve the electronic transfer when the graphene nanoparticles are introduced in the polymers. The interactions between the graphene and polymers are also weak, forming non-covalent bonds; π-π and CH/π bonds are the predominant interactions presented on the systems.The direct consequence of the non-covalent bonds is that graphene nanoparticles are stacked parallel to the polymer and enhance the electronic interchange between polymer and graphene.Following the proposed methodology ,57, the z-axis contains the normal vector of the surface. When the polymer interacts with graphene, carbon atoms can be pushed down (z < 0) or pulled up (z > 0). The action radius is the distance between the maximum and minimum heights near the polymer and directly reflects the internal tensions induced by the polymer–graphene interactions  of electrons. The electronic transport obeys the potential of Equation (2), that consists of some terms of the power series of the dispersion correction. All the results presented here are computed at room temperature (300 K).The macroscopic calculation was carried out in three parts. The first part is the deposition of graphene nanoparticles on the polymer matrix using a Metropolis Monte-Carlo model. The second part is the formation of graphene clusters over the polymer matrix, incorporating the quantum effects and the internal tensions obtained in the previous section. The third part used a phase-type distribution function to obtain the transmission probabilities  as a function of graphene nanoparticles percentage of each simulated set, and we adjust a curve with the sigmoidal Boltzmann equation: σmax as the upper limit of the sigmoidal, (σmax − σmin) is the difference between the upper and lower limit, PT is the percolation threshold, which represents the critical point in which the conductivity changes drastically, and dx represents the slope at the center of the curve. We extrapolate the electrical conductivity , we have two terms whose interactional nature presents a subtle difference. The term R−6, indicating that the electrons find a large mean-free path to promote electronic transport, accelerating behavior change from insulating material to a conductor. Therefore, the percolation threshold comes with a percentage much lower than expected. This accelerating is directly a consequence of the π-π stacking and the action radius. The systems in which the long-range terms are predominate are PS-graphene, PET-graphene, and PEK-graphene and have an action radius long enough to transport the electrons. The electronic transfer mechanism acts via the dispersion forces R−12) are PP-graphene and PU-graphene. The action radius is small due to the CH/π stacking, and the nanofillers have a weak interaction with the polymer, so the electrons are transported locally. The mean-free path of the electrons is short, producing low electronic transport compared with other systems studied here. A larger quantity of graphene nanoparticles are introduced to change insulating material to a conductor and improved the trajectories in which electrons can move. As a consequence of this, the percolation threshold occurs with a more significant nanoparticles percentage. The systems with dominant short-range terms . We constructed a robust simulation at room temperature with microscopic, macroscopic, and experimental facts to simulate the non-covalent interactions as accurately as possible. The non-covalent interactions were characterized in detail with an ab-initio framework and, then, they were included in a Monte-Carlo simulation. The electronic transport is simulated using phase-type distribution, stochastic percolation theory, and Landauer formulation. The electric conductivity of the systems was successfully reproduced in strong agreement with experimental results. We also proved that a stochastic percolation theory with a phase-type distribution is a more appropriate tool because it can incorporate more details than other models, such as considering room temperature or non-covalent interactions. Polymers with aromatic rings in their structure are more compatible with graphene nanoparticles to maximize the conductivity, inducing a π-π stacking that increases the transport of electrons from the graphene to the polymer and vice-versa. For polymers with linear structures, the non-covalent interactions are present mainly by the CH/π stacking. Electronic transport is still promoted, although the electrons are not that accelerated compared with the aromatic polymers. It was observed that the non-covalent interactions dominate the electronic transport mechanism and promoted electrons to be transferred efficiently, diminishing the HOMO-LUMO gap. R of electrons to be transported in the percolation theory. The Monte-Carlo simulation also allows for incorporating the effect of graphene clusterization and considers quantum effects given by graphene–graphene and polymer–graphene interactions. The non-covalent interaction increased the deformation of the nanocomposites. The systems that present a more significant deformation have a higher structural coupling; these are the systems that have cyclic rings and higher adsorption energy. We take the aspect ratio as the deformation radius because it characterizes the neighborhood in which the non-covalent interactions are predominant and connects them with the macroscopic properties. The deformation is used on the Monte-Carlo simulation as the aspect ratio, i.e., the action radius For compounds with low percolation thresholds, such as PS, PET, and PEK, the predominant interactions with the graphene nanoparticles are long-range terms, which produces a long mean-free path for the electrons, which are transported efficiently in the nanocomposite. For high percolation thresholds, such as PP and PU, the prevalent interactions are of the short-range type; this means that the effects induced by graphene on the polymer act locally, so the mean-free path of the electrons is shorter than other polymers. It is observed that this model is the most appropriate to describe these systems.It was proved that the combination of Monte-Carlo simulation with stochastic process based on the phase-type distribution with the last-passenger percolation theory is an excellent approach. As a consequence of the simulation, the electrical conductivity as a function of the percentage of fillers is defined by the Boltzmann sigmoid curve, which allows us to predict the percolation threshold and saturation state correctly at room temperature. The average error of our simulation is around 3%. Specifically, for systems with predominant short-range interactions, our simulation is excellent (≈1% of error). We recognize that interactions of attractive nature contribute significantly to the efficiency of electronic transport by increasing the mean free path of the electrons. The comparison with several experimental studies demonstrates that our model describes the electric transport accurately in polymer-graphene nanocomposites.


Strain modulation is crucial for heteroepitaxy such as GaN on foreign substrates. Here, the epitaxy of strain-relaxed GaN films on graphene/SiC substrates by metal-organic chemical vapor deposition is demonstrated. Graphene was directly prepared on SiC substrates by thermal decomposition. Its pre-treatment with nitrogen-plasma can introduce C–N dangling bonds, which provides nucleation sites for subsequent epitaxial growth. The scanning transmission electron microscopy measurements confirm that part of graphene surface was etched by nitrogen-plasma. We study the growth behavior on different areas of graphene surface after pre-treatment, and propose a growth model to explain the epitaxial growth mechanism of GaN films on graphene. Significantly, graphene is found to be effective to reduce the biaxial stress in GaN films and the strain relaxation improves indium-atom incorporation in InGaN/GaN multiple quantum wells (MQWs) active region, which results in the obvious red-shift of light-emitting wavelength of InGaN/GaN MQWs. This work opens up a new way for the fabrication of GaN-based long wavelength light-emitting diodes. Currently, the high cost of native substrates makes group III-nitrides usually grow on foreign substrates, such as sapphire, SiC, and Si6. However, there are lattice and thermal mismatches between nitride films and foreign substrates, leading to the formation of high-density point defects, threading dislocations, and residual stress in the prepared films and devices, which degrade the working lifetime and efficiency of GaN-based optoelectronic devices9.Due to direct wide bandgap and high stability, group III-nitride semiconductors have been widely used in light-emitting diodes (LEDs), laser diodes and photodetectors13. The epitaxial growth of GaN on graphene forms weak covalent bonds at the interface between graphene and epitaxial layer, which makes the lattice at the interface produce no large strain as the traditional heteroepitaxy, and the stress in films greatly reduced14. This provides a new path for heteroepitaxial growth of GaN films. In addition, the weak force between the epitaxial layer and graphene can make the epitaxial layer be easily released from the substrate and transferred to other materials, realizing some novel device applications, such as flexible devices16. However, the lack of dangling bonds on graphene suppresses the GaN nucleation, limiting the growth of continuous and smooth GaN films on graphene17. To solve this problem, some researches have achieved the epitaxial growth of nitrides on graphene by introducing interfacial buffers or defects on graphene. For instance, Chung et al. realized the epitaxial growth of the GaN-based LED structures on graphene/sapphire substrates by using of high-density, vertically distributed ZnO nanowalls as the interfacial buffer10. Besides, Chen et al. reported the epitaxial growth of AlN films on graphene by nitrogen-plasma pre-treatment18. Although there are a few reports on the epitaxial growth of GaN on graphene, the epitaxial growth mechanism of GaN on graphene is still not clear enough, and the role of graphene in the GaN epitaxial growth process is unclear.Recently, GaN films grown on graphene and other two-dimensional materials have attracted extensive attentionHere, we successfully grew a strain-relaxed GaN film on graphene/SiC substrates by metal-organic chemical vapor deposition (MOCVD). Graphene was directly prepared on SiC substrates by thermal decomposition. The nitrogen-plasma pre-treatment was performed on graphene surface, introducing the C–N-related dangling bonds, which promoted the subsequent epitaxial growth of GaN films. The scanning transmission electron microscopy (STEM) measurements reveal that part of graphene surface was etched by nitrogen-plasma pre-treatment. The growth behavior on different areas of nitrogen-plasma-treated graphene was studied, and then a growth model was proposed based on the STEM results to explain the epitaxial growth mechanism of GaN on graphene. It is worth noting that, the graphene is found to be effective to reduce the biaxial stress in GaN films. Then, we prepared InGaN/GaN multiple quantum wells (MQWs) on the strain-relaxed GaN films. The strain relaxation in GaN films leads to the improvement of indium-atom incorporation efficiency in the MQWs, resulting in the obvious red-shift of light-emitting wavelength. Our work enhances the understanding of epitaxial growth of nitrides on graphene, and provides a new way for the fabrication of nitride long wavelength GaN-based LEDs.−1) and 2D peak (~2700 cm−1) of graphene can be seen in Raman spectra of five measured positions, which indicates that the prepared graphene on SiC substrate by thermal decomposition has good uniformity20. In addition, we calculated the intensity ratio of the characteristic 2D-to-G peak (I2D/IG) of graphene, and the intensity ratio of the defect-related D peak (~1350 cm−1) to the characteristic G peak (ID/IG) of that. The results show that the prepared graphene on SiC substrate is the multilayer one with good quality  measurement results also confirm that AlN buffer is polycrystalline  measurements were performed on the as-grown GaN on untreated graphene. As shown in Fig. ID/IG ratio of the graphene in Raman spectra increases from 0.3 to 0.5. The defect density in graphene can be calculated based on the ID/IG ratio, and it increases from 9.0 × 1010 cm−2 to 2.0 × 1011 cm−223. In order to further study the effect of nitrogen-plasma pre-treatment, X-ray photoelectron spectroscopy (XPS) measurements were conducted for untreated and nitrogen-plasma-treated graphene. Figure 2C–sp2C bond (~284.6 eV) from graphene24. After nitrogen-plasma pre-treatment, two different kinds of C–N bonding configurations appeared in C 1s peak, corresponding to N–sp2C bond (~285.5 eV) and N–sp3C bond (~286.5 eV), as shown in Fig. 4c25. Since the pyrrolic N atom in N–sp3C bond is more reactive than the pyridinic N atom in N–sp2C bond18, N–sp3C bond can provide more nucleation sites for subsequent epitaxial growth of GaN films.The Raman spectra in Fig. Figure To determine the macroscopic orientation and crystal structure of GaN films on nitrogen-plasma-treated graphene, we also performed XRD measurements on GaN films. The XRD 2θ and φ scan results show that GaN film on graphene is a well-aligned single crystal with hexagonal wurtzite structure  phonon mode in Raman spectra is sensitive to the biaxial strain of GaN films, and therefore it can be used to evaluate the biaxial stress in III-nitrides26. For stress-free GaN bulk materials, its E2 (high) phonon frequency is 568 cm−127. Figure 2 (high) phonon frequencies of GaN films grown on graphene and directly on SiC are both less than 568 cm−1, indicating that both GaN films are under tensile stress state28. While, the E2 (high) phonon frequency of GaN on nitrogen-plasma-treated graphene is closer to that of stress-free GaN, which is 567.9 cm−1. The specific biaxial stress value σ of GaN epilayers can be calculated by the formula: σ = Δω/κ, where κ is the stress coefficient, Δω is the Raman frequency shift relative to the E2 (high) phonon frequency of stress-free GaN films. Here, κ = −3.4 cm−1 GPa−1 is adopted for the calculation29. The calculated residual tensile stress value for the GaN films on graphene is only 0.03 GPa, which is much lower than that of GaN films grown directly on SiC substrate (0.74 GPa). This result shows that the residual stress in GaN films can be significantly reduced by inserting graphene.The stress in as-grown GaN films is further evaluated by Raman spectroscopy. The Ec-axis orientation growth. The c-axis-oriented AlN nucleation islands gradually occupy the dominant role, and a single crystal AlN layer with the same orientation is formed by lateral epitaxy. The subsequent GaN films are grown on the AlN layer, as shown in Fig. Based on the above results, we propose a growth model to explain the growth mechanism of GaN films on graphene. As shown in Fig. Based on above results, InGaN/GaN MQWs were grown on the as-grown GaN/graphene/SiC template. For comparison, we also prepared InGaN/GaN MQWs with the same structure on GaN/SiC template under the same conditions. The two samples were grown in one run. Figure 3C dangling bonds, which facilitate the nucleation and growth of subsequent epitaxy. STEM results provide direct evidence that the surface of graphene is partially etched by nitrogen-plasma pre-treatment. Based on the growth behavior on different etched areas of graphene surface after pre-treatment, a growth model is proposed to explain the epitaxial growth mechanism of GaN films on graphene. It is worth noting that, graphene can effectively reduce the biaxial stress in GaN films and the strain relaxation improves the incorporation efficiency of In atoms in InGaN/GaN MQWs. This work provides a feasible way for the epitaxy of strain-relaxed GaN films and opens up a new avenue for the fabrication of GaN-based long wavelength LEDs.In conclusion, we realized the epitaxy of strain-relaxed GaN films on graphene/SiC substrates. Graphene was directly prepared on SiC substrates by thermal decomposition. The pre-treatment of graphene with nitrogen-plasma can generate N–spGraphene was prepared on Si-face 4H-SiC substrates by thermal decomposition. Firstly, 4H-SiC substrates were annealed in an Ar atmosphere at 800–1000 °C for 1 h to remove scratches and oxygen on the surface of SiC substrate. Then, SiC substrates was heated to 1600–1700 °C in an ultra-high purity Ar atmosphere under 800 mbar for 2–5 h to realize surface graphitization.3) were used as Ga, Al, and N precursors, respectively. H2 and N2 were used as carrier gases. Prior to the deposition, graphene/SiC substrates were thermally cleaned in H2 atmosphere at 1100 °C for 5 min. The growth began with the low-temperature AlN buffer layer of about 40 nm thickness grown at 780 °C. Then, the growth temperature ramped up to 1080 °C for the growth of high-temperature AlN buffer layer with thickness of about 160 nm. Subsequently, a 2 μm thick undoped GaN layer was grown at 1050 °C. After that, the InGaN/GaN MQWs were grown on the undoped GaN layer. The MQWs consist of 5 pairs of 2.5 nm thick InGaN quantum well (QW) layers and 15 nm thick GaN quantum barrier (QB) layers. QW and QB layers were grown at 712 and 840 °C, respectively, and they were undoped. For comparison, InGaN/GaN MQWs without graphene interlayer were fabricated directly on SiC substrate. It is worth noting that these two kinds of MQWs samples were grown in one run.GaN films were grown on graphene/SiC substrates by an AIXTRON 3 × 2″ FT MOCVD system. Trimethylgallium (TMGa), trimethylaluminum (TMAl), and ammonia (NHThe surface morphology of graphene and GaN films were measured by SEM (Jeol-7500F) and AFM in tapping mode (Bruker Dimension ICON-PT). Raman spectroscopy  was performed to characterize the quality of graphene and the stress state of GaN films. The chemical states of graphene were measured by an ESCALab 250 Analytical XPS spectrometer with a monochromatic X-ray source . The binding energies of the spectra were referred to that of the C 1s peak at ~284.8 eV. The crystalline quality of GaN films characterized with a Rigaku Ultima IV XRD with Cu Kα radiation (0.154056 nm), and the structural properties of GaN films were investigated by aberration corrected Thermo Fisher Scientific Titan Cubed Themis G2 transmission electron microscope operated at 300 kV and equipped with Bruker Super-X EDX detector. The PL spectra of InGaN/GaN MQWs were measured by a PL system which includes a He-Cd laser  as an excitation source, a Jobin Yvon iHR550 spectrometer, a Syncerity charge coupled device (CCD) and a closed circle helium cryostat.Supplementary information for demonstration of epitaxial growth of strain-relaxed GaN films on graphene/SiC substrates for long wavelength light-emitting diodes.


Although Hb did not affect the cytoplasmic accumulation of TDP-43, Hb attenuated TDP-43-induced toxicity by reducing oxidative stress and mitochondrial dysfunction. Moreover, a shortened lifespan and motility defects in TDP-43-expressing Drosophila were significantly mitigated by dietary treatment with hydroxocobalamin. Taken together, these findings suggest that oral intake of hydroxocobalamin may be a potential therapeutic intervention for TDP-43-associated proteinopathies.TAR DNA-binding protein 43 (TDP-43) is a member of an evolutionarily conserved family of heterogeneous nuclear ribonucleoproteins that modulate multiple steps in RNA metabolic processes. Cytoplasmic aggregation of TDP-43 in affected neurons is a pathological hallmark of many neurodegenerative diseases, including amyotrophic lateral sclerosis (ALS), frontotemporal dementia (FTD), Alzheimer’s disease (AD), and limbic predominant age-related TDP-43 encephalopathy (LATE). Mislocalized and accumulated TDP-43 in the cytoplasm induces mitochondrial dysfunction and reactive oxidative species (ROS) production. Here, we show that TDP-43- and rotenone-induced neurotoxicity in the human neuronal cell line SH-SY5Y were attenuated by hydroxocobalamin (Hb, vitamin B TDP-43 (TAR DNA-binding protein 43) is encoded by the TARDBP gene ; it pred2+ homeostasis [TDP-43 interacts with NF-κB, a key factor contributing to the inflammatory response, and activates NF-κB in microglia. Activated NF-κB induces the production of proinflammatory cytokines, such as IL-1β and TNF-α ,16. Furteostasis ,21. In aeostasis . Moreoveeostasis . In addieostasis . Prolongeostasis .A recent clinical study indicated that methylcobalamin (vitamin B12) is a slightly effective for patients with early-stage ALS. This study suggested that methylcobalamin does not affect all patients with ALS, but it can extend survival and reduce disease progression in patients with early-stage ALS . HoweverHydroxocobalamin (Hb) is a manufactured analog of the vitamin B12 . The cyanide ligand of vitamin B12 is replaced by hydroxide in Hb . There aDrosophila disease model, the short lifespan and climbing defects induced by TDP-43 expression were significantly rescued by hydroxocobalamin treatment. Taken together, these findings suggest that vitamin B12 may be a potential therapeutic target for TDP-43-associated proteinopathies.In this paper, we found that TDP-43-induced neurotoxicity was rescued by hydroxocobalamin treatment. We found that hydroxocobalamin protects cells by regulating mitochondrial dysfunction without affecting cytoplasmic accumulation of TDP-43 aggregates. In addition, in the The following reagents were purchased from the indicated companies: dimethyl sulfoxide , rotenone , mifepristone , MG-132 (MilliporeSigma), PERK inhibitor (MilliporeSigma) and hydroxocobalamin hydrochloride . The following antibodies were purchased from the indicated companies: TDP-43 , phospho-eIF2α , eIF2α , α-tubulin , COX-Ⅳ , cleaved caspase-3 , anti-mouse IgG , anti-rabbit IgG , phospho-PERK (Santa Cruz Biotechnology), and Lamin A/C (MilliporeSigma).The SH-SY5Y human neuroblastoma cell line  was maintained in Dulbecco’s modified Eagle’s medium  supplemented with 10% heat-inactivated fetal bovine serum  and 50 μg/mL penicillin–streptomycin (Gibco).g at 32 °C for 120 min and incubated overnight in a 37 °C CO2 incubator. The medium was changed to DMEM containing 10% FBS to avoid the toxicity of virus particles. Cells were harvested 2 or 3 days after infection.Third-generation lentiviral constructs, including pLenti-C-mGFP-P2A-Puro (vector) and human WT TDP-43, were used to generate lentiviruses as previously described . HEK293TA Cell Counting Kit-8  was used to measure cytotoxicity according to the manufacturer’s instructions. Briefly, SH-SY5Y cells were seeded in 96-well plates and treated with rotenone or Hb for 24 h, in which DMSO was used as a negative control. CCK-8 solution (10 µL) was added to each well and was incubated at 37 °C for 2 h. The absorbance at 450 nm was measured using a microplate reader . Cell viability was reported as a percentage of the control. All experiments were performed in triplicate.6 cells/well) were cultured with/without Hb pretreatment. Cells were then resuspended in 500 μL of binding buffer  and incubated with 5 μL of FITC-conjugated Annexin V according to the manufacturer’s instructions. Subsequently, the cells were incubated for 15 min in the dark at 37 °C. After adding 4 μL of propidium iodide (necrotic cells), flow cytometry was performed within 1 h using a MoFlo Astrios instrument .The numbers of necrotic and apoptotic cells were measured using an Annexin V-FITC apoptosis detection kit  according to the manufacturer’s instructions. Briefly, rotenone-treated SH-SY5Y cells  with freshly added protease and phosphatase inhibitor cocktail  by homogenizing cells. Next, an equal amount of protein lysates was separated on 4–12% Bis-Tris gels  or NuPAGE 3–8% Tris-Acetate gels (Thermo Fisher Scientific) and was transferred to a polyvinylidene difluoride  membrane. The membranes were blocked with TBS blocking buffer containing 5% skim milk (BD Biosciences) or 2% bovine serum albumin (BSA) for 1 h and incubated with primary antibodies for 12 h at 4 °C. Detection was carried out using an ECL-Plus kit . Samples from three independent experiments were used, and the relative expression levels were determined using a Fusion-FX instrument .g for 30 min at 4 °C. Supernatants containing the soluble fractions were harvested. The resting pellets were further extracted with cell lysis buffer containing 2% SDS , sonicated and then boiled at 95 °C for 5 min. The supernatant from this step was collected as an insoluble fraction.Proteins were fractioned according to their solubility by making some modifications to a protocol previously described. Cells were harvested, washed, and homogenized in lysis buffer containing protease and phosphatase inhibitor cocktails. The homogenate samples were centrifuged at 100,000× g for 5 min at 4 °C. Cytosolic supernatants were harvested and frozen. The pellet was then resuspended by vortexing in ice-cold NER buff-er, and the extracts were centrifuged at 16,000× g for 10 min at 4 °C. Supernatants containing the nuclear extract were collected.For subcellular fractionation, cells were lysed by NE-PER nuclear and cytosolic ex-traction reagents kit (Thermo Fisher Scientific) according to the manufacturer’s procedures. Briefly, nuclear and cytoplasmic fractions were obtained in ice-cold CER I and CER II buffer by centrifugation at 16,000× g for 5 min at 4 °C. Supernatants containing the cytosolic extract were harvested, and pellets were solubilized in ice-cold 2% CHAPS in TBS buffer. After vortexing, samples were centrifuged. Supernatants containing mitochondrial extracts were harvested. The extracts were mixed with 4× Bolt LDS Sample buffer and 10× Bolt Sample Reducing Agent buffer and then boiled at 95 °C for 5 min.The mitochondrial fraction was obtained using a Mitochondria Isolation Kit (Thermo Fisher Scientific) according to the manufacturer’s protocol. Briefly, cell fractions were prepared in ice-cold mitochondrial A, B and C buffers through centrifugation at 12,000× For immunocytochemistry, cells were fixed with 4% paraformaldehyde for 30 min at room temperature. Cells were washed three times with PBS and then blocked with 5% BSA for 1 h at room temperature. For cell permeability, the blocking buffer was made of PBS-T . The primary antibody diluted in PBS-T containing 1% BSA was incubated with cells overnight at 4 °C. The next day, cells were then washed three times with PBS and incubated with an Alexa Fluor-conjugated secondary antibody for 1 h at room temperature. Then, samples were mounted and observed using a fluorescence microscope . Photomicrographs from three randomly chosen fields were obtained.4 cells per well, and all cells were then infected with GFP-tagged or GFP-tagged human WT TDP-43. The Hb (10 µM) or vehicle (DMSO) group was transferred to the IncuCyte ZOOM™ apparatus, and incubations continued over 72 h, with images collected every 3 h. All images were analyzed for confluence (%).Images were captured and analyzed to determine cell growth and proliferation using the IncuCyte ZOOM™ Live-Cell Imaging system  as previously described for monitoring the kinetics of proliferation and cytotoxicity of the cultured cells ,42. Incu5 cells/well in 200 μL of growth medium and incubated for 24 h at 37 °C with 5% CO2. After replacing the growth medium with 200 μL of XF assay medium supplemented with 5 mM glucose, 1 mM pyruvate and 4 mM glutamine, which was prewarmed at 37 °C, cells were degassed for 1 h before starting the assay procedure in a non-CO2 incubator. The OCR and ECAR were recorded at baseline, followed by sequential additions of 1 μM oligomycin, 2 μM FCCP, and 0.5 μM antimycin A plus 0.5 μM rotenone. Nonmitochondrial oxygen consumption (in the presence of antimycin A + rotenone) was subtracted from all OCR values, and outlier technical replicates outside the standard deviation of the mean were discarded for both ECAR and OCR. In SH-SY5Y cells, values were normalized to the mean protein level in each well measured using a BCA protein assay kit (Thermo Fisher Scientific).The oxygen consumption rate (OCR) and extracellular acidification rate (ECAR) were measured in TDP-43-transfected SH-SY5Y cells using a Seahorse XF96 flux analyzer . Cell lines were seeded in 24 wells of an XF 96-well cell culture microplate at a density of 1.5 × 10® PrimeScriptTM RT–PCR kit  according to the manufacturer’s instructions using an Applied Biosystems 7500 Real-Time PCR system (Applied Biosystems). Internal control was using 18S rRNA. The 2−ΔΔCt method was used to analyzed relative changes in gene expression [The TDP-43-overexpressed cells were isolated RNA using the TRIzol Plus RNA Purification Kit (Invitrogen) according to the manufacturer’s instructions and 100 ng of RNA were synthesized into cDNA templates at 37 °C for 120 min using a High-Capacity cDNA Reverse Transcription kit (Thermo Fisher Scientific). Quantitative RT–PCR was conducted using the one-step SYBRg for 3 min and resuspended in 500 μL of buffer containing 20 mM HEPES pH 7.4, 10 mM KCl, 2 mM MgCl2, 1 mM EDTA, 1 mM EGTA, and 1 mM DTT. The homogenates were incubated on ice for 20 min and centrifuged at 720× g for 5 min. Transfer supernatant (contain cytoplasm) into a fresh tube and keep on ice. Then, the supernatants were centrifuged at 10,000× g for 5 min for the isolation of cytoplasmic fraction. Finally, DNA was extracted from the supernatant or whole cell using the QIAamp DNA Blood Mini kit according to the manufacturer’s protocol  and 100 ng of DNA was used to quantitative RT-PCR. All primer sequences used in this study are found in Cells were collected at 600× Drosophila stocks were maintained on standard cornmeal agar media at 24 °C unless indicated otherwise. UAS-TDP-43 was described previously [eviously . All stoTDP-43-overexpressed adult male flies (0 to 1 d old) were divided and moved into individual vials contained RU-486 (Mifepristone) or EtOH only fly growing media (n > 100). Flies were transferred into new media every two-day, dead flies were recorded. Adult climbing ability was evaluated using a previously described method .p < 0.05 and are indicated as follows: * p < 0.05; ** p < 0.01; *** p < 0.001; and n.s., not significant.Data were analyzed using one-way ANOVA followed by a post hoc analysis as indicated, depending on the variables compared . Differences were considered significant when Rotenone is a natural pesticide that increases ROS production and ER stress by impairing the mitochondrial electron transport system ,46,47,48Next, we tried to determine whether Hb exerts a protective effect against other types of stress, such as proteotoxic stress. MG132, a potent ubiquitin proteasome system inhibitor, induces the death of SH-SY5Y cells. However, Hb treatment did not affect MG132-induced cytotoxicity in SH-SY5Y cells B.Previous studies showed that the inhibition of mitochondrial complex I activity induces ROS production, ATP depletion and the loss of the mitochondrial membrane potential ,51,52. MATF4/CHOP/GADD34, and upregulation of these genes plays an essential role in cell death [ATF4/CHOP/GADD34 transcripts in rotenone- or rotenone/Hb-cotreated SH-SY5Y cells using real-time PCR. We observed increased levels of the ATF4, CHOP, and GADD34 transcripts in cells exposed to rotenone, and their levels were significantly decreased by Hb treatment  . SH-SY5YWe performed immunoblot analyses to elucidate the effect of Hb on TDP-43 protein levels. The level of the exogenous TDP-43 protein was not affected by Hb treatment. Therefore, Hb does not appear to exert a direct effect on the TDP-43 protein level A. Next, Recent studies have reported that the inhibition of TDP-43 mitochondrial localization blocks mitochondrial dysfunction and TDP-43-induced neurotoxicity ,58. We pATF4, CHOP, and GADD34, were significantly increased in TDP-43-infected cells compared to the controls, and Hb treatment significantly reduced the expression levels of those genes , and ALS [2+ overload has been shown to contribute to necrosis or apoptosis by inducing mitochondrial dysfunction, abnormal generation of ROS, and ER stress [2+-sensitive dye, for 1 h to examine intracellular Ca2+ homeostasis in TDP-43-expressing cells. As shown in 2+ overload was observed in TDP-43-expressing neuronal cells and was significantly reduced by Hb treatment. A previous study suggested that chronic stress caused by the misfolded mutant TDP-43 protein induces inappropriate release of Ca2+ from the ER to the cytoplasm and eventual programmed necrosis [2+ concentrations in the cytoplasm drive TDP-43-mediated neurotoxicity. Taken together, these data indicate that Hb modulates cell survival by alleviating the mitochondrial dysfunction induced by TDP-43 in neuronal cells.Furthermore, we examined whether TDP-43 affected the mitochondrial membrane potential. GFP- and GFP-tagged human WT TDP-43-expressing cells were then analyzed using flow cytometry to quantify the fluorescence intensity of TMRE, a fluorescent dye that labels mitochondria in a membrane potential-dependent manner. The TMRE intensity was significantly lower in TDP-43-expressing cells than in controls. Moreover, Hb treatment significantly restored the mitochondrial membrane potential in TDP-43-expressing cells C. Consis and ALS ,67,68,69R stress . Subsequnecrosis . Thus, iA reduced mitochondrial membrane potential and increased mitochondrial permeability regulate the release of mitochondrial DNA (mtDNA) into the cytoplasm and activate the cyclic GMP-AMP synthase (cGAS) stimulator of the interferon genes (STING) pathway ,73. MoreThe cGAS-STING signaling pathway is known as a major mediator of inflammation in the environment of infection, cellular stress, and tissue damage . Next, wATF5, LonP1, HSP60, and HSPA9) genes in TDP-43-expressing neuronal cells. The transcription of mtUPR-related genes was upregulated by the expression of TDP-43. Subsequently, the increased expression of the LonP1, HSP60, and HSPA9 genes was reversed by Hb treatment. However, the expression of the ATF5 gene was not affected by Hb (In addition, the mtUPR is the first stress protective response initiated by mitochondrial damage, eventually mitigating damage by removing or repairing misfolded proteins . We perfed by Hb C. These Drosophila model of TDP-43 proteinopathies, which expresses human TDP-43 in the nervous system. In our previous studies, we established a Drosophila model of TDP-43 proteinopathies in vivo and showed that overexpression of TDP-43 led to neurodegeneration [We next investigated whether Hb inhibits TDP-43-induced toxicity in vivo using a neration ,77. We iVitamin B12 deficiency is associated with central nervous system lesions, including subacute combined degeneration of the spinal cord, suggesting that vitamin B12 plays an important role in the spinal cord and brain ,78. In a2+ signaling. Furthermore, mitochondria are known to be key centers mediating TDP-43 cytotoxicity in the development and progression of ALS [Mitochondria are important organelles participating in various cellular processes, including ROS generation, ATP synthesis, and intracellular Can of ALS ,85. NeurDrosophila models. First, we investigated mitochondrial dysfunction upon the overexpression of TDP-43 in the human neuroblastoma cell line SH-SY5Y and confirmed that Hb treatment significantly alleviated the loss of the mitochondrial membrane potential and intracellular Ca2+ imbalance caused by TDP-43 expression (In this study, we examined whether the neurotoxicity induced by TDP-43 was alleviated by Hb treatment. Hb treatment attenuated TDP-43-induced global mitochondrial dysfunction in mammalian neuronal cells and pression . Moreovepression .Drosophila disease model, the short lifespan promotion and climbing defects induced by TDP-43 expression were significantly rescued by Hb treatment. However, Hb did not affect the aggregation and mislocalization of TDP-43. Mitochondrial dysfunction, oxidative stress and UPS impairment are the major components of TDP-43-induced neurotoxicity [Cells have a mitochondrial quality control system called the mtUPR for the repair and recovery of damaged mitochondria. mtUPR activation in mitochondria promotes cell survival and organelle repair. Recent studies have reported the role of the mtUPR in AD, PD, and ALS ,86,87. Htoxicity ,22,76,84


The ability to precisely control moiré patterns in two-dimensional materials has enabled the realization of unprecedented physical phenomena including Mott insulators, unconventional superconductivity, and quantum emission. Along with the twist angle, the application of independent strain in each layer of stacked two-dimensional materials—termed heterostrain—has become a powerful means to manipulate the moiré potential landscapes. Recent experimental studies have demonstrated the possibility of continuously tuning the twist angle and the resulting physical properties. However, the dynamic control of heterostrain that allows the on-demand manipulation of moiré superlattices has yet to be experimentally realized. Here, by harnessing the weak interlayer van der Waals bonding in twisted bilayer graphene devices, we demonstrate the realization of dynamically tunable heterostrain of up to 1.3%. Polarization-resolved Raman spectroscopy confirmed the existence of substantial heterostrain by presenting triple G peaks arising from the independently strained graphene layers. Theoretical calculations revealed that the distorted moiré patterns via heterostrain can significantly alter the electronic structure of twisted bilayer graphene, allowing the emergence of multiple absorption peaks ranging from near-infrared to visible spectral ranges. Our experimental demonstration presents a new degree of freedom towards the dynamic modulation of moiré superlattices, holding the promise to unveil unprecedented physics and applications of stacked two-dimensional materials. For instance, twisted bilayer graphene (TBG) with a magic twist angle can flatten the electronic band structure near zero Fermi energy, which allows achieving Mott insulating behavior and unconventional superconductivity2. Besides, twisted transition metal dichalcogenide (TMD) heterobilayers have enabled trapping interlayer excitons in the potential wells created by moiré superlattices6.The formation of moiré superlattices in twisted layers of two-dimensional (2D) materials has recently become a crucial method to realize unprecedented photonic and electronic properties that are unattainable in the constituent layers13. Heterostrain is inequivalent strains on the two constituting layers of stacked 2D materials, which leads to the slippage of one layer over the other due to inequivalent lattice deformation18. Theory results have recently predicted that heterostrain can modulate the local atomic registry of moiré superlattices and enable intriguing properties such as flat moiré bands in TBG12, topologically protected helical modes in twisted TMD19, and excitonic instability in TBG13. The effect of heterostrain is expected to be far more significant than that of homostrain on altering moiré patterns7, which may enable discovering a new class of physical properties beyond what have thus far been observed in the absence of heterostrain13. For instance, heterostrain-enabled one-dimensional (1D) moiré potentials have shown linearly polarized photoluminescence emission with two orders of magnitude higher intensity20.Very recently, heterostrain in twisted layers of 2D materials has arisen as a powerful, new degree of freedom to tailor moiré patterns and the resulting physic properties of the stacked 2D materials22, which requires the precise control of the twist angle and heterostrain during device fabrications. Recent experimental studies have demonstrated the continuous tuning of the twist angle, which substantially alleviates the strict requirement for controlling the twist angle during the fabrication23. However, controlling heterostrain dynamically has yet to be experimentally realized, limiting the feasibility of heterostrain-enabled on-demand manipulation of moiré superlattices.Overall, the desired physical properties of moiré superlattices are very sensitive to the modulation of the moiré potential landscape16, which played a key role in achieving a large heterostrain of up to ~ 1.3%. The induced heterostrain in TBG devices was dynamically tunable by continuously changing the bending radius of the PET substrate. Raman spectroscopy provided unambiguous evidence for the generation of a substantial heterostrain by presenting triple G peaks that arise from both unstrained and strained graphene layers having a single degenerate mode of the G peak and two split G+ and G− peaks, respectively. Strong polarization dependence of the triple G peaks further confirmed the formation of heterostrain. We also verified the influence of the experimentally obtained heterostrain on the modulation of moiré superlattices and the electronic band structures of TBG through tight-binding simulations. The 1.3% heterostrain was predicted to allow achieving multiple absorption peaks including one in the near-infrared spectral range that is attributed to the optical transition between the two saddle points, which is forbidden in the absence of heterostrain.Here, we present a generalized method for dynamically tuning heterostrain in TBG to modify moiré superlattices. TBG devices were assembled on a flexible PMMA-coated PET substrate by mechanical stacking. A relatively large twist angle of 13.2° was intentionally used to minimize the interlayer friction force2) layer to allow convenient identification of monolayer graphene. The number of graphene layers was identified via various methods including Raman spectroscopy and optical contrast (see Supplementary Note 1 for more details on the sample identification). The crystal orientation was determined from the cleaved angles of exfoliated flakes24. The cleaved edge was aligned to the long side of a PMMA-coated PET substrate on a transfer stage.Figure 2/Si substrate  by −1/% is the strain coefficient. Table Figure mentclass2pt{minimmentclass2pt{minimmentclass2pt{minim−1 with the full width at half maximum (FWHM) of 16 cm−1  and G (green) peaks as shown in the bottom two panels of Fig. T peak remains unchanged while the G peak shifts by ~ 37 cm−1, which provides strong evidence for the development of substantial heterostrain in the TBG device. The measured peak positions of the three peaks, GT, G and G, at different bending radii are summarized in Fig. Interestingly, the substrate bending causes the single G peak to split into multiple peaks that are clearly discernable as shown in the bottom three panels. At a bending radius of 2 cm . In addition, heterostrain increases the number of pronounced DOS peaks (marked as red and green arrows). These new DOS peaks can be attributed to the strongly modified electronic band structures under the influence of heterostrain as shown in Fig. The changed electronic band structures in the presence of heterostrain result in the altered density of states (DOS) Fig. e, which . The calculated Re (30. Unstrained TBG (blue curve) shows strongly enhanced optical absorption  possesses multiple peaks enhanced over 2 We also calculated the real part (Re) of the dynamical conductivity, ces Fig. f. The sp6. Moreover, the dynamically tunable moiré superlattices enabled by heterostrain may achieve unprecedented physical properties. It is also worth noting that such heterostrain in TBG can also be achieved in an integrated strain engineering platform on a silicon substrate32.In summary, we demonstrated a strain engineering platform that enables the dynamic tuning of heterostrain in TBG. Raman spectroscopy measurements confirmed the existence of heterostrain by showing triple G peaks; the unstrained top graphene layer showed the G peak that is the same as in the pristine MLG whereas the strained bottom graphene layer presented the two split G peaks, which also showed strong polarization dependence. It was verified that the heterostrained TBG possesses distorted moiré superlattices, which strongly influence the electronic band structures and optical properties. Our heterostrain platform gives a new approach to tune the moiré materials continuously and accurately, thus may find important applications in tunable electronics and optoelectronics based on moiré-engineered graphene. This approach is very general and can be employed for modulating moiré superlattices in twisted transition metal dichalcogenide (TMD) heterostructures as well, which are expected to play important roles in engineering moiré excitons for a variety of applications including quantum emission2 substrate . Number of graphene layers was identified by analyzing optical contrast and Raman spectra. Long graphene strips were selected as bottom layers of TBG, while smaller monolayer flakes were selected as tops layers. Both the selected bottom and top layers has straight edges, such that crystal orientation could be identified from flake edges.Graphene flakes were prepared by mechanical exfoliation of Kish graphite  by scotch tape and deposited onto Si/SiOA 135-μm thick PET substrate was cut into 1 cm × 5 cm rectangles. PET substrates were cleaned by acetone, isopropanol alcohol (IPA) and deionized (DI) water, and then dried at 65 °C for 5 min. About 400 nm polymethyl methacrylate  was spin-coated onto PET at 4500 rpm for 90 s.Twisted bilayer graphene was mechanically stacked on PMMA-coated PET with a home-made transfer stage. First, long edge of bottom graphene was aligned along horizontal direction by rotating the sample stage. At the same time, PMMA-coated PET thin film was attached to a PDMS stamp of ~ 4 mm × 2 mm × 0.6 mm, which was adhered to a glass slide. Bending direction of PET rectangle was also aligned to horizontal direction, such that uniaxial strain will be applied along long side of bottom graphene. Then Glass/PDMS/PET/PMMA stack was used to pick up the bottom graphene layer. After baking at 180 for 2 min, bottom graphene is firmly adhered to PET substrate. Next top graphene was aligned 13.2° to horizontal, which was subsequently picked up by Glass/PDMS/PET/PMMA/Bottom graphene. Finally, detach PET substrate from glass slide and PET/PMMA/TBG was obtained. Cured PMMA can successfully transfer strain from PET to bottom layer of TBG during the bending process.Graphene G peaks were measured by Raman spectroscopy  with a 100× objective and 1800 g/mm grating. Laser wavelength was 532 nm. Before measurement, laser power was adjusted to low level to avoid heating effect. Lorentz fitting was applied to determine peak position and FWHM.Supplementary Information.


We investigate the Landau damping of acoustic phonons (We perform self-consistent analysis of the Boltzmann transport equation for momentum and energy in the hypersound regime i.e.,  LDOPW) is the loss of energy from the collective motion of plasma waves to individual particles. This causes plasmons to decay by exciting an electron below the Fermi level2. The mechanism of LDOPW has been observed in various systems, such as plasma oscillations (Langmuir waves) and accelerators3. In semiconductors, Landau damping of acoustic phonons (LDOAP) occurs in the hypersound regime during electron–phonon interactions5. This has been studied using Raman spectroscopy6, and high-resolution electron-energy-loss spectroscopy (HREELS)7.Landau damping of plasma waves 10, acoustomagnetoelectric effect (AME)13, acoustothermal effect (ATE)14 and acoustomagnetothermal effect (ATME)16. The mathematical relation between absorption coefficient 20 and confirmed experimentally in GaAs/AlGaAs22 and GaAs/LiNbO323 SSLs. Azizyan25 calculated the absorption coefficient in a quantized electric field, while Shmelev and Zung24 calculated the absorption coefficient and renormalization of the short-wave sound velocity. Cerenkov emission (CE) is one of the most commonly used methods for investigating acoustic effects29. When a Non-quantized electric field (ED) with a drift velocity 28.The interaction of acoustic phonons with charge carriers in bulk semiconductor materials causes an amplification of acoustic waves and was predicted by Tolpygo and Uritskii in 1956SAW) in the hypersound region is described as quantized lattice vibrations or surface phonons, which typically extend to 1013 Hz. SAW is generated by the deformation of the material caused by the intraband transitions of electrons under an applied field31. Theoretical and experimental studies of acoustic wave effects in graphene35, quantum wells (QWs)36, carbon nanotubes41, and rectangular quantum wires42 have been investigated in the megahertz (MHz), the gigahertz (GHz) and the terahertz (THz) regions. Thalmeier et al.43 observed Landau oscillations as a function of gate voltage in graphene. Zhang et al.44 obtained a strong absorption when the carrier density and the field were increased as a result of electrons colliding with the acoustic phonons under a drift electric field. Such interaction can also generate sound waves. Considering acoustic phonons as quantized sound waves of frequency (LDOCE). LDOCE occurs when the drift velocity is less than the speed of sound in a material. The absorption of the phonon energy is determined by the energy balance of the system. As the frequency of the acoustic phonon increases, the absorption also increases, until there is a resonance beyond which the absorption decreases. This phenomenon has been observed in several graphene-based AE experiments and has been used in the fabrication of sensing devices such as humidity sensors46, photodetectors47, and gas sensors48.In low-dimensional structures, the motion of surface acoustic wave  into GNRs creates a tunable multiband absorption effects, which opens an energy gap (N), the quantized wave vector B and the electron momentum. B varies with the width of the GNR, the lattice constant (Pi). To the best of our knowledge, there has been no theoretical investigation of LDOCE in GNR even though some experimental evidence of the phenomenon exists35. Poole et al.35 reported a nonlinear AE in GNR of width DC current. They observed a resonance between the measured current maxima, after which the current decreased. Liang et al.48, Zheng et al.49 and Okuda et al.50 reported similar behavior, where acoustic charge transportation was induced by SAW propagation in the graphene. Morgado et al.51 also reported negative Landau damping in bilayer graphene, where they measured a DC electric current induced by a static voltage across the graphene sheet. In this work, we study the nonlinear AE in SLG and GNR-500 with degenerate energy dispersion in the hypersound regime. We adopted the Boltzmann kinetic equation for the electron system interaction with the sound waves and calculate the absorption coefficient (fk), thus affecting those electrons whose velocities in the direction of sound propagation are close to the sound velocity. Herein, we theoretically examine the effect of DC fields on LDOCE in an SLG/GNR-500.The quantum Hall effect is observed when sound waves in a material are subjected to magnetic fieldsLDOAP, we analyzed the effect of electron–phonon interactions in a gate-controlled single SLG and GNR-500. An in-plane current I was applied along the x-direction of the graphene sheet, which was biased by the presence of the source-to-drain voltage 52, expressed as:k is occupied and the final electron state k′ is empty. fk is the unperturbed Fermi–Dirac distribution function. The factor A being the area of the material, the summation in Eq. . The absorption coefficient relates to the AE current via the Weinrich25 relation, as follows:Considering Thus, the acoustoelectric current Integrating and simplifying Eq.  yields6\58 indicates the contribution of an in-plane acoustic phonon. In Fig. 5 cm−1. The plot shows a nonlinear AE current AE current does not exhibit a simple linear dependence on THz, and then increased at higher frequencies. A similar trend was observed when the temperature was increased to 30K. However, at 50K and 70K, the increase in 34), where they measured the acoustoelectric current for several temperatures at various frequencies in the MHz region. However, in this study, the frequencies are in the THz region.From Eq. , \documementclass2pt{minimmentclass2pt{minimT) is shown as a 3D plot in Fig. T, the graph decreased to a minimum and then increased to a point and remained constant at higher temperatures, while the dependence of D = 0.9vs, 0.92vs and 0.94vs, which depicts a linear relationship. However, Γq decreases when vD increases.To further illustrate this, the simultaneous dependence of the mentclass2pt{minimmentclass2pt{minimAE current. Thus, Fig. 57), where the AE current varied linearly with the frequency. Figure 29. In Fig. 57, where acoustic-phonon frequencies above 10 THz were attained. The field E in the SLG can be calculated using L is the length from the source to the drain electrode in the graphene), the in-plane current n is the electron density) can be calculated.The Weinreich relation entclass1pt{minimaentclass1pt{minimaentclass1pt{minimaSLG into 54 with the energy dispersion given by53B is the quantized wave vector. By considering that the acoustic phonon and the electric field are directed along the GNR axis, GNR, the energy level degenerates. At low temperatures, when Patterning mentclass2pt{minimN is the width of the graphene, Pi is the sub-band index. The absorption reveals the characteristic feature of the acoustic phonon spectrum in the materials that occurs in the Terahertz frequency range. In addition to the parameters used in Fig. 54). The twin peaks occur as a result of electron transport in the dual-band formed in the GNR. In the first band, the electrons are initially absorbed until they encounter a gap, where they lose their energy. They then gains energy in the second band by absorbing the energy of the confined phonons. This occurs at low drift velocities of In Eq. , \documementclass2pt{minimThe first gap occurs at 35). In Figs. q is shown in Fig. 48, Okuda et al.50, and Morgado et al.51. In the Terahertz range, the simulated results of absorption in graphene obtained by Ullah et al.55 are in qualitatively agreement with Fig. Therefore, knowing, s in Eq. . Using tSLG can be calculated by using L is the length from the source to the drain electrode in the graphene), the in-plane current n is the electron density) can be calculated.The We have theoretically demonstrated the acoustoelectric current generation in graphene nanoribbon resulting from Landau damping of acoustic phonons. The AE current in a single layer of graphene was calculated when the temperature and the electric fields were applied. Graphene nanoribbon exhibited a larger acoustoelectric current than a single layer of graphene when a non-quantizing field was applied. The acoustoelectric current shifts as the drift velocity is varied. This makes acoustoelectric current in graphene nanoribbon tunable and a good acoustic wave filter for phonon spectroscopy.Supplementary Information.


We study the lattice configuration and electronic structure of a double moiré superlattice, which is composed of a graphene layer encapsulated by two other layers in a way such that the two hexagonal moiré patterns are arranged in a dodecagonal quasicrystalline configuration. We show that there are between 0 and 4 such configurations depending on the lattice mismatch between graphene and the encapsulating layer. We then reveal the resonant interaction, which is distinct from the conventional 2-, 3-, 4-wave mixing of moiré superlattices, that brings together and hybridizes twelve degenerate Bloch states of monolayer graphene. These states do not fully satisfy the dodecagonal quasicrystalline rotational symmetry due to the symmetry of the wave vectors involved. Instead, their wave functions exhibit trigonal quasicrystalline order, which lacks inversion symmetry, at the energies much closer to the charge neutrality point of graphene. The electronic structures of such systems—for example twisted bilayer graphene6, graphene on hexagonal boron nitride (hBN)13, and twisted bilayer transition metal dichalcogenides15 with small twist angles 3, mini Dirac points formation13, Hofstadter’s butterfly16, the emergence of superconductivity17, correlated phases18, and orbital magnetic moment19.When two or more two-dimensional atomic layers which do not share a common periodicity are overlaid, an additional periodicity in the form of moiré interference pattern emerges28. Owing to the momentum mismatch21, quasicrystalline twisted bilayer graphene exhibits the electronic structure of almost decoupled bilayer graphene at most energy ranges. Nevertheless, it also hosts unique electronic states which satisfy the 12-fold rotational symmetry28. Such quasicrystalline states arise from the resonant interaction between the states at specific wave vectors via the rotational symmetry of the quasicrystal as well as the translational symmetry of the constituent atomic layers28. The red and blue hexagons in Fig. 28. Thus, even transition metal dichalcogenides (TMDC) or square lattices can show the quasicrystalline states.A special case occurs when two hexagonal lattices are overlapped at mentclass2pt{minimmentclass2pt{minimmentclass2pt{minim30. The lattice mismatch between graphene and hBN results in a hexagonal moiré superlattice potential with a superlattice period 13. Recently, Leconte and Jung show that BN/G/BN at specific configurations can host two hexagonal moiré patterns overlaid at a twist angle of 31. However, the interaction mechanism responsible for such unique electronic states in BN/G/BN, as well as the actual electronic band structure, and whether the wave functions actually satisfy the symmetry of the quasicrystal have not yet been investigated.Recently, rapid progress has been made in stacking more than two incommensurate atomic layers and a number of studies have investigated the effects of multiple moiré superlattice potentials on the electronic structure. The most notable example among them is a double moiré system, which is composed of a graphene layer encapsulated by hBN layers (BN/G/BN)entclass1pt{minimaentclass1pt{minimaentclass1pt{minimamoiré patterns in double moiré superlattice are arranged in a dodecagonal (12-fold) quasicrystalline configuration. Then we reveal the resonant interactions that bring together and hybridize twelve degenerate Bloch states of monolayer graphene and show that such interactions reconstruct the band dispersion of pristine graphene at these wave vectors. Compared to the resonant states of quasicrystalline twisted bilayer graphene where the actual atomic lattices are arranged in a dodecagonal configuration28, the resonant states of BN/G/BN appear at the energies much closer to the charge neutrality point of graphene. However, their wave functions show the quasicrystalline order with a three-fold rotational symmetry rather than fully satisfying the 12-fold rotational symmetry of the double moiré pattern.Here, we investigate the conditions where the two hexagonal A and B) sublattices. Graphene has carbon atoms in both sublattices, while hBN has nitrogen atom on A site and boron atom on B site. The lattice constant of hBN, 32, is slightly larger than that of graphene, 33. Here, we do not consider the lattice relaxation between graphene and hBN35, since the effects of such relaxation on the electronic structures is an order of a few meV. Nevertheless, our effective theory that respects the lattice symmetry is able to properly describe both the gap at the primary Dirac point and the asymmetric gap opening at the two inequivalent mini Dirac points13, as well as the orbital magnetism of the structure19.We consider a trilayer system composed of graphene sandwiched by hBN. Both graphene and hBN are two-dimensional honeycomb lattice whose unit cell comprises of two ,38, 39 and graphene on hexagonal boron nitride13. In this work, we scaled 39. The effective potentials by hBN to graphene, 13 , there are more sets of states, with different wave numbers, that show the resonant interaction between the constituent monolayer states. However, the set in Fig. It should be noted that this is not the only resonant coupling in this system. As shown in previous work on quasicrystalline twisted bilayer graphene . For (2), on the other hand, we agree that the parameters used in this work might not be accurate. The difference in the interlayer interaction strength Finally, we discuss several factors that may affect the results in this work. (i) Effects of the theoretical model and parameters: In this work, we described the quasicrystalline resonant states by the effective model in the framework of a tight-binding Hamiltonian. Then, it is natural to ask how more accurate models, such as first-principle methods, affect the results. In our effective model, we describe the electronic states by using a few monolayer Bloch states which contribute significantly to the states. In first-principle methods, we get fully coupled wave functions of the states, and may analyze the contributions of each monolayer Bloch state by the projection of the wave functions to the Bloch states. The difference between the two models mainly comes from (1) the interaction between the resonant chain Eq.  and the hain Eq. , which ant}ψ Eq. , which aform Eq.  with sli28, the graphene encapsulated by TMDC layers will also exhibit the resonant states respecting the quasicrystalline rotational symmetry. The difference between the lattice symmetry of the hBN layer (honeycomb lattice) and the chalcogen layer  makes a phase difference between the A-to-A and A-to-B interaction in Eq. ((ii) Effects of using TMDC as encapsulating materials: We can get similar quasicrystalline resonant states in the system composed of a monolayer graphene encapsulated by two TMDC layers at suitable angle. Since the metal atom in a TMDC layer is far from the interface, the dominant interlayer interaction comes from the orbital hybridization between the t(q) Eq.  should b35. Thus, our systems, especially the structure with an angle of A-to-A and A-to-B in Eq. ((iii) Effects of lattice relaxation: Incommensurately stacked atomic layers tend to exhibit local lattice relaxation, especially when the moiré pattern is sufficiently large(iv) Tuning conductivity by gating: It is well-known that the conventional quasicrystals are poor conductors at the energies where the quasicrystalline states are dominant . And the van der Waals quasicrystals would be also likely poor conductors at the energies where the quasicrystalline states are dominant , as we can expect from the large band curvatures and the wave functions distributed selectively on a limited number of sites. Thus, if we tune the Fermi energies near the quasicrystalline states by gating, which is possible only when the states are within a feasible range from the charge neutrality point as in the current system, then we will be able to tune conductivity significantly by gating.moiré patterns are arranged in a dodecagonal quasicrystalline configuration. We first find the condition which gives a We investigated the lattice configuration and electronic structures of a double moiré superlattice of which two hexagonal atomic lattices are arranged in a dodecagonal configuration, the resonant states of double moiré superlattice lack the 12-fold rotational symmetry; they hexagonal quasicrystalline order at a specific point We then reveal the resonant interaction which brings together and hybridize twelve degenerate Bloch states of monolayer graphene as well as the band dispersion around the resonant states. Compared to the resonant states of quasicrystalline twisted bilayer graphene, of which