According to published studies in the field, random choice and random estimation are the only options for tackling judgment and decision-making tasks where the elements from which to infer a required criteria are not recognized. In Campitelli and Labollita (2010), participants were asked to estimate the nationality and Elo rating of chess players based on their surnames. In the present study I re-analyze those 123 participants from Campitelli and Labollita (2010) who declared not to have recognized any player. Even in this scenario of null recognition, they managed to correctly infer the Russian players' nationality and Elo ratings; it is likely that successful and ecologically rational heuristics were used. I found evidence of new structured probabilistic environments external to the lab, likely to have generated a number of undirected and involuntary associations in the memories of the participants, who may have used them in their heuristics to infer the criteria requested. The results support the models of limited rationality: despite the scarcity of available information, the fact that the heuristics did not guarantee success, and the risk of overestimating the heuristics’ effectiveness while underestimating their own biases, participants still favored them over random guesswork, thus suggesting an adaptive use. I invite a revision of what is considered “good reasoning” when applied to problems in environments of uncertainty that call for satisfactory, rather than optimal, solutions. This research provides the basis for new studies in the field of heuristics under previously unexplored conditions, and a new perspective for the analysis of prior works, towards a better understanding of the relationship between cognition and the environment. Heuristics and biases initiated by Kahneman and Tversky  Hamburg(b) KasselCriterion refers to a characteristic of reality about which one must judge or decide . In this example, Hamburg would be chosen more frequently because it tends to be more generally recognized, and since this city is indeed the most populated, this would yield average success rates above random chance. The recognition heuristic predicted the results of the 2003 and 2005 Wimbledon tennis matches with equal or greater precision than experts and ATP rankings  that involve new and unrecognized elements . Example scenarios in a social context include picking the right people out of a group of strangers for a given task, evaluating the best way to act in a new place or situation; assessing which new foods, movies, books or music to consume; judging among different possible solutions to new problems; etc.2 rating of a set of chess players on the sole basis of their surnames. One of the tables contained only non-Argentine players, including players with Russian nationality and non-Russian players with Slavic surnames.3 Another table contained only Argentine players, some of them with Slavic surnames. The participants recognized almost none of the players' surnames.In the present study I re-analyzed part of the data presented in Russia to an unrecognized Karpov on the basis of the suffix -ov; they may have estimated a high Elo rating for him on the assumption that Russians —or those with the suffix -ov— are better at chess). The authors assumed that the participants: (a) had found some surnames that “seemed Russian” (p. 187); (b) knew that "surnames ending in -ov tend to be Russian" (p. 186); (c) knew that Russians "are good at chess" (p. 184); (d) knew that "Russians have been dominating chess for a long time" (p. 188); (e) had used this knowledge to infer nationalities; (f) had used this knowledge to infer Elo ratings.Seeing that the estimation of nationality and Elo rating yielded success rates above chance, Campitelli and Labollita conjectured that the participants must have resorted to indirect knowledge (inferences) for their answers  In the estimation of nationality, the surnames of Slavic origin  to compose a heuristic capable of yielding success without recognition; the ecological rationality of these heuristics with regard to those environments. Finally, I will offer an explanation as to how all these elements may have facilitated the inference of the Russian players’ nationality and the Slavic players’ relative Elo ratings.To infer is to arrive at a conclusion from another certain element , linguistic elements located at the end of a word; (b) the capacity of human beings to detect proper names in an environment; (c) the ability to detect and record suffixes in words, including proper names; (d) the ability to detect and record regularities and linguistic relationships, including proper names and morphemes; (e) that certain experiences may have favored the association between Slavic suffixes  and Russian nationality above other nationalities; (f) that certain experiences may have favored the association between Slavic suffixes (not only the Russian ones) and chess. Assuming that participants had no prior knowledge of these cognitive and environmental aspects, it can be surmised that they were able to detect and register said aspects without direct instruction and through implicit learning.4Although most published studies agree that participants must be able to recognize the element or elements presented to them before they can access additional information, the participants involved in the present study seem to have managed the latter despite the lack of recognition. I posit that the environment they were exposed to before the study of ov to the name of a child ; in Poland, -sky or -skiy; typical of Ukraine are -nko and -enko. However, no univocal correspondence can be drawn between suffixes and nationalities, for suffixes can spread geographically. Human beings are able to detect surnames , not just the Russian players with surnames ending in -ov and -ev: (1) The association of Russia with chess, which resulted in the estimation of higher ratings for Russian-looking surnames, with suffixes used as cues for their identification; or (2) The association of certain suffixes with chess, which resulted in the estimation of higher ratings for the surnames that included said suffixes. Let's consider the plausibility of each scenario. The dominance held first by the USSR and later by Russia in the field of international chess . The subject thus associates the suffixes with Russia, and uses them later to infer this nationality. This is an environment of high uncertainty, as defined by Russia or related terms might not be representative of its prevalence in Russian surnames. The ecological correlation indicates how frequently surnames with Slavic suffixes are mentioned by the mediator in proximity or in reference to Russia . The substitute correlation indicates to which extent those mentions match the associations that the subjects created between the suffixes and Russia  with Russia is to be expected.The criterion inaccessible to the subject  is reflected by an accessible mediator (the frequency with which the surnames with Slavic suffixes —not only Russian— are reported in proximity or in reference to  Russian . A heuriRussia and related terms). The subject thus associates these suffixes or Russia with chess, which leads to the inference of a higher relative rating for chess players whose surnames include Slavic suffixes or who are Russian (using the suffix as the sole basis for discrimination). There’s uncertainty here as well: it may be that not all players with Slavic suffixes mentioned by the media have relatively higher Elo ratings, or they might be mentioned for reasons other than their performance in chess. The ecological correlation indicates the frequency with which Slavic suffixes are mentioned by the media within the context of chess and in proximity or in relation to Russia and related terms; the substitute correlation indicates to what extent these mentions correspond with the subject’s associations. The suffix validity measures the actual relationship between Slavic suffixes and Elo ratings for this external environment. In this task, it represents the proportion of players with Slavic suffixes that actually had a comparatively higher Elo rating. The criterion inaccessible to the subject (the Slavs’ higher relative ratings) is reflected by an accessible mediator . Of the 157 participants, I excluded the 34 that recognized at least one of the chess players, as my interest lies only with those who declared not to recognize any. I then removed the few illegal values received  without disqualifying the participants; outliers were preserved. One participant who submitted too many illegal responses was excluded. The mean age of the remaining 123 participants is 23.8 .The study by The participants of The tables had four columns. The first column contained the names of the players. In the second column, the participants had to indicate whether they recognized each player; in the third column they had to indicate the nationality of each one ; in the fourth column they were asked to indicate their estimated Elo ratings. 1200 to 2850), (b) ArgNonArg (Argentine/non-Argentine), (c) RusNonRus (Russian/non-Russian), (d) SlavNonSlav (Slavic/non-Slavic), and created a number of dummy variables for the suffixes: (e) Suffix -ov (with -ov/without ov), (f) Suffix -ev (with ev/without ev), (g) Suffix -enko (with -enko/without -enko), (h) Suffix -cki (with -cki/without -cki). Also, for each player, it was codified (1/0) the success or failure of the judgment of their nationality. The dependent variables were: (a) nationality accuracy , and (b) estimated Elo rating.I coded all the items shown in M) hit rate was calculated for all the values of each independent variable. In the case of the Elo rating, the mean estimated rating was calculated for each value of each independent variable. In both cases, the standard deviation (SD) and the standard error (SE) of the mean were calculated for all levels or values, with a confidence interval (CI) of 95%. Correlations were used to analyze the existence, direction and strength of the relationships between the variables. To test the hypotheses, inferential analyses were performed using t tests for paired or related samples (the data to be compared came from the same participants), with a significance (α) of .05. The p values were obtained through two-tailed tests, and the size of the Cohen effect d was calculated.For nationality estimation, the mean  = 11.26, p < .001, Cohen’s d = 1.02.The success rate was significantly higher for the Russian players than for the non-Russians; ev, corresponding to the Russian Bareev, with the hits of the players without said suffix; that is, everyone else. The differences were significant: t(122) = 3.14, p < .001, Cohen’s d = 0.285.To investigate the extent to which the Slavic suffixes correlated with the correct estimation of Russian nationality, I compared the hits obtained by the one player whose surname contained the suffix -enko, corresponding to the Russian Jakovenko, was significantly higher than the success rates of the surnames without said suffix; t(122) = 3.75, p < .001, Cohen’s d = 0.34.The success rate of the one surname with the suffix -ov and surnames without it was not significant; t(122) = 1.35, p = .18, Cohen’s d = 0.12. Unlike the two surnames with the suffixes -ev and -enko, not all surnames with the suffix -ov belonged to Russian players. ov that belonged to non-Russian players.As expected, the difference in success rates between surnames with the suffix -ov with all the surnames that didn’t include it: the difference was significant, t(122) = 9.16, p < .001, Cohen’s d = 0.83; this despite the fact that the set of surnames without -ov included surnames with the suffixes -ev and -enko, both of which had yielded significant success rates when tested against surnames without those suffixes.I then compared the surnames of Russian players that included the suffix -ov, I compared all the Russian surnames that included the suffix -ov with the Russian surnames that did not, i.e., surnames with the suffixes -ev and -enko, both of which had yielded significant success rates. The results remained significant: t(122) = 4.68, p < .001, Cohen’s d = 0.42.To more accurately establish the influence of the suffix -ev and -ov, only 33% of the participants applied a heuristic such as “ev is a Russian suffix,” whereas a heuristic like “ov is a Russian suffix” was much more prevalent: the set of Russian players with surnames ending in -ov yielded a success rate of 52%).The second and third columns show the actual number of players of Russian nationality in each suffix group; the fourth column shows the percentage of players identified as Russian by the participants. Thus, the validity of Russia for the whole set of suffixes was 56%, since five of the nine surnames with Slavic suffixes belonged to Russian players. The participants correctly assigned 45% of that 56% to Russia. These successes reveal the strength of the associations binding these suffixes to Russia in the participants’ memories, which influenced the level of adherence to the applied heuristics  = .70 between these variables. Averages for both estimated and actual Elo ratings were calculated for all chess players, showing a correlation t-test on paired samples of estimated ratings for the Slavs and for the non-Slavs showed significantly higher estimates for the former: t(122) = 2.89, p < .001, Cohen’s d = 0.56.The participants tended to assign more points to the Slavic players. A t(122) = 6.15, p < .001, Cohen’s d = 0.56.At least part of this difference could be explained by the low ratings estimated for Argentines overall, considering that the set of Slavic players included only two Argentines  against the eight Argentines included with the non-Slavs. I then compared the average estimated ratings for Argentines and non-Argentines, which indeed revealed that rating estimations for non-Argentines had been significantly higher: ov had got significantly higher estimates than those without the suffix ov; i.e., all the other surnames: t(122) = 6.46, p < .001, Cohen’s d = 0.58.To ascertain the extent to which Slavic and Argentine origins accounted for the difference seen in the ratings estimated for Slavs and non-Slavs, I investigated the relation between suffixes and the ratings estimated for the Slavic players. The surnames with the suffix -ov and eight Argentines among the rest, it was clearly feasible that the lower ratings estimated for the Argentines in general had brought down the relative ratings of the group without the suffix -ov. However, even the ratings estimated for the non-Argentines with surnames ending in -ov were significantly higher than the ratings estimated for the non-Argentines with surnames not ending in -ov; t(122) = 2.89, p = .005, Cohen’s d = 0.26.Because again there were two Argentines among the players with surnames ending in -ev and -enko received the lowest estimates among the non-Argentine Slavs, and ranked in the bottom four of all non-Argentine players. To find out if these ratings accounted for the significantly lower estimates obtained by the surnames of non-Argentines that didn’t include the suffix -ov compared to those non-Argentines that did, I compared the surnames of non-Argentines ending in -ov against the surnames of the non-Argentines that didn’t have a Slavic origin : even here, the non-Argentines with surnames ending in -ov showed higher ratings than the rest of the non-Argentines; t(122) = 2.57, p = .011, Cohen’s d = 0.23.By contrast, the surnames with the suffixes -t(122) = 1.93, p = .056, Cohen’s d = 0.17.The Slavic Argentines, however, did not get higher ratings than the non-Slavic Argentines; ov and higher estimated ratings, the Argentine player whose surname included the suffix -ov, Kovalyov, did not get a higher rating than the rest of the Argentines; t(119) = 0.61, p = .545, Cohen’s d = 0.06.Despite the relation between the suffix -ov was generally higher than the ratings of the rest of the players, and the participants thought along the same lines: the correlation between the estimated and actual ratings of the players with surnames ending in -ov was .47 .The second column shows the associative strength of the Slavic suffixes with the actual ratings of the players whose surnames contained those suffixes, and summarizes their relative position as shown in ov, -ev and -enko present in the surnames, and evaluate them as useful based on basic cognitive abilities and environmental characteristics, namely: the suffixes -ov, -ev and -enko appear in Slavic surnames; the participants were able to identify surnames without direct instruction and without intention; they could also indirectly and implicitly identify and retain regularities appearing in surnames, such as suffixes, after only a handful of brief exposures (ov and -ev) may have resulted in the higher success rates seen in the estimation of Russian nationality, even though the suffix -ev showed the weakest relation, followed by the suffix -enko (whose link to Russia was corroborated despite being Ukrainian). The Russian players whose surnames included the suffix -ov scored a higher number of hits than the rest of the players (including Russians with surnames ending in -ev and -enko), corroborating that -ov was not associated to nations such as Gashimov’s Azerbaijan or Aleksandrov’s Belarus.Even without recognizing the players’ names, the participants correctly estimated Russian nationality to a significantly higher degree than other nationalities. I propose that the participants resorted to previously created memories that allowed them to detect the suffixes -xposures . The heuConsidering that participants were asked to estimate the nationality of chess players, it is plausible to think that mass-assigning Russian nationality to all players based on the association between Russia and chess would have sufficed to get success rates above random chance. However, the evidence suggests this was not the strategy applied, given that:The hit rate for the Russian players would have been 100%, and not 45%.The hit rate for the non-Russian players would have been 0% and not 11%.A quick examination of individual results reveals that no subject estimated the nationality of all Russians correctly without estimating some other nationality correctly as well.Russia except for some other nationality which they also assigned correctly, while most of the hits for non-Russian nationalities came from another set of participants who did not mass-assign Russia and failed to identify any Russian player. This scenario, however, doesn’t account for the significant differences in success rates between the Russians with surnames ending in -ov (52%) and the Russians with surnames not ending in -ov, i.e., with the suffix -ev or -enko (35%).There is another improbable, but not impossible explanation: that the significant success rates were the result of a set of participants massively assigning ov. This would explain the hit rates for the Russians overall as well as the differences between the Russians with surnames containing the suffix -ov and those without it. But this scenario can also be ruled out: even if a second set of participants had acted as described, a quick glance at the results reveals that only 17 subjects correctly assigned the Russian nationality to all Russians. Considering that they also assigned correctly at least one other nationality, it follows that not even them assigned Russia blindly.There is another, more unlikely scenario: that a set of participants mass-assigned the Russian nationality except for some other nationality which they also assigned correctly, while the hits for non-Russians were scored by another set of participants who also identified correctly some of the Russian players based on the suffixes in their surnames, particularly -Russia could have been chosen. If all world countries were considered, the probability of choosing Russia by chance would be close to 1/200. If we then consider the probability of correctly assigning Russia to one or more Russian players by chance, the expected hits would be much lower than those achieved. However, it would be incorrect to assume that the participants knew all the countries in the world. What would be an appropriate number? One hundred nationalities? Fifty? It’s anyone’s guess. A relative comparison with the hits obtained for the other nationalities avoids this problem. If, nevertheless, an approximation is wanted, it could be assumed conservatively that this sample of subjects knew on average 25 nationalities, in which case the probability of choosing Russia by chance would be 1/25. Compounding this with the probability of correctly assigning Russian nationality to one or more Russians, the expected successes should still be much lower than those obtained. On the other hand, the request to estimate the nationality of chess players could have triggered an association with Russia that eliminated the need for choice, but even the expected success rate of one Russian correctly identified in five attempts would still be significantly lower than the results obtained.Could the Russian successes be ascribed to chance? In fact, why did I compare the hits for the Russians with those for the rest of the players, instead of comparing them against random chance? The comparison with chance requires establishing the absolute number of nationalities out of which ov than they did to the rest of the players, a result supported by the cognitive abilities and environmental characteristics explained. The Slavs with surnames ending in -ev and -enko, on the other hand, were assigned comparatively low ratings. The superior performance associated with the suffix -ov persisted even when Argentines were excluded from both subsets (they obtained a significantly lower average rating than non-Argentines), and even when the Slavs with surnames ending in -ev or -enko were excluded from the non-Argentines subset.Even with no recognition, participants assigned significantly higher ratings to the Slavic players with surnames ending in -ov were assigned higher ratings may be explained by (a) an association between Russia and good chess performance, which led to the assignment of more points to surnames with the suffix -ov because they looked Russian (it was one of the suffixes associated with Russia) or (b) an association between -ov and good chess performance, which led to the assignment of more points to surnames with that suffix. The first association is based on Russia's dominance in the field of international chess  scored significantly higher points than the rest of the Argentines. Although the evidence is limited to a sample of a single player, the heuristic that led to the assignment of high ratings to the surnames with the suffix -ov may have been applied to Kovalyov in a compensatory way .recognized the elements presented cannot be ruled out. The implications are huge, since at least part of these investigations might have included variables that introduced confusion or interactions unsuspected until now. For example, many city names used in recognition tasks may have contained suffixes  that influenced the participants’ decisions when facing not only two unrecognized cities, but also two recognized cities or even a recognized city and an unrecognized one. Additionally, in each case these morphemes might have exerted some influence before or after the subjects detected the degree of familiarity, fluency, availability, recognition, etc., of the cities presented to them.However, these existing controversies make the findings in this research even more relevant, since the use of linguistic cues in the large number of heuristics studies where the participants The results provided evidence on the exploitation of information present in a probabilistic environment external to the laboratory  by way oRussia and related terms, with a higher frequency than other nationalities. Although the substitute correlation could not be obtained either, the assumption is that the mediators had disseminated a larger number of surnames with Slavic suffixes in connection with Russia and related terms than they did in connection with other countries, although perhaps unevenly: the associative force was greater for the suffix -ov than for -ev or -enko. ov, -ev or -enko are actually Russian).The evidence provided by the successful estimates of Russian nationality is consistent with the environment depicted in ov in the context of chess (the results do not directly require that these mentions be made in the proximity of or connected with Russia and related terms). The value of the substitute correlation could not be obtained either, but it must be assumed that mediators had disseminated at least the suffix -ov in the context of chess, since the surnames with this suffix scored significantly higher ratings. ov, -ev or -enko actually have higher relative ratings).The evidence provided by the assignment of higher ratings to Slavic players in the absence of recognition is consistent with the environment depicted in Russia to the Russian player Jakovenko (whose surname contains a Ukrainian suffix) corroborated the hypothesis that the suffix -enko would be associated with Russia, we can only guess which countries were picked by the participants with incorrect answers. Ukraine? Which other nationalities were assigned to the Russian players with surnames containing the suffix -ov? Were Gashimov, Alexandrov and Topalov, who were not Russian and did not score any hit, also considered Russians? We have no answer for these questions.The re-analysis of the judgment-making task described in cki, who could have provided additional information about this suffix, nor were included Argentines with the suffixes -ev and -enko.The stimuli did not include non-Argentine players with the suffix No data could be obtained from the real environments in terms of ecological correlation, the substitute correlation, the suffix validity for Russian nationality and the suffix validity for Elo ratings. These would have allowed me to analyze the results in more depth.It was not possible to carry out an individual, per-subject analysis (it would have required many more answers), which is a mandatory requirement for the study of heuristics according to some researchers of the fast-and-frugal heuristics program . For an introduction to the aforementioned requirements, the debate they elicited and the analytical methodology adopted, see According to published studies in the field, random choice and random estimation are the only options for tackling judgment and decision-making tasks where the elements required to infer a criteria are not recognized e.g., . The preThe results support the use of models of limited rationality to characterize human psychology, since participants applied heuristics to achieve success rates above chance level, despite the risk of overestimating the heuristics’ effectiveness and underestimating the participants’ own biases, a behavior justified in evolutionary terms e.g., . I thus My hope is that this study will provide a basis for new studies in the field of heuristics under previously unexplored conditions, and a new perspective for the analysis of previous works, towards a better understanding of the relationship between cognition and the environment.


We study the nanocars’ lateral and rotational diffusion as well as the wheels’ rolling motion on two kinds of graphene substrates—flexible single-layer graphene which may form surface ripples and an ideally flat graphene monolayer. We find that the graphene surface ripples facilitate the translational diffusion of Nanocar and Nanotruck, but have little effect on their surface rotation or the rolling of their wheels. The latter two types of motion are strongly affected by the structure of the nanomachines instead. Surface diffusion of both nanomachines occurs preferentially via a sliding mechanism whereas the rolling of the “wheels” contributes little. The axial rotation of all “wheels” is uncorrelated.We provide a comprehensive computational characterization of surface motion of two types of nanomachines with four C These biomolecular systems inspired the development of artificial machines that function at the molecular level5. The widespread function of the controlled molecular motion in fundamental natural processes suggests that notable rewards can be gained by improvements of synthetic molecular machines7. Nanocars constitute one example of artificial molecular machines with chassis, axles, and wheels designed for nanoscale transport on various surfaces9. Understanding the molecular motion on surfaces is essential for controlling the dynamics and functioning of molecular machines10. In particular, one of the long-standing questions to address is the relationship between the design of nanomachines and their diffusion properties12.Natural molecular machines are in the heart of the cellular machinery of living organisms, performing complex vital functions, and transferring materials with high efficiency14. Tour and colleagues synthesized nanocars specifically for the transportation of other molecules. They built a variety of nanocars that consisted of chassis and wheels. The spherical shape and stability of Buckminsterfullerene, C60, motivated them to use fullerene moieties as the first types of wheels for such Nanocars and Nanotrucks18. A number of computational studies of nanocars’ motion on a variety of substrates were reported in the past, including C60-based Nanocars and Nanotrucks on metal surfaces using either the rigid-body22 or all-atomic24 molecular dynamics (MD) methods. Nemati and co-workers investigated the role of vacancies25, impurities26, and step-like surface defects27 to control the diffusion of C60 and C60-based nanocars. Lavasani’s group29 demonstrated how the chassis structure was affecting the diffusive motion of carborane-wheeled nanocars on a gold surface.Synthetic chemists suggested a variety of structural designs intended to increase the mobility of nanocars on surfaces30, making them promising materials for a wide range of applications. In particular, graphene can be considered a potential surface for nanocar operation in nanoscale molecular transporting applications. Such potential applications recently stimulated studies of nanocars on such all-carbon based material surfaces. Ejtehadi and co-workers32 studied the diffusive motion of C60 on graphene and on a variety of graphyne structures33. Savin et al.34 characterized the thermally-induced diffusion of C60 fullerene on graphene nanoribbons. Jafary-Zadeh et al.35 created a transporting pathway on graphene to confine the diffusive motion of C60. Ganji et al.36 theoretically investigated the motion of a carborane-wheeled nanocar on graphene and graphyne surfaces using the density functional theory.In the past decade, all-carbon-based materials such as few-layers graphene, graphyne, carbon nanotubes, or graphene nanoribbons have been recognized for their unique electronic and structural properties37. As observed by the scanning tunneling microscopy, the thermally-induced ripples in graphene form standing waves that evolve erratically38 Such ripple waves could in principle affect the motion of nanocars due to occasional variation of the contact level and interlock effects to hinder molecule translation39. Although several works reported studies of the motion of a single molecule (e.g. C60) on graphene42, the dynamics of nanocars on the flexible graphene surface that can form ripples has not been investigated yet. Furthermore, little work has been done to delineate the role of the chassis rigidity in the surface dynamics of nanomachines. To the best of our knowledge, no such studies have been reported for nanomachines moving of graphene surfaces.Monolayers and few-layers of graphene are not flat and exhibit a wavy morphology of the surface, with ripples and out-of-plane deformations60 wheels in each, but different in their chassis rigidity: the Nanocar and Nanotruck.In this work, we study several effects that can control the dynamics of nanomachines on graphene surfaces: (1) the role of substrate flexibility; (2) the role of the chassis flexibility. We do this by comparing the results of all-atomic molecular dynamics in a variety of atomistic models. To examine the first effect, we consider the motion of nanocars on single-layer graphene (SLG) and frozen layer graphene (FLG) surfaces. To examine the second effect, we choose two nanocars with four C43 with C60 wheels , a 3 × 4 nm molecule; and (b) a rigid chassis Nanotruck  a 2 × 3 nm one. To be able to study graphene flexibility (surface ripples) and elucidate the effects, we define two types of substrates:Single-layer of graphene (SLG) in which all of graphene’s atoms are allowed to move, which leads to the surface ripple formation. This substrate is the best approximation of the SLG that can be fabricated experimentally. The absence of vertical interactions with other layers (as would be the case for graphite or multi-layer graphene), leads to the formation of pronounced ripples . This design corresponds to a hypothetic case of an ideally flat graphene surface, without ripples and without thermal motions.We study the motion of two types of previously synthesized fullerene-based machinesels Fig. : (a) a f2 square sheets containing 5744 carbon atoms. The graphene sheet is positioned at By considering the motion of Nanocar and Nanotruck on two graphene substrate types, we have four systems to study Fig. . To stud44 (http://www.ks.uiuc.edu/Research/vmd/). Molecular interactions are described using classical force fields as implemented in the Largescale Atomic/Molecular Massively Parallel Simulator (LAMMPS 22Aug2018 version) software45. Tersoff potential is used to describe covalent bonds in graphene and nanomachines. Lennard–Jones 6–12 (LJ6-12) potential is used to describe the non-bonded interaction between each atom of graphene with each atom of nano-machine:For visualizing the initial and output structures we have used VMD 1.9.2 software package49. The cut-off radius, Here, σ and ε are the van-der-Waals (vdW) radius and depth of atomic interaction potential for each pair of species, respectively. The parameters related to each atom pairs are listed in Table 50. For each system, the simulations are performed for temperatures ranging from 5 to 1000 K.MD trajectories are integrated for 40 ns for each system in the NVT ensemble. The velocity Verlet integration scheme with the integration time step of 1 fs is used. Data recorded every 200 timesteps, resulting in 200,000 data points for each simulation. The Nose–Hoover thermostat is used to maintain the target bath temperature. The thermostat damping parameter that determines the rate of heat exchange between the system and the thermostat (Tdamp) is set to 100 fs, which is a typical value used in molecular simulationsTo compute the desorption temperatures, we utilize the following procedure. At high temperatures, the molecule can escape the substrate by overcoming the van-der-Waals energy and move away to distances greater than 30 Å where the interaction energy becomes negligible. Therefore, we treat the molecules that move away from the surface by 30 Å or more and never return during the simulation (40 ns) as a desorbed case. When we observe such “desorption” events, we reduce the temperatures by 25 K to examine nearby temperature values and test whether desorption still occurs at lower temperatures. If the desorption process is still observed, we lower our estimate of the desorption energy and repeat the process. Otherwise, we consider the obtained value as the resulting desorption temperature with a 25 K error bar.51:To quantify the translational motion of nanomachines, we compute the mean square displacement (MSD) for every type of simulation (as defined by the system type and MD conditions). MSD quantifies the mobility of molecules due to random-walk-like motion. The MSD is used to compute the surface (2D) diffusion coefficient, 52.Here, entclass1pt{minimaThe displacement of the molecule in the vertical direction may facilitate lateral diffusion since the lateral displacement barriers would decrease when the molecule moves away from the surface. This type of motion is temperature-activated. Figure 60, the average distance is smaller for the former than for the latter, reported earlier to be 6.4 Å53. Already at this temperature, one may observe the signs of surface rippling as manifested in larger molecule height fluctuation for the flexible SLG as opposed to the FLG system with constraints on the motion of surface atoms. Surface ripples intensify the oscillation of the molecule around the equilibrium distance. Even at a low temperature, the height of the molecule shows the trace of the graphene surface ripples. The surface rippling effect is enhanced with temperature, leading to the z value of Nanocar COM to fluctuate stochastically between 4.5 and 6.5 Å  is notably larger than the experimental value. This remarks that the inclusion of the rippling effects is crucial for computing an accurate description of thermodynamics of the interaction of molecules with graphene.The Nanocar COM z coordinate oscillations lead to more probable desorption of the molecule from the substrate. We examine the affinity for Nanocar and Nanotruck to desorb from the substrate based on the outcomes of the 40 ns MD simulations for each type of system in a range of temperatures higher than 1000 K (no desorption occurred at temperatures under 1000 K). For each combination of temperature and system, the simulations are repeated 3 times. Each repetition corresponds to a distinct initial velocity distribution (different seed numbers). We find that the desorption temperatures for both systems are comparable Table . For botOur interpretation of the observed trends is as follows. On the more flexible SLG surface, the average curvature at the point of surface/adsorbate contact is non-zero. As a consequence, some parts of the nanocar molecule  are positioned farther than the optimal distance, whereas other parts of the molecule  would prevent the molecule from getting even closer to the surface. This picture changes dynamically—the “close contact” regions become the “bent-away” ones, changing back and forth over time. As a result, the average substrate/adsorbate energy decreases in comparison to what it could be on the ideally flat surface, leading to decreased desorption energies. On the contrary, on the ideally flat surface (as modeled here by the FLG system), the interactions are maximized due to the absence of the “bent-away” regions.Our calculation on graphene ripples during the time evolution of SLG simulations shows that ripples amplitude (standard deviation of z components of graphene atoms) is increasing with temperature and saturate to about 1 Å at high temperatures. The average peak-to-peak distance of the ripples is computed to be 25 ± 5 Å, which is on the order of the Nanocar and Nanotruck size. The ratio of the ripple peak-to-peak distance to the nanomachine’s size is also consistent with our rationalization of the desorption temperatures.55. Thomsen et al.56 directly measured the freestanding graphene roughness (ripple amplitude) as about 1.14 Å using diffraction tilt analysis in the transmission electron microscope (TEM) method. Kirilenko et al.57 reported that a graphene roughness root mean square of 58 reported the peak heights of the rippled graphene to range from 0.2 to 0.4 nm and periodicities (peak-to-peak distance) to range from 3 to 10 nm.The peak-to-peak distances computed in this work are in good agreement with previous theoretical and experimental studies on rippled graphene, which reported the graphene roughness to be between 75.2 to 109.0 pmTo quantify the lateral diffusion of Nanocar and Nanotruck on graphene with and without surface ripples, we compute the diffusion coefficients for all systems for a range of temperatures Fig. . The raw59. In the view of static interactions, like a “lock-key” or “host–guest” type, the relationship between the molecule mobility and the flexibility of surface is counterintuitive; “more bent” supposedly means stronger molecule/SLG interactions or lower energy level. However, since the ripples on 2D graphene are dynamic (proved by experiment and STM imaging38), the surface bends dynamically so that the energetically favorable points are transient and quickly turn into energetically unfavorable configurations. The fluctuation of potential energy profile (shifting of minimum position) in time due to rippling , creates configurations that have negative potential energy value at one time suddenly turn to positive potential value at another time. Hence, the potential energy is averagely more positive in the system with a flexible substrate. Consequently, the desorption energy decreases, resulting in higher mobility and diffusion coefficient of the molecule.The flexible freestanding graphene (SLG) surface show bending opposite to the fixed graphene (FLG). This bending phenomenon is observable in experimental microscopy2/ps at room temperature. This value is an order of magnitude less than the room-temperature diffusion coefficient (50 Å2/ps) for C60 on a graphene sheet53. We attribute this difference to the greatly increased adsorbate/surface interaction energy for the NC or NT moving on graphene monolayer, as compared to a single C60 molecule moving of such surface. However, the molecular size is not the only determinant of the molecule’s diffusion coefficient. If an increase of the molecule’s size is associated with its vertical  elongation, the atoms that are more distant from the surface would contribute only little to the surface/adsorbate interaction energy due to the short-range nature of the van der Waals interactions. Thus, having the planar alignment of most atoms in the nanomachines is an effective way to slow down the machine’s diffusion60.The computed diffusion coefficient for Nanocar and Nanotruck on SLG is on the order of 5 Å60 molecule (39.2 meV), suggesting that the fullerene wheels as a part of nanocars do not interact as strongly with the substrate as they would be on their own. In other words, combining them via the chassis facilitates the motion of 4 fullerene wheels together. The larger activation energies on the FLG than they are on the SLG are consistent with the above “bending-away” explanation of the differences in the activation energies for desorption.Using the Arrhenius plot and diffusion coefficients at high temperatures Fig. a, we comThe rotational motion of nanomachines on the surfaces is characterized by the temporal evolution of the components of angular velocity . As a consequence, the surface diffusion coefficients are amplified on the flexible graphene surface for both nanomachines. The corresponding activation energies decrease by 20% (from 90.88 to 72.58 meV) for Nanocar and by 33% (from 100.90 to 67.56 meV) for Nanotruck on the flexible graphene as compared to the frozen surface.We demonstrate that both the surface and chassis flexibility critically affect the dynamics of nanomachines on graphite surfaces. The presence of surface ripples increases the magnitude of the nanocar/substrate vertical distance fluctuations and decreases the desorption temperature, regardless of the substrate molecule  than for more rigid Nanotruck structure (126.71 meV on SLG and 128.59 meV on FLG). The sliding mechanism is found to be dominant over the rolling one for both types of nanomachines, although more pronounced in the Nanotruck, where the wheels’ rotation is hindered to a larger extent. We demonstrate that the axial wheels’ rotation in Nanocar and Nanotruck is uncorrelated—each wheel rotates completely independently of all other wheels.Supplementary Information.


Hence, the most credible criterion for diagnosis remains histology. After diagnosis, regular follow-up for systemic manifestations is recommended. Asymptomatic patients with hepatosplenic sarcoidosis have a good prognosis without any medical intervention, while patients with abnormal labs or symptoms must commence treatment.Sarcoidosis is an idiopathic, chronic, multisystem, granulomatous, inflammatory disease involving almost all organs. Sarcoidosis can occur with an atypical presentation of hepatosplenic involvement, like in the case of our patient. In this case report, we present a rare case of extrapulmonary sarcoidosis with isolated involvement of the liver and spleen in a 39-year-old Caucasian female. There is a possibility of this isolated involvement of an organ in the complete absence of pulmonary disease, which makes the diagnosis of sarcoidosis very difficult as it is usually not suspected. Ultrasound and CT are important in ruling out other differential diagnoses, but a definitive diagnosis is possible only on histological examination, differentiating sarcoid lesions from  Sarcoidosis is a chronic, idiopathic, multisystem, noncaseous, granulomatous disease , 2. The The gastrointestinal tract is very rarely the primary site in sarcoidosis; however, reported cases have commonly involved the liver and spleen in 80% of the cases but are usually asymptomatic , 3. IsolRoutine lab investigations are futile; however, peripheral lymphopenia with CD4 depletion, raised serum angiotensin-converting enzyme (s-ACE), lysozyme, hypercalcemia, and hypercalciuria may help narrow differentials . CriteriDue to the rarity of exclusive extrapulmonary manifestations of sarcoidosis, especially involving the gastrointestinal tract, there are very scarce literature data published on diagnosis, management, and clinical course of the disease . We presA 39-year-old Caucasian female presented with complaints of intermittent nausea, vomiting, and abdominal pain for two months associated with weight loss of 30 pounds. The vomiting was nonbilious, and she also had reduced oral intake secondary to nausea. On examination, her vitals were a blood pressure of 100/60 mm Hg, pulse rate of 120/min, respiratory rate of 18/min, afebrile, and oxygen saturation of 98% in room air. She had no palpable lymph nodes with unremarkable cardiac and respiratory exams but had epigastric and right upper quadrant tenderness; the spleen was palpable 3 cm below the costal margin, and the liver span could not be assessed due to tenderness (Murphy's sign was positive).Laboratory data identified anemia with a normal white blood cell count (WBC). They also demonstrated lactic acidosis of 6.4 mg/dl, alkaline phosphatase of 451 units/l, albumin 2.7 gm/dl, and the ionized calcium to be 1.62 meq . The cheComputed tomography of the abdomen with contrast Figures –4 identiAn upper gastrointestinal biopsy was performed to rule out peptic ulcer disease/malignancy; however, it showed chronic inflammatory changes. A hepatobiliary iminodiacetic acid (HIDA) scan had ruled out cholecystitis. An endoscopic retrograde cholangiopancreatography was performed, and it ruled out cholecystitis and showed cholelithiasis and nonobstructing bile duct without any evidence of any mass. A special set of labs was sent to rule out other etiologies of infiltrative disease , which aFinally, exploratory laparoscopy  was perfBased on the findings of histopathology and elevated calcium levels, a diagnosis of extrapulmonary sarcoidosis was established. The patient was started on steroid therapy and improved. Hypercalcemia improved slightly but remained persistent above normal . She wasSarcoidosis is characterized by noncaseating granulomas formed by the accumulation of inflammatory cells . The sarThe extent of granuloma infiltration is positively associated with the amount of various inflammatory mediators released . It can α hydroxylase in sarcoid alveolar macrophages that are responsible for changing 25-hydroxyvitamin D to 1, 25-dihydroxy vitamin D (the active form of vitamin D) [The literature records an approximate of 30% of cases of sarcoidosis in extrapulmonary locations, most common of which was abdomen , with only 2% presenting as isolated cases without a concomitant thoracic disease . Anothertamin D) , 12. Thetamin D) . Mild hytamin D) . Alternatamin D) . Prednistamin D) , 12.As per the diagnostic criteria, sarcoidosis is a systemic granulomatous disease that should involve several organs, and the involvement of a single organ will not form a diagnosis . An exceHepatic sarcoidosis occurs in 1–40 per 100,000 cases . HoweverACE has been shown to be raised in 60% of cases, while hypercalcemia or hypercalciuria has been reported in 10–40% of patients . AlthougDiagnosis is highly dependent on a compatible clinical presentation and radiographic findings; however, definitive diagnosis is only established with the histological presence of epithelioid noncaseating granuloma of the lymph node, lung, the or organ's specimen . As granTreatment is based on the symptoms and severity of the disease . The excInfrequently, hepatic sarcoidosis has led to a chronic cholestasis syndrome presenting with pruritis, jaundice, hepatomegaly, and markedly raised serum alkaline phosphatase and cholesterol . Histoloβ blockers, splenorenal, or transjugular intrahepatic portal-systemic shunt (TIPS), a splenectomy can also be used, or for refractory cases, a liver transplant is curative [Portal hypertension seen in hepatic sarcoidosis may also be permanent if a resultant of fibrotic changes from biliary fibrosis or cirrhosis, which will, in turn, be unresponsive to corticosteroids or any other intervention being used to treat sarcoidosis . Howevercurative , 11. It Splenic sarcoidosis typically shows association with lung disease; however, 25%–33% of patients have also exhibited normal chest X-ray , 5. LaboMost patients with splenic involvement of sarcoidosis will not necessitate treatment as a spontaneous resolution of splenomegaly is common (66%), especially when the spleen is <4 cm below the left costal margin , 11. MedTo summarize, we report a case of systemic sarcoidosis with isolated extrapulmonary involvement of the liver and spleen. Identifying systemic locations radiographically is particularly tricky due to the wide array of imaging features found, which often overlap with that of other pathologies. It is important for the clinician to identify the pulmonary and extrapulmonary manifestations of the disease and recognize the radiographic findings in order to reduce morbidity and mortality . Biopsy This case highlights the diagnostic challenge that presents with isolated extrapulmonary sarcoidosis. Our case was of an extremely uncommon form of sarcoidosis as hepatosplenomegaly and hypercalcemia are rarely present without pulmonary involvement. The isolated hepatosplenic disease is a precursor for systemic disease; therefore, patients in this setting should be closely followed by their physicians for relapse.


Graphene has been recently proposed to be integrated with silicon photonics to meet these goals because of its high mobility, fast carrier dynamics and ultra-broadband optical properties. We focus on graphene photodetectors for high speed datacom and telecom applications based on the photo-thermo-electric effect, allowing for direct optical power to voltage conversion, zero dark current, and ultra-fast operation. We report on a chemical vapour deposition graphene photodetector based on the photo-thermoelectric effect, integrated on a silicon waveguide, providing frequency response >65 GHz and optimized to be interfaced to a 50 Ω voltage amplifier for direct voltage amplification. We demonstrate a system test leading to direct detection of 105 Gbit s −1 non-return to zero and 120 Gbit s−1 4-level pulse amplitude modulation direct detection.The fast carrier dynamics and ultra-broadband optical properties of graphene make it suitable for optical communications. Here, the authors demonstrate a photo-thermo-electric graphene photodetector integrated on a Si waveguide featuring 105 Gbit s The speed of these connections will also increase, with 5G devices expected to reach 575 Mbps in wireless links for the broad community of users by 20231. As a result, next optical network and interconnect technologies will be developed to meet the increasing bandwidth connectivity demands. One of the next major transitions will be the general availability of 400-Gigabit Ethernet (GbE) technology2, along with the development and standardization of the 800-Gigabit Ethernet (GbE) technology for optical transceivers providing higher capacity at a reduced cost, footprint, and power consumption3. Even more demanding the sixth generation of the wireless network (6G) will require >1000 Gb s−1 per user and beyond4.The global number of devices connected to the IP network is growing at a compound annual growth rate (CAGR) of 10%, and is expected to exceed 28 billion connected devices by 20236. Si photonics transceivers have reached the market and with a potential growth at a CAGR exceeding 20% according to market analysts8. Typical Si photonics transceivers may include: modulators based on Si junctions realized by implantation doping9, modulators based on germanium (Ge) or silicon-germanium (SiGe) epitaxy11, photodetectors based on Ge epitaxy12.In this scenario, Si photonics technology plays an essential role as it offers the possibility of cost-effective large volume production, thanks to the availability of well-established silicon fabrication facilities and the relatively low cost and high abundance of the material−1 data rate measured in a IM-DD (intensity modulation direct detection) optical signal13.State of the art Ge photodetectors integrated in a Si Photonics platform have featured 90 Gb sIn the comparison with InP based detectors, the bandwidth limit of a waveguide integrated InP based detector for telecommunications is higher than the Ge case and it can reach, however, the complexity of the detector and the cost of the InP platform is not comparable with the cost structure of Si Photonics or graphene integrated in Si Photonics, and with the possibility of mass production offered by CMOS foundries.14. In particular, graphene has been recognized as a promising material to be integrated on Si photonics to fulfill the requirements of next generation transceivers for datacom and telecom applications15. Graphene is an allotrope of carbon with atoms arranged on a one-atom thick hexagonal lattice16. The peculiar atomic structure, made of covalent bonds, determines a linear dispersion between energy and momentum with the conduction and valence bands meeting in single point (Dirac point) in the momentum space, with no energy gap17. This feature leads to intriguing electronic and optical properties, e.g., ultra-high carrier mobility18 and enhanced electric field effect19 that allows tuneable electronic and optical properties by electrical gating20. Moreover, graphene can be grown on a sacrificial material by chemical vapor deposition (CVD)21 and then transferred on top of any fully passive photonic waveguide platform, e.g., Si or silicon nitride (SiN), in order to realize broadband photonic integrated photodetectors22, fast electro-absorption23, and electro-refraction24 modulators, with a potential impact on the cost of future graphene photonic transceivers15.Conversely 2D materials have recently emerged as viable alternative enablers for Si photonics devices12. The first is the ultra-broadband optical absorption of graphene from the UV to the far infrared and beyond, which is due to the gapless band structure25. Moreover the fast dynamics of hot carriers (HCs) upon optical excitation, with relaxation times of the order of few ps28, enables optical to electrical conversion at bandwidths exceeding hundreds of GHz30.Graphene photodetectors offer several advantages over the typical Ge photodetectors−131 and fast operation, however they operate under a bias voltage and significant dark direct current (DC) that can be in the order of several mA’s35. So high DC currents may introduce two main impairments in the design and implementation of a photoreceiver for optical communication, i.e., when we consider the circuit including the read-out electronics. The first is the noise arising from the photodetector. The noise analysis of graphene photodetector based on bolometric or photoconductive is typically not reported, and the effect of the large dark current on the signal integrity is not discussed. In general, those high DC currents may contribute to the overall noise in graphene devices37. The second impairment arises when we consider the coupling of the photodetector to the transimpedance amplifier (TIA), used to convert the photocurrent into a voltage signal to a level that can be processed by the electronics downstream of the TIA38. When the input DC components exceeds several mA the TIA may operate in a nonlinear regime, or may even saturate the output, introducing undesirable output offsets and reducing significantly the linear dynamic range needed to preserve the signal integrity39. Capacitive DC blocking is generally unfeasible at the input of TIAs because it requires large capacitors to preserve the signal, which are difficult to be integrated within the TIA electronics because of the large area required; moreover, the parasitic due to external DC blocks may deteriorate the TIA performance in terms of noise and bandwidth41. Depending on the application, the DC current may be canceled using specific cancellation circuits, differential inputs or balanced photodetection38. In the first case, high dark DC currents may still run the TIA into nonlinear regime because the cancellation is obtained with a feedback control after amplification38. In the case of differential input or balanced photodetection, large DC currents may give rise to an input DC component which may be still too high depending on the common mode rejection ratio (CMRR) of the differential amplifier, or on the balance of the photodetectors currents38. For these reasons, low dark DC currents are always desirable to improve the signal integrity and graphene photodetectors based on the PB or PC effects may introduce strong limitations to the TIA design. In photo-thermoelectric (PTE) based photodetectors, a photovoltage is generated through a thermoelectric effect induced by photon absorption42. PTE effect is highly efficient, as a large portion of the photon energy is transformed in electron heat owing to the ultrafast carrier scattering and weak coupling to phonons in graphene43. In particular, absorbed photons generate HCs with a carrier temperature spatially distributed along the graphene layer following the optical intensity distribution44. By inducing a spatial profile of the Seebeck coefficient in the material, e.g., by electrical gating, an electromotive force is generated by thermoelectric effect (Seebeck effect) which is proportional to the spatial gradient of the HC’s temperature47. The generated photovoltage does not require an externally applied bias, allowing zero dark current operation and direct voltage generation46. These properties are very appealing in terms of noise and power consumption, as PTE allows direct connection between the graphene photodetector and the read-out electronics without TIAs15 or allowing the use of a voltage amplifier. This is a potential breakthrough for this technology as the scalability of TIAs towards high frequencies (>50 GHz) is challenging, because of intrinsic design trade-offs48. In fact, the bandwidth of a TIA is inversely proportional to the feedback resistance, which sets the gain of the TIA. Increasing the bandwidth comes then in a tradeoff with the gain which should be high enough to amplify the signal and reduce the input referred noise current38. For these reasons the scalability of TIA’s towards high bandwidths is challenging. In fact, only a few >50 Gbit s−1 capable direct detection optical receivers or transimpedance amplifiers have been demonstrated to date13. In the case of our PTE 50 Ω-matched voltage photodetector, a linear low noise wide-bandwidth preamplifier can be used which is a technology already commercially available up to 66 GHz analog bandwidth.Most of the devices demonstrated so far are based on the PB and PC effects, showing good current responsivity up to 0.5 AW−153. These devices are based on the enhancement of the gradient of HC’s temperature through the improvement of the optical absorption by means of photonic structures confining the optical field in ~100 nm gaps53 or by exploiting the resonance of a microring resonator50. Despite the remarkable voltage responsivity53, detection of an optical data transmission using PTE-based graphene photodetectors operating in unbiased condition has not been demonstrated yet because of the high impedance of the devices. The optimization of the photovoltage signal in a PTE detector requires setting the detector at an operating condition near the charge neutrality point (CNP), i.e., where the conductivity of graphene is lowest. For this reason, typical PTE photodetectors exhibit output resistance from several hundreds to thousands of Ohms53, i.e., too high for proper matching to the typical 50 Ω impedance of the test instruments.Waveguide integrated graphene detectors based on PTE effect have been reported in recent years showing voltage responsivity in the range 3.5–28 V W−1 and a 3 dB bandwidth of 70 GHz, limited only by the instrumentation, showing no roll off in the measured range. We optimized the design of the PTE detector to match 50 Ω resistance to be suitable for data communication system tests. We demonstrate the detection of high baud rate optical data stream, in absence of dark current, by testing our device up to 105 GBaud Non-Return-to-Zero (NRZ) On-Off-Keying (OOK) and 60 GBaud 4-level-Pulse-Amplitude-Modulation (PAM4) for a net bit rate of 120 Gb s−1.Here we report on a PTE graphene photodetector integrated on a Si photonic waveguide having a voltage responsivity of about 3.5 V W−1 with a NRZ optical whereas in this work the detected NRZ signal was at 105 Gb s−1 and 120 Gb s−1 with PAM4 modulation format. Moreover the present data rate measurements could be extended to higher speed because a direct measurement of the graphene photodetector bandwidth showed a value of at least 128 GHz32 and, from another experimental estimation greater than 270 GHz30. These values indicate the potentiality of graphene in Si Photonics to scale beyond the limits of Ge detectors.The relevance of this demonstration is that graphene is a material that can be easily integrated on Si Photonics waveguide and it has the advantage with respect to Ge used for Si Photonics detectors, to scale in speed. In fact the highest data rate measured with a Ge detector in a Si photonics waveguide is 90 Gb s55  using poly-vinyl alcohol (PVA) as gate dielectric. The use of PVA allowed to preserve the good quality of graphene after polymer deposition but, at the same time, posed severe limitations: large hysteresis of graphene field effect curves56, contact resistance larger than 5000 Ω µm, and lithographic limitations as discussed in ref. 54. In this work, we moved to the SOI platform to exploit the steeper mode profile of the Si waveguides, which is due to the higher index contrast with respect to SiN. The steeper mode profile corresponds to a steeper profile of the temperature of the hot electrons, i.e., higher derivative and by consequence higher responsivity , which is an important parameter in order to match the 50 Ω impedance target.In refs. tox = 100 nm thick SiN layer  separated by a 150 nm large gap , have been reported59, while high quality exfoliated graphene on hexagonal boron nitride (hBN) substrate  has been demonstrated to exhibit S = 183 µV K−160. In this work, we used a CVD grown single crystal graphene with mobility as high as 130,000 cm2 V−1 s−1 at room temperature when transferred on hBN substrates62. A single crystal graphene channel is important not only for the high Seebeck coefficient, but also for the absence of grain boundaries that may be responsible for non-uniform control of the Seebeck coefficient along the graphene channel63.The photodetector has been integrated on top of a transverse electric (TE) silicon on insulator (SOI) waveguide designed for single mode operation at 1550 nm wavelength, with core cross section 480 nm × 220 nm Fig. . The topyer Fig. . The phoh W Fig. . The gene 2 Fig. , \documeRch) and the contact resistance (Rc)  as64:The device geometry shown in Fig. 46 to the case of a waveguide integrated photodetector . We simulated the DC behavior by setting µc = ±130 meV, corresponding to the maximum (positive) Seebeck coefficient on one side of the junction and to the minimum (negative) on the other side, in order to simulate the maximum voltage responsivity RV. Then we swept the channel dimensions L and W to study how they affect the maximum RV. In particular, the channel length L has a minimum impact on the generated photovoltage, as long as it is larger than the optical mode width in the transverse direction . The voltage responsivity RV decreases with the device width W, reaching half of its maximum at about W = 100 μm , causing a worse impedance matching resulting in a lower maximum power transfer (PLMAX ≈ −7 dB). Figure VG1 and VG2 (with source drain voltage VSD = 0 V), for the optimum design (L = 1.5 μm). The responsivity map shows the expected PTE six-fold pattern with an absolute maximum of ~10 V W−1 in the np and pn regions, for effective gate voltages VG1 − VCNP = −5V, VG2 − VCNP = 5 V (np region), and VG1 − VCNP = 5 V, VG2 − VCNP = −5V (pn region), respectively.In order to find the maximum of the photovoltage, we calculated the Seebeck coefficient of the device as a function of the gate voltage, i.e., chemical potential µc Fig.   and Gold (Au) was used to realize the source and drain metal contacts. Then, we transferred single-layer of hBN to protect the first layer graphene from the subsequent plasma-enhanced chemical vapor deposition (PECVD) of 100 nm of SiN used as gate dielectric. The second graphene layer was grown, transferred, and patterned using the same procedures utilized for the first layer. Top gate contacts were deposited using the same process as for the first graphene channel. We used Raman spectroscopy65 to characterize the two graphene crystals (see “Methods” section).We fabricated the device on a standard SOI platform with 220 nm thick Si overlayer and 2 μm thick buried oxide (BOX) (see “Methods” section). We used high quality single crystal graphene grown by chemical vapor deposition (CVD) and transferred on the Si waveguides by a semi-dry transfer technique demonstrated previouslyWe have experimentally characterized the static behavior of the PTE photodetector by mapping the photovoltage Fig.  and the 46. We show a photovoltage map having a maximum absolute value of about 6 mV for an optical input power at the detector equal to 1.65 mW (see Methods), which results in a voltage responsivity of about 3.5 V W−1 for VG1 = −1 V and VG2 = −8 V. The asymmetric photovoltage map may be explained by an asymmetry in the energy dependence of the carrier relaxation time in graphene between the n-type and p-type transport60. This behavior leads to an asymmetric Seebeck coefficient profile60 with respect to the charge neutrality point. The device resistance in proximity of the maximum responsivity is about 90 Ω, which is higher than the designed 50 Ω. The difference can be ascribed to deviations in the sheet and contact resistances of the fabricated device with respect to the design. We measured the linearity of the photovoltage as a function of the input optical power . This is the main difference with respect to the previously reported process developed for the fabrication of graphene modulators23, for which a SiN thickness of ~20 nm has been used between the two graphene layers. Although the first graphene layer  is protected by hBN to preserve the material quality, the process needs further improvements. An improved encapsulation66 would give results closer to what is predicted by our simulation . PTE operation does not require an applied voltage between the source and drain electrode (bias-free). We used a bias-tee to monitor the DC component of the photovoltage and to optimize the responsivity (see “Methods” section). We found the maximum responsivity (~3 V W−1) for gate voltages close to the ones of the maximum RV in the DC map, i.e., VG1 = −1 V and VG2 = −8 V.Although the device resistance was larger than the designed 50 Ω, we used the fabricated PTE photodetector to demonstrate the detection of high baud rate optical data streams. In a first set of experiments, we used the device to detect a Non-Return-to-Zero (NRZ) On-off-Keying (OOK) optically modulated signal at 28 Gb s−11 has been obtained for an input optical power of 3.5 dBm in back-to-back configuration, i.e., by connecting through a short fiber (few meters) the detector to the transmitter.A 50 Ω matched commercial RF amplifier with 23 dB gain and 35 GHz bandwidth has been used to amplify the electrical signal generated by the photodetector. Figure 3 Mach Zehnder modulator (MZM) used to modulate the optical CW signal (see “Methods” section). After back-to-back transmission the output voltage of the detector is amplified using a commercial amplifier with 22 dB gain and 65 GHz bandwidth. A real time oscilloscope and offline digital signal processing (DSP) is used for data acquisition, signal recovery and performance assessment. A block diagram of the setup is shown in Fig. In order to test our graphene detector at higher baud rates, we performed a second set of experiments involving a digital-to-analog converter (DAC) based optical transmitter with digital pre-emphasis. This is used to compensate for DAC and driver losses and for the limited bandwidth of the LiNbOWe tested our device at 60 GBaud using an NRZ OOK and a four level Pulse Amplitude Modulation (PAM4) format, and at 105 GBaud NRZ OOK. The collected eye diagrams and the corresponding histograms of the signal amplitude at the optimum sampling point are shown in Fig. −5 (NRZ) and 1.1 × 10−2 (PAM4). In order to show the high bandwidth of the device, we repeated the experiment up to 105 GBaud NRZ data transmission. The collected eye diagram  nucleation seeds the Cu foils and patterned by optical lithography. Regular arrays of graphene crystals were grown at 1060 °C with background pressure of 25 mbar using a 4″ BM Pro cold-wall reactor. Sample enclosure and Argon (Ar) annealing were used to control the nucleation density62. After growth, a PMMA layer was spin-coated on the Cu foil and an adhesive frame was attached to the perimeter of the sample. Electrochemical delamination of the graphene crystals was used to separate graphene from the Cu growth substrate by applying a voltage of −2.4 V with respect to a Cu counter-electrode in a 1 M NaOH solution. The delaminated graphene array on the PMMA membrane was thoroughly rinsed in deionized water. We then aligned the array precisely to the target waveguides using a micrometric 4-axis stage and laminated it at 90 °C. The sample was heated at 105 °C for 5 min to improve the adhesion. The PMMA support was then removed in acetone. EBL and reactive ion etching (RIE)  were used to pattern graphene by using PMMA as an etch mask. After the transfer and patterning of the first graphene layer, metal has been thermally evaporated to realize top contacts. We used a stack 7 nm of Ni and 60 nm of Au, followed by lift-off in acetone. The fabricated graphene channel was next coated with a protective layer of a commercially available large-area polycrystalline single-layer hBN provided by Graphene Laboratories Inc. hBN was used to provide protection to the first layer graphene with respect to the plasma used during the subsequent PECVD (350 °C) of the 100 nm SiN dielectric film. The second graphene layer used as gates was grown, transferred and patterned with the same process described for the first layer. Finally, metal contacts to the graphene gates have been realized with the same thermal evaporation of Ni and Au.We used electron beam lithography (EBL) to realize single mode transverse electric (TE) polarized Si photonic waveguides with cross section 480 × 220 nm on a standard SOI substrate with 220 nm thick Si overlayer and 2 μm thick BOX. The waveguide is provided with single polarization grating couplers designed to couple the light to the fundamental TE mode of the Si waveguide. The waveguides were then covered with a with a thin layer of tetraethyl orthosilicate (TEOS) and a thick boron-phosphorus TEOS (BPTEOS) cladding which was next thinned down to a final thickness of ~25 nm on top of the waveguide. Graphene was grown on copper (Cu) foils by deterministic seeded growth by chemical vapor deposition (CVD)−1, showing a low level of sub-µm strain fluctuations (and thus relatively high carrier mobility)67, comparable to exfoliated graphene on SiO2. Due to subsequent hBN transfer and SiN deposition an increase of the FWHM(2D) peak is reported, obtaining ∼25.5 and ∼32.5 cm−1, respectively, indicating an increase in strain fluctuations and thus lower carrier mobility.Raman spectroscopy has been used to characterize the quality of the SLGs used for photodetectors fabrication. All the Raman spectra have been collected in a Renishaw InVia spectrometer, equipped with a 532 nm excitation laser, at laser power ~1 mW and acquisition time of 4 s. The measurements have been performed for each fabrication step. Starting from pure transferred graphene, the Raman spectra has a 2D peak with a single Lorentzian shape and FWHM(2D) ∼25 cmStatic characterization of the graphene photodetector has been performed by using two electrical source-meters: the first was used to sweep the gate voltages with two independent channels, the second was used to set an open circuit (zero current) between source and drain and to read the generated photovoltage. A ground-signal (GS) probe was used to probe the source and drain, while DC needle probes were used to contact the gates. A CW laser source was amplified by an Erbium-doped fiber amplifier (EDFA) and coupled to the chip with a single mode optical fiber coupled to the input grating coupler. A fiber-based polarization controller was used to match the required polarization at the input grating coupler. After the input grating coupler, we used an integrated 3 dB splitter: one output branch of the splitter was coupled to the PTE photodetector, while the other branch was used to monitor the optical power through an output grating coupler. After the PTE photodetector, another grating coupler was used to monitor the optical power at the device output. In this way we could perform a precise characterization of the insertion loss of the device and properly evaluate the optical power at the device input. We estimated a total insertion loss of −13 dB due to the grating coupler efficiency (−5 dB), the 3 dB splitter (−3 dB) and propagation loss in the access waveguide (−5 dB). This last is due to particle  deposition on the access waveguide which is not protected with cladding. Optical power dependent measurements were done by using a fiber-based variable optical attenuator (VOA) after the EDFA.−1. A LiNbO3 MZM having 30 GHz bandwidth was used to modulate the optical signal. A variable optical attenuator (VOA) was used to perform the BER measurements as a function of the input optical power. A 50 Ω matched commercial RF amplifier with 23 dB gain and 35 GHz bandwidth was used to bring the electrically generated signal to a level readable by a digital sampling oscilloscope (DSO) and by the BER tester.The first set of measurements was performed by using a commercial pattern generator and BER tester at 28 Gb sThe chip level Graphene photodetector was interconnected on a probe station with the same fiber coupling scheme described above. For RF interconnection we used a 67 ground-signal (GS) probe to access the electrical signal generated by the photodetector. A 67 GHz bandwidth bias-tee was used to impose zero DC current to the device.We used the same MZM of the previous setup for the measurement of the frequency response. Port A of the VNA was used to drive the MZM and the second port to measure the scattering parameter S21 at the output of the graphene photodetector. We used a commercial 70 GHz bandwidth photodetector to measure the response of the setup, i.e., modulator, cables, probes, and connectors. The electrical amplifier was not used for the frequency response measurement.−1 DAC to generate the PAM data. Pre-calculated data were sent out periodically. In the transmitter digital signal processor, we applied raised cosine pulse shaping and in addition we compensated for the DAC, driver amplifier and modulator low pass characteristics. The electrical signal is modulated onto a 1550 nm optical carrier supplied by an external cavity laser, the modulator was biased at quadrature. The optical signal was amplified using an EDFA before launching onto the photodetector. The electrical response of the device is amplified using a 65 GHz bandwidth amplifier having 22 dB gain. Next, we digitized the data in a real time oscilloscope at 33 GHz bandwidth and stored the data for subsequent digital signal processing (DSP). The offline DSP incorporates resampling to 2 sample/symbol to simplify filter implementation. Next, we applied the channel compensation using a linear feed forward equalizer, where the filter taps where adapted respectively. Finally, we assessed the performance by counting the bit errors to determine the bit error ratio (BER) as well as the signal to noise ratio (SNR).The second set of measurements was performed at higher speed. In the transmitter we used an 88 GSa s−1 DAC and generated NRZ data at 105 GBaud. The data where amplified in a 65 GHz driver and modulated using LiNbO3 modulator. In the receiver we digitized the data at 256 GSa s−1 and 80 GHz bandwidth. Further details were identical to the second experiment.In a third experiment we further increased the speed by replacing the DAC and ADC. In the transmitter we applied a 120 GSa sSupplementary Information


Due to the presence of a monovacancy defect on the surface, the frictional forces were significantly enhanced. The effects of the PT model parameters on the frictional properties of monovacancy-defective graphene and SLMoS2 were analyzed, and it showed that the spring constant of the pulling spring xc is the most influential parameter on the stick–slip motion in the vicinity of the vacancy defect. Besides, monovacancy-defective SLMoS2 is found to be more sensitive to the stick–slip motion at the vacancy defect site than monovacancy-defective graphene, which can be attributed to the complicated three-layer-sandwiched atomic structure of SLMoS2. The result suggests that the soft tip with a small spring constant can be an ideal candidate for the observation of stick–slip behaviors of the monovacancy-defective surface. This study can fill the gap in atomic-scale friction experiments and molecular dynamics simulations of 2D materials with vacancy-related defects.Using numerical simulations, we study the atomic-scale frictional behaviors of monovacancy-defective graphene and single-layer molybdenum-disulfide (SLMoS Atomic-scale friction has been at the forefront of scientific interest over the decades. Generally, the study on the friction at atomic-scale is significant because it can result in a fundamental understanding of how friction happens as well as to facilitate the development of nanomechanical components ,2,3. WitAs one of the most remarkable discoveries in nano-tribology, the atomic-scale stick–slip phenomenon appears in the time domain as a series of saw-tooth signals, and its period usually corresponds to the unit cell of the surface potential ,12. This2), are ideal candidates suited for atomic-scale frictional studies because these materials are air-stable, chemically inert [2 [2 have focused on atomically flat surfaces [Atomically-thin laminar two-dimensional (2D) materials, such as graphene and single-layer molybdenum-disulfide  caussurfaces  and 14.8surfaces ). Besidesurfaces ,34.2. A modified interaction potential considering the Schwoebel–Ehrlich barrier is developed for the tip-defective surface interaction potential of the PT model. To study the mechanisms that control the frictional characteristics of the graphene and SLMoS2 with vacancy defects, we changed the effective masse of the system, the damping of the system, the sliding velocity of the tip, and the spring constant of the pulling spring to examine how the atomic-scale frictional behaviors depend on these variables. Ours is the first study revealing the influences of the classical PT model parameters on the atomic-scale frictional properties of a monovacancy-defective surface, and this work can make up for the deficiency of the LFM experiments and MD simulations when studying the atomic-scale frictional behaviors of 2D materials with vacancy-related defects.In this work, we employ a novel numerical simulation method to explore the atomic-scale frictional properties of the monovacancy-defective graphene and SLMoS2 consists of a 2D hexagonal honeycomb lattice where the Mo layer is covalently sandwiched between the bottom S layer and the top S layer. The vertical distance between two S layers of SLMoS2 is approximately 3.24 Å. The atomistic models of monovacancy-defective graphene and SLMoS2 are achieved by constructing a defect-free monolayer film first and then introducing the monovacancy defect in the center of the surface/top layer, as shown in the inserts in 2. The sliding was applied by moving the tip along the zigzag (ZZ) on the center line of the monovacancy-defective graphene and SLMoS2. The areas of the graphene and SLMoS2 film were 76.26 × 62.48 Å2 and 166.23 × 142.59 Å2 in the X–Y plane, respectively. The single-atom tip was generated for the atomic-scale friction according to the PT model, which consisted of a single carbon atom and was set as a rigid body in order to avoid the mass loss caused by the tip wear during the atomic-scale friction process. The constant-force mode is applied in the model and the loading force on the tip is kept at 2.5 nN. The schematic diagrams of the atomic-scale friction of monovacancy-defective graphene and SLMoS2 are shown in Graphene consists of an isotropic hexagonal honeycomb lattice of carbon atoms. SLMoSxc and yc represent the spring constants of the pulling spring, xm and ym represent the effective masses of the system, tx and ty represent the actual positions of the tip, Mx = My = mtV represent the equilibrium positions of the tip without potential, mV represents the sliding velocity of the tip, Vint  represents the tip–surface interaction potential, xγ and yγ represent the damping of the system. The frictional forces xF = xc (Mx − tx) and yF = yc (My − ty) of the PT model are composed of a dissipative part and a conservative part, which are given by the damping term and the tip–surface interaction potential, respectively [In the atomic-scale friction process, stick–slip behaviors can be explained by the classical PT model, which simplifies the single-asperity friction into one point-mass (tip) pulled along a corrugated potential by a driving support (spring) . The claectively . Theoretectively . In the intV y, which can be described as0V represents the initial value of tip-sample interaction, xa and ya represent the sample’s lattice constants in the ZZ and AC orientation, respectively. In the ZZ orientation, xa is 2.46 and 3.16 Å for graphene and SLMoS2, respectively.The tip–surface interaction potential of the classical PT model in Equation (1) is governed by the corrugated potential VLJ, which has been used to accurately describe the frictional properties at atomic-scale steps [2. The VLJ can be described as follows:ir represents the distance between the ith surface atom and the tip, r0 and E0 represent the equilibrium distance and the binding energy, respectively.In order to quantify the tip–surface interaction potential, the Lennard–Jones (LJ) potential le steps ,34, is tVlong are varying, which means a second contribution to the tip–surface interaction potential should be considered. A modified interaction potential Vtotal containing the periodic interaction Vint  between the tip and surface as well as the sharply increasing potential barrier at the vacancy defect site simulating the long-range interaction potential Vlong is constructed to reflect the tip–surface interaction of the defective graphene and SLMoS2 with monovacancy defects, which is shown as follows:Vlong can be described by the model [Vlong is shown as follows:E represents a constant of the order of an electronvolt, b1 represents the effective barrier width at the vacancy defect site, b2, c, and d are the constants representing a recovery of the potential away from the vacancy defect.In the presence of the vacancy defects, the surface state is similar to that of the atomic-scale surface steps. According to previous LFM studies on the monovacancy-defective graphene ,30 and the model ,37,38 baxF in the PT model, we develop the modified interaction potential Vtotal by fitting the LJ potential curve and set it as the approximate tip–surface interaction potential of the monovacancy-defective graphene and SLMoS2. Relevant parameters for the LJ potential VLJ and the long-range interaction Vlong are shown in In order to obtain the numerical description of the frictional force VLJ) and then develop the modified interaction potential  through fitting the LJ potential (VLJ). By introducing the potential Vtota into Equation (1), we can calculate the path of the tip on the sample surface and obtain the frictional forces. Finally, we discuss the effects of the parameters  of the classical PT model on the frictional force and the stick-slip behaviors of monovacancy-defective graphene and SLMoS2.We first calculate the tip–surface interaction potential by LJ potential 1/2 ≈ 10−3 N·s/m. Owing to the presence of the monovacancy defect, the changes in the tip–surface potential and frictional force of the monovacancy-defective graphene and SLMoS2 can be clearly observed. There are the large positive tip–surface potential and frictional force occurring when the tip approaches the vacancy, indicating the attraction from the vacancy. After passing the vacancy, the tip feels a large attractive force from the vacancy again. The enhanced frictional force in the vicinity of the vacancy defect is in agreement with that in the previous works about the monovacancy-defective graphene [2 [graphene ,30, and graphene ,32, whicgraphene ,35,36,38phene [2 .2, we plot the position of the single-atom tip versus the sliding distance curves, as illustrated in 2. It can be attributed to the difference in the curvature of the tip–surface interaction V″  at the vacancy defect site of defective graphene and SLMoS2 (V″carbon = 0.91 for the monovacancy-defective graphene and V″SLMoS2 = 17.18 for the monovacancy-defective SLMoS2) because the stick–slip phenomenon occurs on condition that the elastic constant xc of the pulling spring  should be less than or equal to the curvature of the tip–surface interaction potential V″ [In order to explore the stick–slip motions during the frictional process of the monovacancy-defective graphene and SLMoSntial V″ . Besidesntial V″ .xF vs. the sliding distance D for four effective masses xm of the system  are shown in cx, Vm, and xγ are set to 10 N/m, 40 nm/s, and 10−3 N·s/m, respectively. It is seen that all the xF-D curves of the monovacancy-defective graphene are almost the same, as shown in 2, however, the amplitude of the minimum frictional force xFmin increases with xm , and the other frictional forces including the maximum frictional force xFmax and the periodic frictional forces  remain basically unchanged, as shown in The relations of the frictional force P vs. the sliding distance D for the above four effective masses xm of the system are shown in P vs. D curves of the monovacancy-defective graphene and SLMoS2 with different xm, which means the stick–slip motion in the vicinity of the vacancy defect is nearly independent of the effective masses xm of the system.The relations of the position of the single-atom tip xF vs. the sliding distance D for four different dampings xγ of the system  are shown in xc, Vm, and xm are set to 10 N/m, 40 nm/s, and 10−8 kg, respectively. The results show that the frictional forces xF of the monovacancy-defective graphene and SLMoS2 increase with the damping xγ. It can be explained by Equation (1) that the frictional force xF = xc (Mx − tx) = xγ, which is in agreement with the definition of the frictional force in the PT model [2 increase with decreasing xγ, as shown in xγ is in accord with the physical meaning of the damping term in the PT model, namely, the term considering the mechanisms of the energy dissipation in atomic-scale friction [The relations of the frictional force PT model . Howeverfriction ,16.P vs. the sliding distance D for the above four dampings xγ of the system are shown in P vs. D curves of the monovacancy-defective graphene with different xγ are coincident, and this trend is similar to that of the monovacancy-defective SLMoS2 except for a little shift in the stick–slip regime at the defect position for the case of xγ = 10−2 N·s/m. It indicates that the damping xγ of the system has little effect on the stick–slip motions in the vicinity of the vacancy defect.The relations of the position of the single-atom tip xF versus the sliding distance for five different sliding velocities Vm . The xγ, x,c and xm are set to 10−3 N·s/m, 10 N/m, and 10−8 kg, respectively. It is seen that the frictional forces of the monovacancy-defective graphene and SLMoS2 increase with the mV. The result can be explained by Equation (1) that the atomic-scale frictional force xF = xc (Mx − xt) = xc (Vmt − xt) [Vm, which has been demonstrated in previous work [2 almost keep constant at different sliding velocities Vm.mt − xt)  is positous work . BesidesP vs. the sliding distance D for the above four sliding velocities Vm are shown in xm and xγ, the variations in the P vs. D curves of the monovacancy-defective graphene and SLMoS2 with different Vm are extremely small and can be neglected, which indicates that the stick–slip motion in the vicinity of the vacancy defect is approximately independent of the sliding velocity Vm. The result seems to contradict previous studies suggesting that stick–slip motions can also be suppressed or even ruined by thermally activated jumps when the tip scans at a low velocity [The relations of the position of the single-atom tip velocity ,42. Nevexc  of the monovacancy-defective graphene and SLMoS2 in this work , the spring constant of the pulling spring xc has the most remarkable impact on the stick–slip motion in the vicinity of the vacancy defect, which suggests that the soft tip with small spring constant can be suitable for the observation of the stick–slip motions in the atomic-scale friction experiments of the monovacancy-defective 2D materials. Otherwise, the stiff tip with larger spring constant can be suitable for the observation of the low-dissipative motions or the superlubricity phenomena in the atomic-scale friction experiments of the monovacancy-defective 2D materials.The relations of the position of the single-atom tip t SLMoS2  can be c2 based on a classical PT model with a modified interaction potential considering the Schwoebel–Ehrlich barrier. It was found that the frictional forces are significantly enhanced due to the presence of a monovacancy defect on the surface. The effects of the PT model parameters  on the frictional properties of monovacancy-defective graphene and SLMoS2 were analyzed. It revealed that the spring constant of the pulling spring xc has the most remarkable impact on the stick–slip motion in the vicinity of the vacancy defect compared with other parameters. In addition, it is more sensitive to the stick–slip motion at the vacancy defect site for the monovacancy-defective SLMoS2 than that for the monovacancy-defective graphene, which can be due to the complicated three-layer-sandwiched atomic structure of SLMoS2. This study suggests that a soft tip with small spring constant can be an ideal candicate for the LFM experiment of stick–slip behaviors of the monovacancy-defective surface, and it can provide valuable complementary information for atomic-scale friction experiments and MD simulations of 2D materials with vacancy-related defects.In this work, we employed a numerical simulation method to explore the atomic-scale friction of monovacancy-defective 2D graphene and SLMoS