Fundamental principles for designing high-performance thermally conductive graphene-based polymer composites are reviewed in detail.The reasoning behind using the preconstructed graphene 3D networks for fabricating thermally conductive composites and recent progress are discussed in-depth.Insight into the existing bottlenecks and opportunities in developing preconstructed 3D networks of graphene and their thermally conductive composites is also presented. Electronic devices generate heat during operation and require efficient thermal management to extend the lifetime and prevent performance degradation. Featured by its exceptional thermal conductivity, graphene is an ideal functional filler for fabricating thermally conductive polymer composites to provide efficient thermal management. Extensive studies have been focusing on constructing graphene networks in polymer composites to achieve high thermal conductivities. Compared with conventional composite fabrications by directly mixing graphene with polymers, preconstruction of three-dimensional graphene networks followed by backfilling polymers represents a promising way to produce composites with higher performances, enabling high manufacturing flexibility and controllability. In this review, we first summarize the factors that affect thermal conductivity of graphene composites and strategies for fabricating highly thermally conductive graphene/polymer composites. Subsequently, we give the reasoning behind using preconstructed three-dimensional graphene networks for fabricating thermally conductive polymer composites and highlight their potential applications. Finally, our insight into the existing bottlenecks and opportunities is provided for developing preconstructed porous architectures of graphene and their thermally conductive composites. Among all the thermally conductive materials, polymer composites have significant advantages because of their lightweight, easy processability, low cost, and superb stability. Most polymers are typically insulative with extremely low thermal conductivity of 0.1–0.3 W m−1 K−1 , graphen−1 K−1 , 5. The −1 K−1 , 7, comm−1 K−1 , 9, and −1 K−1 –13.Typically, the thermal conduction and other properties  of graphene/polymer composites are largely determined by the dispersion and distribution of graphene sheets in the polymer matrix. To achieve efficient thermal transport in polymer composites, highly interconnected graphene networks should be formed. Conventional methods to fabricate thermally conductive graphene/polymer composites rely mainly on directly mixing the graphene with polymers by in situ polymerization , 15, solRecently, the preconstruction of three-dimensional (3D) continuous networks of graphene sheets followed by backfilling polymers has been proved to be a very effective method to fabricate composites with improved performances. The preformed conducting networks can be well maintained during subsequent compounding with polymers, avoiding aggregation of graphene sheets in polymer matrices and hence enabling high thermal conductivities at relatively low graphene loadings while preventing mechanical performance degradation of polymers , 21. MorAlthough great progress has been made, hitherto, the evolution of using preconstructed 3D networks of graphene sheets for fabricating thermally conductive polymer composites has not been discussed in depth and recent progress has also not been well recognized and analyzed. To the best of our knowledge, there remains a lack of comprehensive summaries and guidance on how preconstructed graphene 3D conducting networks can be designed for functionalizing polymers facing thermal management applications. To this end, the present review aims to provide a focused and critical review on thermally conductive graphene/polymer composites and highlight the recent advancements in designing novel composites with preconstructed graphene networks as fillers. The characteristics of this review include: (1) the key factors that affect the thermal conductivity of graphene/polymer composites and strategies for achieving high thermally conductive properties are reviewed in detail; (2) the reasoning behind using the preconstructed 3D graphene networks for fabricating thermally conductive polymer composites is discussed in-depth; (3) the potential applications toward thermal managements of the graphene/polymer composites, such as thermal interface materials (TIMs), phase change materials (PCMs), photothermal conversion materials, and thermal switches, are demonstrated; and (4) the challenges and perspectives regarding the development of preconstructed graphene 3D networks and their thermally conductive polymer composites are also presented.Focusing on polymer composites with graphene as fillers, the main factors that influence the thermal conductivities include: 1) intrinsic properties of graphene in terms of sheet quality, lateral size, thickness (layer number), aspect ratio, and interfacial compatibility with polymer matrix; (2) dispersion and distribution of the graphene in polymer composites; and (3) graphene loading level  of graphene sheets also significantly affect thermal conductivity of the as-formed networks. Theoretically, increasing lateral size is beneficial for enhancing thermal conductivity of graphene sheets and hence performances of composites since the sheet edge can scatter phonons Fig.  37, 42,,42, 43. graphene .Fig. 3ScCompared with high-quality graphene sheets, multilayer graphene nanoplatelet (GNP) with large lateral size and high aspect ratio is a cost-effective alternative for fabricating thermally conductive polymer composites . In the −1 K−1 at a graphene loading of 10 wt% [−1 K−1 of neat PA6 [For graphene/polymer composites, the large thermal resistance caused by phonon scattering at the interface between graphene sheets and matrix would hinder the efficient heat transfer seriously . To reduf 10 wt% . Covalenneat PA6 . It shouneat PA6 .Fig. 4a −1 K−1 along the vertical direction and 0.63 W m−1 K−1 along the horizontal direction at an ultralow graphene content of 0.92 vol%. Evidently, graphene sheets can largely overlap with each other to provide highly continuous conducting pathways along the vertical direction and the thermally insulating epoxy resin that fills in the oriented graphene channels can effectively suppress the heat transfer along the horizontal direction, thus enabling the unique anisotropic properties of the composite [Directional thermally conductive networks, which can provide highly effective heat transfer pathways and lead to reduced percolation threshold along specific directions, can be formed by controlling the alignment/orientation of graphene sheets in the composites. Various methods have been reported to tune the aligning behavior of graphene in polymer matrix with the aid of external forces, electric fields, and magnetic fields. For example, the controllable alignment of graphene fillers in polymers can be achieved by modifying the graphene with magnetic particles and adjusting their orientation by an external magnetic field during the processing process, and the thermal conductivity of the graphene/epoxy composite made by this method is twice higher than that of the composite with randomly dispersed graphene sheets –59. Despomposite . Other eomposite , 62.−1 K−1 at a low graphene loading of 4.28 wt% [The thermal conductivities of graphene/polymer composites defer to the percolation theory, and the content of graphene is the decisive factor determining the thermal conductivity of polymer composites , 64. A h4.28 wt% . On the 4.28 wt% . Qi et a4.28 wt% .2) drying of their precursors including modified graphene suspension and RGO hydrogels. The insufficient interconnections between the graphene sheets in low-density graphene networks inevitably lead to large contact thermal resistance and low graphene concentration, limiting the enhancement in thermal conductivity of polymer composites [−1 K−1 at a graphene loading of 12 wt% [−1) followed by high-temperature annealing, by which a very high density of up to 100 mg cm−3 for the resulting GAs can be achieved [Typically, most reported preconstructed graphene networks are obtained by CVD synthesis and freeze-drying/supercritical carbon dioxide  (PCBT) composites by in situ ring-opening polymerization of cyclic butylene terephthalate with GNPs uniformly dispersed in the monomers . Compareπ–π interactions between graphene sheets are stronger than the interactions between graphene and polymers. To tackle this issue, various methods, such as adding surfactants/additives and modifying the surface of graphene sheets are developed. The addition of surfactants can lower the surface tension between the solid graphene sheets and polymer liquids, which is effective in promoting the dispersion of graphene sheets and suitable for many polymer systems. The additives that possess good compatibility with both graphene and polymer matrices can be added during the compounding process. Chen et al. reported that the presence of GO in graphene/PA6 composite can improve the dispersion of graphene in PA6 as the GO can simultaneously interact with graphene by π–π interactions and with PA6 by forming covalent bonds [The challenge in the process of dispersing graphene sheets in polymers by the above-mentioned methods is the easy aggregation of graphene sheets during the blending processes as the van der Waals forces and nt bonds . Surfacent bonds . For exant bonds . Howevernt bonds , 94.2O3 particles can reduce the aggregation of graphene in polylactic acid (PLA) and the contact thermal resistance at the interface of fillers, resulting in an enhanced thermal conductivity of the graphene/Al2O3/PLA composite [Alternatively, the addition of second thermally conductive fillers with specific configurations is also effective for improving thermal conductivity of graphene/polymer composites on the basis of the synergistic effect between different conductive fillers . For exaomposite . The synomposite . Adding omposite –103. Foromposite .In summary, in the above-mentioned methods to fabricate thermally conductive graphene/polymer composites, the aggregation of graphene sheets cannot be effectively avoided during direct blending/compounding processes, and thus the efficient thermal conducting networks can usually be formed at high graphene loadings, resulting in limited thermal conductivities and even degraded mechanical properties of the composites. Moreover, the conventional fabrication methods suffer from poor controllability of the filler distribution and configuration of conducting graphene network in polymers, resulting in composites with monotonous functions.Preconstruction of 3D graphene networks followed by backfilling of polymers can enable the formation of efficient thermal conduction pathways and the fine control of graphene dispersion in composites, representing an effective way to fully utilize graphene for functionalizing polymers Fig. . Because−1 K−1 (448% enhancement) at an ultralow GA loading of 0.50 wt% [Fabrication of 3D graphene networks by self-assembly relies on forming bonding, cross-linking, or physical interactions between the graphene precursors (mainly GO and RGO), through which a balance between the electrostatic repulsive forces and the bonding interaction is achieved, ensuring the integrity of the 3D interconnected networks while preventing the excessive aggregation of the graphene components , 123. Th0.50 wt% . Note th0.50 wt% –127.Fig.In the template method, isotropic graphene 3D networks are formed by growing/depositing graphene layers on the skeletons of porous templates via chemical vapor deposition (CVD) or impregnation with graphene dispersions, and the templates can be removed by post-treatments –142. Pop−1 K−1 along with outstanding shape stability [Growing graphene on the template via a CVD method can generate 3D networks composed of ultra-thin and high-quality graphene layers, which typically possesses better thermal conduction than the network formed with RGO. However, the challenge of this method lies in preventing the structure collapse during the template removing process because the as-formed graphene networks are typically very brittle . Great etability .Fig. 8Sc−1 K−1 at a graphene content of 6.8 wt%, which is 4473% higher than that of pure epoxy resin [−1 K−1 at a filler content of 4.89 wt% [Besides, graphene networks can be obtained by depositing graphene sheets on the skeleton of polymer sponge templates by vacuum-assisted impregnation, and the templates can be removed by pyrolysis. For example, Liu et al. immersed a PU foam into a dispersion of graphene, and the foam was then dried after suction filtration or centrifugation. The surface of the PU foam skeleton was covered by a continuous graphene layer, and a freestanding graphene 3D network was obtained after the pyrolysis of the PU foam. In the above-mentioned work, the as-fabricated epoxy composite exhibited a thermal conductivity of 8.04 W mxy resin . In anot4.89 wt% . In addi4.89 wt% . Meanwhi4.89 wt% . Althoug4.89 wt% , 152, fu4.89 wt% , 152.As a newly emerged manufacturing technology that promises high design freedom, 3D printing can be used to accurately produce objects with complex shapes/structures . The outDesigning of highly printable inks with appropriate rheological properties is the key to applying 3D printing technique for generating 3D graphene architectures. In addition, post-treatment protocols, such as drying and thermal annealing after printing, should be carefully designed to convert the 3D printed wet materials to freestanding structures. The post-treatments can also largely determine the quality  of the printed devices. Ma et al. designed an aqueous GO ink, which presents favorable 3D printability even at a low solid concentration without requiring additional additives or freeze operations. With this ink, 3D graphene networks with desired configurations were easily fabricated via 3D printing followed by freeze-drying, chemical reduction, and thermal annealing . Zhang eIn summary, preconstruction of isotropic graphene 3D networks followed by compounding with polymers is a simple and effective strategy to create thermally conductive composites, through which significant enhancement of thermal conductivity can be easily realized even with very low graphene loadings. However, the resulting composites generally exhibit isotropic heat conductance and monotonous conducting behaviors, which limit their potentials for advanced thermal management applications.The composites with anisotropic graphene networks can benefit from the anisotropic thermal conductivities of the conducting networks for enhancing heat transfer along with specific directions even at low graphene loadings. Due to the unique 2D layered structure and high intrinsic in-plane thermal conductivity of graphene sheets, their alignment can be controlled to form anisotropic graphene networks with high continuity along specific directions, providing highly efficient thermally conductive pathways , 163. CoCreating anisotropic graphene networks by self-assembly is a simple method that allows on-step synthesis of desirable structure without requiring complex processing procedures. However, it is quite challenging to control the alignment of graphene sheets during the assembly process, which requires rational compositional design of precursors. One of the most commonly used methods to achieve anisotropy of graphene structure is to form GO liquid crystals in precursor suspensions, and the orientation behavior of the graphene sheets in liquid crystals can be transferred to the ultimate macroscopic 3D network after the assembly process .According to Onsager’s theory, 2D sheets in dispersions can form liquid crystals once the concentration exceeds a critical value , 171. Co−1 K−1, which is nearly 3 times of the thermal conductivity perpendicular to the orientation direction of graphene sheets [−1 K−1 at an extremely low graphene loading of 0.32 vol% [The orientation of GO liquid crystals can be further tuned by creating shear flow during the processing processes. For example, in the filtration process of graphene dispersion, the orientation direction of graphene sheets is perpendicular to the direction of the liquid flow , 178, whe sheets . In anote sheets . Similare sheets , 183. So.32 vol% . Moreove.32 vol% –186.Directional freeze-casting is another simple yet effective method for fabricating graphene networks with orientated porous structures, which enables precise structural controllability, easy scalability, and versatility , 188. Th−1 K−1 at a graphene loading of 0.92 vol% [−1 K−1 at an ultralow graphene loading of 0.75 vol% [Using the directional freeze-casting method to construct anisotropic graphene structures has been widely demonstrated for fabricating high-performance thermally conductive materials in recent advancements. For example, Lian et al. fabricated an anisotropic GA with GO liquid crystal dispersion as the precursor. After backfilling with epoxy, the composite exhibited a through-plane thermal conductivity of 2.13 W m.92 vol% . It is w.92 vol% , 193. Fo.75 vol% .−1 K−1 at a low filler loading of 2.30 vol% [The most significant advantage of using the directional freeze-casting method to fabricate graphene 3D networks is its high controllability on the alignment of graphene sheets. Through rational design of the freeze-casting process, many novel graphene 3D structures can be easily formed –197. For.30 vol% .Fig. 11SIn addition to the layered structures, radially aligned structures of graphene networks can be created by a modified directional freeze-casting method, as schematically shown in Fig. Another advantage of the directional freeze-casting method is that the pore size, pore wall thickness, and layer spacing of the as-fabricated graphene networks can be tuned by adjusting the freezing parameters –205. For2 and Ni foams are commonly used anisotropic templates for materials that can be deposited by CVD method [2 template, which can be removed later by hydrofluoric acid (HF) solution [−1 K−1 at a filler loading of 8.3 wt% [−1 K−1 [The template method allows the materials to inherit the structure of the templates, and therefore, anisotropic graphene networks can be obtained by depositing graphene on the skeleton surface of the templates with an anisotropic porous structure Fig.  212, 21. SiO2 anD method . Anisotrsolution , 216. Sh 8.3 wt% . Some na 8.3 wt% –220. For 8.3 wt% , 222. Ot 8.3 wt% . Liu et  [−1 K−1 .Fig. 14S−1 K−1 at a graphene content of 12 wt% [−1 K−1 at the graphene loading of 4.5 wt% [−1 K−1 [The anisotropy of graphene networks can be realized by post-processing, such as stacking, compaction  and rollf 12 wt% . In anot 4.5 wt% . Dai et  [−1 K−1 . Rolling [−1 K−1 .Fig. 15TIn summary, designing anisotropic graphene conduction networks in composites can greatly take advantage of the intrinsic in-plane thermal conductivity of graphene sheets and enable highly efficient heat transfer along selected directions, which is very promising for thermal management applications. However, creating anisotropic graphene networks requires complicated synthesis processes, which might limit mass production. Thus, further efforts are still needed to explore more efficient and cost-effective ways, ensuring their future practical applications.Although pure graphene networks have great potentials in forming thermally conductive pathways for polymer composites, their low density and relatively weak sheet interconnections would inevitably hinder the further improvement in thermal conductivity of their polymer composites. Thus, functional additives, especially commercially available thermally conductive materials, such as GNPs , 77, 228−1 K−1 at the graphene content of 19.0 vol%, much higher than that of the composite fabricated with pristine GAs without the adding of GNPs [−1 K−1 [Commercial GNPs suffer from the poor processability and easy aggregation when serving as fillers. However, GNPs have higher thermal conductivities than the RGO sheets because of their low-defect feature. To improve the thermal conductivity of graphene networks and their polymer composites, GNPs can be added into the graphene networks to form 3D hybrid networks. The graphene network serves as not only a main thermally conductive network but also a supporting framework for accommodating the GNPs and preventing their aggregation, while the presence of the GNPs can prevent excessive shrinkage of the graphene network during the fabrication process, reflecting a favorable synergy effect . An et a of GNPs . Another [−1 K−1 .Fig. 16a−1 K−1 [BN nanoplatelets are also ideal fillers for fabricating thermally conductive polymer composites because of their 2D layered structure, excellent chemical stability, and extraordinary anisotropic thermal conductivity –240. Mea−1 K−1 . Shao et−1 K−1 . It has −1 K−1 , 246.Additionally, CNTs are 1D carbon nanomaterials with a hollow cylindrical fiber-like structure, performing excellent thermal conductivity and mechanical properties , 248. ThCellulose nanofibers (CNFs) are usually incorporated into the graphene networks to improve the connectivity between GNPs while strengthening the resulting graphene-functionalized PCMs –255. TheThermally conductive graphene/polymer composites are highly promising for applications where efficient heat dissipation and thermal management are needed , 264–266−1 K−1 at an extremely low graphene content of 1.11 vol%, showing a great potential as TIMs [TIMs are a kind of materials that are located in between two components to reduce thermal resistance between them for preventing overheating of the powerful devices by efficiently transferring heat from heat-producing devices  to heat-dissipating components . In addition to high thermal conductivity, an ideal TIM should also possess satisfactory mechanical properties and long-term stability, which can prevent performance failure during operation , 270. Ep as TIMs . Hou et  as TIMs . Liu et −1 K−1 for the 1-octadecanol to 9.50 W m−1 K−1 and the resultant composite has a high melting enthalpy of 196.2 J g−1 [PCM promises sustainable energy conversion and can provide useful thermal management by absorbing and releasing thermal energy during its phase changing process. An ideal PCM should have high thermal conductivity, high heat of fusion, high specific heat, proper density, high melting point, high shape stability, and long-term reliability during repeated cycling. However, most of conventional pristine PCMs  suffer from problems of low thermal conductivity and poor shape stability, which hinder the wide applications of these PCMs. Incorporating graphene sheets as the thermally conductive fillers into pristine PCMs is promising for enhancing their thermal conduction and comprehensive performances –274. The.2 J g−1 . Notably.2 J g−1 , 275–277−2 [−2, respectively [With the rapid industrial development, the energy crisis and related water pollution problems are becoming increasingly serious. Different from non-renewable fossil resources, solar energy is considered a kind of green energy resource. Obviously, efficient conversion of solar energy to usable thermal energies represents one of the most promising and sustainable routes to relieve energy crisis and environmental issues , 279. Be−2 . Liu et ectively .In addition to the above-mentioned applications, thermal switch is an emerging application of graphene composites, which provides dynamic thermal management to allow the devices to function well at dramatically varied conditions. A thermal switch can provide switchable regulation of the heat dissipation pathways via changing its thermally conducting properties. Thus, the materials for this application should be thermally conductive and their thermal conductivity should be sensitive to external stimuli . In addition, these materials are also required to have satisfactory mechanical properties and durability , 284. FoFrom the aspects of graphene networks, their thermal conduction is largely affected by the quality of the graphene building blocks. The most popular method to construct high-quality 3D graphene networks is using GO as the precursor for assembly followed by high-temperature annealing. The defect-free feature of thermally healed graphene can endow the 3D network with excellent thermal conductivity but would also lead to poor structural stability due to the poor interfacial interactions between the high-quality graphene sheets, which brings difficulty to subsequent compounding process, especially in mass production. Thus, scalable and efficient approaches to combine superb conductivities and good structural robustness into one high-quality graphene network are highly demanded.Regarding the design of anisotropic networks, various methods, e.g., ice templating method, has been proved to be effective. However, the long-range order and customizability of the as-obtained graphene network still needs to be improved. Thus, some efforts should be focused on optimizing the existing methods and understanding their fundamental principles and mechanisms for achieving better controllability.Although the preconstruction of 3D graphene networks can ensure the high continuity of the conductance pathways in polymer matrix, the interfacial thermal resistance between graphene and polymer is still a critical obstacle for further enhancement of thermal conductivity of the composites. More attention should be paid to this issue, making it possible to approach the upper limit of thermal conductivity of graphene-based polymer composites.Most previous efforts have been focused on improving thermal conductivity of materials. However, integrating more functions  into the graphene-based polymer composites might bring more opportunities for broadening their future applications. In addition, more investigation is needed to understand the roles of graphene-based polymer composites in practical applications for expanding their commercial potentials. At present, there is still a long way to go for scalable production and commercial application of polymer composites with preconstructed graphene conductance networks. However, the development of techniques for tuning the graphene dispersion behavior in polymer matrices will continue to support the design and preparation of next-generation functional composites for thermal management applications.In this review, we have discussed the recent progress in improving thermally conductive properties of graphene-functionalized polymer composites with a focus on preconstruction of 3D graphene conducting networks. Achieving high thermal conductivity for polymer composites relies on the formation of highly continuous and high-quality thermal conduction network in polymer matrices, which is the key to ensuring efficient heat transfer. Conventional processing methods, such as solution mixing and melt compounding, usually suffer from the aggregation of graphene sheets during the mixing/compounding processes, and thus effective thermal conduction networks can only be formed at high graphene loadings, which would result in limited thermal conductivities, high cost, and degraded mechanical properties of the composites. In comparison, preconstruction of 3D graphene networks followed by backfilling polymers/monomers provides a promising route to fabricate thermally conductive composites with improved performances. The preformed conductive networks can be well maintained during the mixing/compounding process without producing agglomeration of graphene sheets in polymer matrices, ensuring the high thermal conductivity of the as-fabricated composites at low filler loadings while avoiding performance degradation of polymer matrices. The thermally conductive behavior of the resultant composites can be modified according to practical application scenarios by configurational/microstructural designs of preconstructed 3D networks, such as designing anisotropic conductive networks for enabling directional conduction behavior, which provides unique flexibility and versatility for composite fabrication. Although significant progress has been achieved, many challenges remain and there is still much to be developed for controllable preconstruction of graphene networks and the fabrication of their composites.


Cutaneous sarcoidosis can manifest after doing a permanent makeup (PMU), such as tattooed eyebrows. A 41-year-old Chinese woman, with a tattoo in the eyebrows, developed yellow–brown plaques in her eyebrows for several months. A dermatopathological examination revealed non-caseating granulomas consistent with cutaneous sarcoidosis. For months, topical corticosteroids were applied, which showed little effect. Furthermore, a physical evaluation of the patient revealed no apparent involvement of other body organs except bilateral hilar lymphadenopathy with few diffuse reticulonodular opacities. On the basis of fully informed consent, the patient agreed to a 6-month initial follow-up to avoid unnecessary PMU. Sarcoidosis is an inflammatory granulomatous disease characterized by non-caseating epithelioid granulomas in multiple organs, for which the etiology and pathophysiology are unidentified. In roughly a quarter of cases, cutaneous sarcoidosis is the initial manifestation of the disease , 2. OverA 41-year-old Chinese woman presented to our clinics with a slowly enlarged rash on the bilateral eyebrows, which had developed for several months without itching or tenderness. The patient exhibited no other symptoms, such as coughing.On physical examination, extensive black–brown tattoos on both eyebrows were observed. There were grouped reddish and yellow–brown infiltrative papules, some of which coalesced into plaques scattered over the tattoo . There wThe patient disclosed that she had tattooed her eyebrows 3 months before the rash appeared. She was treated with topical clobetasol propionate cream for over 2 months, nevertheless, there was no notable improvement. She denied any history of trauma, sojourn, or contact with animals. Prior to her dermatology clinic visit, she had no other sarcoidosis-related signs or symptoms. No sarcoidosis-related family history was reported.The results of laboratory tests such as serum angiotensin-converting enzyme (ACE) levels and T-spot were within normal limits . EnhanceA biopsy of yellow–brown plaque within the eyebrow tattoo indicated non-caseating granulomas throughout the dermis consistent with a diagnosis of cutaneous sarcoidosis . GrocottTattoo-associated sarcoidosis was diagnosed based on the clinical manifestation of yellow–brown plaque and histopathological findings of non-caseating granulomas at the tattoo site. Lung involvement is considered stage I . Since tApproximately, 10–20% of the global population is tattooed . NotwithOur patient had an eyebrow tattoo with the purpose of seeking beauty and yet got the opposite result, and the treatment result was not satisfactory. We are aware that PMU may contain more complementary colors and shape alterations than conventional tattoos. Theoretically, repeated tattooing and reintroduction of foreign material into the skin may activate the immune system . CliniciThe original contributions presented in this study are included in the article/supplementary material, further inquiries can be directed to the corresponding author.Ethical review and approval was not required for the study on human participants in accordance with the local legislation and institutional requirements. The patients/participants provided their written informed consent to participate in this study. Written informed consent was obtained from the individual for the publication of any potentially identifiable images or data included in this article.SN: data collection, formal analysis, and writing—original draft. KL, CG, NY, ZC: writing—review and editing. ZW: conceptualization, resources, and writing—review and editing. All authors contributed to the article and approved the submitted version.


In this paper the extended method of lines (E-MoL) is proposed for the analysis of multilayer graphene-loaded three dimensional structures in cylindrical coordinates. Accordingly, the impedance and admittance matrices are defined as the ratios of the electric and magnetic fields at each plane of the stack. The impedance and admittance parameters are transformed from the input to the output of the structure through layers and interfaces, from which, the scattering parameters are extracted. It is assumed that there is an anisotropic graphene layer at the interface of two successive layers. The impedance and admittance transformations at the interfaces are extracted in the cylindrical coordinates. Then the impedance and admittance values at all planes of the stack and consequently, the scattering parameters of the whole structure are derived. To validate the presented method, two validation benchmarks are provided at the microwave frequency band. A circular waveguide and a coaxial cable loaded with graphene plates are analyzed and the results are compared with those of CST simulation software which show good accordance. It is observed that the E-MoL, as a semi-analytical semi-numerical method, is much more time-efficient than the CST software numerical procedure. This 2D material is a promising candidate in electronics and electromagnetics and has attracted the researchers’ attention all around the world in the recent years3. Nowadays, graphene sheets with dimensions up to 30 cm are fabricated, and this has led to the use of graphene in the new microwave and millimeter wave applications4. Graphene sheets have remarkable electric properties like controlling their surface conductivity through applying electromagnetic fields or DC voltages. This feature is used to design tunable electronic or electromagnetic devices6. New nano-sized electronic and electromagnetic components and devices such as antennas, flexible electronic devices, touch screens and high-speed transistors are examples of the states of the art in the graphene world. The unique properties of graphene are due to its gapless electronic band structure10.Graphene is a one-atom thick allotrope of carbon arranged in a hexagonal lattice with extraordinary properties11 per unit length equivalent circuits are proposed for the accurate characterization of propagation in different graphene-loaded waveguides. For that purpose, analytical expressions for the graphene conductivity as well as lumped circuit components are calculated through which the propagation of surface waves along spatial graphene waveguides is illustrated. The finite difference time domain (FDTD) method has the advantage of solving transient broadband problems in one simulation. In12, the FDTD method is exploited to investigate the electromagnetic interaction with graphene by treating it as a surface boundary condition and sampling the computational space. Recently, in13 the magnetized graphene is characterized by an anisotropic surface boundary condition using FDTD. Physically, the aim of the proposed method in13 is to incorporate magnetically-biased graphene formulation into electromagnetic wave scattering problems macroscopically by modeling the graphene with a conducting sheet. Li et al.14 introduce the discontinuous Galerkin time-domain (DGTD) method to characterize the transient response of the graphene from microwaves to terahertz frequencies. Having considered an infinite graphene sheet with its finite surface conductivity14, deals with resistive boundary conditions for the graphene. Moreover, the method of moments (MoM) is used for the diffraction analysis of graphene nanoribbons in15. The authors also try to model non-local effects of graphene by the MoM analysis. In16 graphene nanoribbons are analyzed using space-domain MoM with the restriction that the method is valid only for low wavenumbers. Lastly, the theory of characteristic modes is used to characterize the input impedance and efficiency of a plasmonic graphene-based antenna17. In19, based on integral equations governing the surface current density of magnetically biased graphene, an analytical approach is proposed to analyze an array of graphene ribbons.Various methods have been used to analyze multilayer three-dimensional graphene-loaded structures. In22. This makes MoL especially appropriate to deal with general multilayered structures loaded with complicated boundy conditions of arbitrary shapes, where the wave propagation in the direction perpendicular to the layers stacking is treated analytically. In directions transverse to the layers the structure is discretized and is sloved numerically. MoL can be used to analyze 2D and 3D structures that require 1D and 2D discretizations, respectively23. The MoL enjoys the advantages of both analytical and numerical methods while avoiding the shortcomings of each method when modeling multilayered structures. In25, we have proposed MoL for the analysis of 2D structures including graphene plates in Cartesian coordinates. To verify the efficiency of the method, several 2D graphene-loaded structures such as microstrips, striplines and parallel-plate waveguides are presented and analyzed. In26, we extend the MoL for the analysis of graphene-loaded 3D structures in Cartesian coordinates. Besides, different graphene-based periodic structures again in Cartesian coordinates, are studied in27 using MoL.The approaches mentioned above have advantages and disadvantages. Pure analytical methods are very time-effective but are able to solve only certain simple structures. On the other hand, fully numerical methods are capable of analyzing complex structures, but generally they are very time consuming. The method of lines (MoL) is a simple, fast, and accurate approach that solves an electromagnetic problem analytically in one coordinate direction and numerically in other coordinate directions29.In this paper the MoL is extended in cylindrical coordinates for the analysis of multilayered structures with an arbitrary number of layers loaded with graphene plates of arbitrary shapes. Here the graphene plates are treated as layers represented by surface boundary conditions. To do so, the impedance and admittance transformation formulas through a graphene plate are extracted. Having obtained the transformations, one can compute at every plane of the structure the impedance and admittance values, and subsequently the scattering parameters are derived. For the purpose of validation, the MoL results are compared with those of CST full wave simulation software which are in good accordance. In the first example, we assume a circular waveguide loaded with graphene sheets and perform a parametric analysis in terms of the graphene chemical potential for different numbers of plates. The second example deals with a coaxial cable loaded with annular graphene sheets. The proposed method is general and can be used to analyze generic 3D multilayered stackings in cylindrical coordinates with applications in absorbers and radiating structures. Note that the MoL is a pure classical theory which is applied to Maxwell’s equations and thus it is not able to model quantum mechanical phenomena such as Klein tunneling which occurs in graphene sheetsThe rest of the paper is organized as follows: in “In this section, the generalized transmission line (GTL) equations are first given in cylindrical coordinates to analyze structures that require two-dimensional discretization. Then, the impedance and admittance transformation formulas in a homogenous layer are given. The presence of graphene at the interface of two adjacent layers will result in a new set of boundary conditions through which the impedance and admittance transformation formulas at the interface are extracted. As a result, the impedance and admittance values are derived in each layer of the multilayer structure. Having obtained all impedances and admittances, the electromagnetic fields all over the structure and subsequently the scattering parameters of the whole structure are achievable.In what follows, we assume that the constitutive parameters are defined by:z direction propagation. The first and second equations of Ampere's law and Faraday's induction law result in30:z-direction. Using the third equations of the Ampere’s Law and Faraday induction’s Law, the longitudinal field components 30:First, we present the GTL equations suitable for Then, we combine the two first-order differential equation systems in Eqs.  and 6)  6) in orThese equations are called as wave equations. To solve these equations using MoL, the fields and their derivatives in transverse directions should be discretized.30:30:In this section, we present the discretization of the fields components in the cross section as well as the solution of the GTL equations in the discretized form. The discretization scheme is shown in Fig. and use the following abbreviations:As a result, Eqs. –8) are  are 8) aIn Eqs.  and 16)16), \docNow we are going to solve Eq. . For thiIntroducing into Eq. , one obtSince The general solution of Eq.  can be gd in Eq. , the chad, are obtained as30:Having known the electric and magnetic fields in each plane according to Eq. , the relOn the other hand, the electric and magnetic fields at each plane are related to each other through impedance/admittance matrices as follows:Consequently, the impedance and admittance transformation formulas between planes A and B are as follows:B. Besides, the two sides of this interface are distinguished by + and − indices.To analyze the whole structure, it is necessary to be able to pass through the graphene plates at the interface of two adjacent layers by transforming the impedances and admittances through the graphene interface. As shown in Fig. or equivalently As shown in Fig. This equation must be transformed to the cylindrical coordinates system, which will be performed as below. The transverse electric field components must be continuous at the interface. Hence,The transverse magnetic field components in cylindrical coordinates at The boundary conditions for the magnetic field components at plane Then, transformation of d by Eq.  into cylThen, the s in Eq.  are sepaDefining the electric and magnetic field components in cylindrical coordinates asrite Eq.  in the vIn this step, we need to discretize the field components and graphene parameters in their appropriate places as shown in Fig. As mentioned earlier, the field components, for example n of Eq.  can be eAccording to Eq. , we rewrSubstituting ^ in Eq.  results Multiplying Eq.  by \docug to Eq.  the relaFinally, the admittance matrix at Thus, transformation of admittance at graphene interface will be done using Eq. . Note thStarting from the output of the multilayer structure and using the formulas provided for impedance and admittance transformation through layers and interfaces, the input impedance and admittance can be obtained. Usually the load impedance is considered as the output wave impedance of the output waveguide which is normalized to be the identity matrix, i.e. Using the admittance transformation formulas, the input admittance Consequently, for the scattering parameter If the modes are ordered properly, the first element in the In order to calculate the transmission coefficient, the field coupled to the output port should be divided into the injected field at the input port. To do this, the fields should be calculated at the whole structure and they must be transformed in a numerically stable manner. The general solution of the wave equation in the Cartesian coordinates can be written as Eq. . The indThe forward and backward parts are connected by the characteristic impedance Then, the forward and backward parts can be obtained using the total fieldsUsing Eqs.  and 51)51), the Using the vectors The total field at the plane B is computed asUsing the definition of the impedance at any arbitrary plane, the above equations are written asThen, supposing that the graphene plate is placed between the layers, the transmission coefficient is obtained. First, we assume that a graphene plate is located between the two layers of the structure, as shown in Fig. The values of the admittances from Eq. . Assuminsing Eq. , the totThe electric field at the interface of the plane A is continuous and hence From Eq. , the valTherefore, we haveThen, the transmission coefficient matrix is calculated asThe first element of the matrix As shown in Fig. Therefore, the forward and backward fields at the plane Consequently, using Eq. , the totConsidering the continuity of the electric field components at the plane Since the electric field at the plane rom Eqs. –63) we  we \docuBy substitution of Eqs.  and 52)52) in 665\documeAs a result, from Eq. , the traHence, in general, for an Note that the scattering matrices To validate the proposed method, two multilayer graphene-loaded structures are examined in the cylindrical coordinates system: a circular waveguide and a coaxial cable. Both structures are analyzed for different values of graphene chemical potential and varying numbers of graphene plates. The results of the proposed method and CST simulations are compared to each other.14. In this model the relaxation time 7.In this section, as an example of a graphene-loaded multilayer structure, graphene plates are placed inside a circular waveguide. The cross-section of the waveguide is shown in Fig. 11, for the graphene chemical potentials Figure Figure Table In this section the graphene plates are placed inside the coaxial cable and the structure is analyzed in terms of the chemical potential and the number of graphene plates. The cross-section of the coaxial cable is shown in Fig. Figure Considering the reflection and transmission coefficient plots, increasing the chemical potential increases the graphene conductivity and thus reduces its transparency which results in an increase/decrease in the reflection/transmission coefficient, respectively. In other words, the reflected and transmitted powers of the waveguide can be tuned by an electric voltage controlling the graphene plate. This finds applications in tunable microwave waveguide attenuators. Also, this can be utilized in phased array antennas to control the feeding amplitude of each element of the antenna array. Note that no resonant behavior is observed in the reflection and transmission coefficients because the resonance frequency of a graphene plate is far beyond the microwave frequencies. This nearly flat response offers wideband microwave devices.In this paper, an extended method of lines (E-MoL) is presented for the analysis of graphene-loaded multilayer structures in the cylindrical coordinates. To do so, first, the impedance and admittance transformations imposed by graphene plates are obtained in the cylindrical coordinates system. Having the impedance and admittance transformations, the impedance and admittance matrices can be calculated in each plane of the structure. Then from the input impedance of the structure the reflection coefficient is derived. Finally by transferring the fields from the input to the output of the multilayered stack, the transmission coefficient is computed. To validate the proposed method, a circular waveguide and a coaxial cable loaded with graphene plates are analyzed and the results are compared with the CST full wave simulations. The proposed theory has the potential to model multilayered absorbers and radiating structures accurately and efficiently which is a topic of the future research. The MoL can be generalized to model complicated boundary conditions other than graphene in planar and quasi-planar waveguide structures in integrated microwave and optical circuits and also in circular and conformal antennas. The graphene-loaded optical fibers are attractive optical devices in which the dispersive properties of graphene emerges and can be characterized using the E-MoL preseted in this paper.


It focuses on the hidden medical curriculum, exploration of holistic care and communication skills.PsychED Up is an extra-curricular course for 3Develop a responsive and sustainable template for course evaluation Obtain rich and specific feedback across multiple domains which can be translated into course improvements Work collaboratively with former students Empower current students with the knowledge that their input is valuableEmbedded evaluation in start of term course development sessions to engage faculty in evaluation processes Faculty survey to determine what student feedback would be most useful Questionnaire finalised Collaborative design and refinement of questions, confirmed sub-sections and scopeRevised questionnaire: - Included rationale at the start - Questions tailored to faculty development needs - Greater quantity of prompted questions - Specific questions for large group presentation, small group teaching, actors’ performances and students’ reflections - Quantitative ratings and open-space questions thoughtfully paired Reduced time between sessions and obtainment of feedback Quality and quantity of feedback: - High response rates: 32/30 (2 duplicates) mid-term, 29/30 end-of-term - High-quality filling of open-space feedback allowed consolidation of themes to improve the courseCo-designed questionnaire brought focus and organisation to questions leading to richer, more personalised responses for faculty More detailed reflections were attributed to better student understanding of the questionnaire rationale, and knowledge that they would aid course improvement Created a robust system for collecting long-term feedback for PsychED Up and will continue making iterative amendments


Jsc) and carrier generation rate (G) using the 2D finite difference time domain (FDTD) method. In comparison with the standard Si-based solar cell which records Jsc = 16.9067 mA/cm2 and G = 1.48943 × 1028 m−3⋅s−1, the graphene/Si QD IBSC with 2 layers of QDs presents Jsc = 36.4193 mA/cm2 and G = 7.94192 × 1028 m−3⋅s−1, offering considerable improvement. Finally, the effects of the number of QD layers (L) and the height of QD (H) on the performance of the graphene/Si QD IBSC are discussed.Recent experiments suggest graphene-based materials as candidates for use in future electronic and optoelectronic devices. In this study, we propose a new multilayer quantum dot (QD) superlattice (SL) structure with graphene as the core and silicon (Si) as the shell of QD. The Slater–Koster tight-binding method based on Bloch theory is exploited to investigate the band structure and energy states of the graphene/Si QD. Results reveal that the graphene/Si QD is a type-I QD and the ground state is 0.6 eV above the valance band. The results also suggest that the graphene/Si QD can be potentially used to create a sub-bandgap in all Si-based intermediate-band solar cells (IBSC). The energy level hybridization in a SL of graphene/Si QDs is investigated and it is observed that the mini-band formation is under the influence of inter-dot spacing among QDs. To evaluate the impact of the graphene/Si QD SL on the performance of Si-based solar cells, we design an IBSC based on the graphene/Si QD (QDIBSC) and calculate its short-circuit current density ( Jsc) of 38.04 mA/cm2 [The intermediate-band solar cell (IBSC) proposed by Luque and Marti is a concept that allows the Shockley–Queisser limitation to be overcome . In this4 mA/cm2 . Rocha e4 mA/cm2 .Jsc [The design of Ge/Si QDIBSC has also been discussed. In 2013, a group of researchers developed a top-down process to fabricate a type-II Ge/Si QD for use in all Si-based IBSC applications. The theoretical calculation revealed that with many Ge/Si QDs well-aligned and closely packed, their wave functions diffuse into neighbors and couple with each other, forming quasi-continuous minibands. So the Ge/Si QD superlattice (SL) was inserted into the Si p–n junction and induced an additional two photon transition, which increased photocurrent . In 2016Jsc . In 2017Jsc .According to recent studies, graphene has been widely exploited to enhance the performance of the thermionic and dye-sensitized solar cells –13. Due sp2 hybridization, bonded with four carbon atoms. We delete the carbon atoms which are located outside of the shell. The graphene layers form strong bonds with bare Si via covalent bonding to Si.This section describes the design of the graphene/Si QD. To simulate the graphene/Si QD, we first create a  Si–Si nanotube with 0.7 Å bond distance as the QD shell. Then to design the QD core, we use the multilayer graphene (MLG) sheets with AA stacking and 0.3-nm distance between graphene layers. In this way, each carbon atom of the second layer is placed exactly above the corresponding atom of the first carbon layer. Next, an interface of MLG (core) and Si nanotube (shell) is constructed. Finally, we shift the shell toward the core, so that MLG is surrounded by Si nanotube. Each Si atom pushes the nearest carbon neighbors away, inducing distortion in the local area. Si atoms at the graphene edge prefer The developed interaction pulls the carbon atoms in graphene layers towards the silicon atoms and creates a stable bonding between them. Despite strong Si–C bonds there are no interactions between graphene layers. The weak Van der Waals interlayer coupling in graphene multilayers exert a significant influence on the energy levels, leading to new properties. MLG structure presents an electrical bandgap derived from intrinsic optical bandgap generated by the confinement of carriers and the biased electrical field, mainly due to weak anti-localization behavior of carriers , 19. FigSeveral methods have been developed to fabricate graphene/Si structures. Earlier studies showed formation of graphene on silicon by annealing epitaxial SiC film grown on silicon substrate at 1500 K . TransfeA single QD is not able to make a mini-band. The question is that how many neighbors should be included in the Hamiltonian? According to the previous studies, including only the first neighbors is not enough for the mini-band creation, the inclusion of second and often the third neighbors is necessary. As a result, the SL is designed by involving three neighbors as is shown in Fig. In general, it is difficult to simulate electronic devices in which quantum effects play an important role. Due to advances in nanotechnology, dimensions of electronic devices have been shrunk down to nanoscale. As electrons are trapped in nanoscale regions, the electronic states can be quantized and their behavior can only be described by the Schrödinger equation. The finite-difference time-domain (FDTD) method has been employed in modeling metamaterials and conventional Maxwell–Schrödinger systems with electromagnetic fields .k-points for simulation. The unit cell includes 18 carbon atoms and 144 Si atoms with sp2 hybridization, where reformations such as elimination and shifting some atoms are applied to an initial design in order to obtain the basic structure as is shown in Fig. k-point sampling grid, cutoff energy of 160 Ry, the Hamiltonian matrix elements that are related to the orbitals that participate in bonding between atoms, and periodic boundary conditions are used to perform these calculations. The SK-TB formalism is an extension of Bloch’s original method that shows all of the correct symmetry properties of the energy bands and provides a solution for the single-particle Schrödinger equation at each sampling k-points in the irreducible Brillouin zone (IBZ) [h, m, V, Ψ, and E are the Plank constant, electron mass, potential energy, the wave function, and eigenvalues of energy, respectively. Wave functions are approximated by the combination of Bloch functions. The electron wave functions can be obtained through:C, and Ф are wave vectors, weight coefficients, and Bloch function, respectively. If there are n wave vectors considered in every unit cell and there are N unit cells in crystal lattice, whose position are denoted by For calculating the electronic band structure of the graphene/Si QD, the SK-TB method is performed using ATK software. The SK-TB method or linear combination of atomic orbitals (LCAO) is a semi-empirical method that is primarily used to calculate the band structure and single-particle Bloch states of a material. For large systems containing up to hundreds of atoms, the density function theory (DFT) is used to find the true ground state density and ground state energy of an interaction system without explicitly calculating the many-electron wave function. A unit cell that describes the periodicity of SL is defined to reduce the sampling size of ne (IBZ) –26. Equae as Eq. :3\documeE should become optimum through Eqs. ::E shouldJsc) and electron–hole generation rate (G) using Lumerical software. Figure Y. The periodic and PML boundary conditions are chosen in X and Y directions, respectively. Using nanostructures such as QDs often causes an open-circuit voltage drop which is observed when sub-bandgap states are introduced [To evaluate the impact of graphene/Si QD SL on the performance of the Si-based solar cell, we design and simulate a graphene/Si QDIBSC. We obtain the short-circuit current density (troduced . This drJsc and G) of both the Si-based solar cell and the graphene/Si QDIBSC, the solar generation rate analyzer is exploited. This analyzer consists of the Poisson’s equation, the carrier continuity equation for electrons in the CB and holes in VB, and the transport equations in drift–diffusion model. Poisson’s equation relates variations in the electrostatic potential to local charge densities. The continuity and the transport equations describe the way that the electron and hole densities evolve as a result of transport, generation, and recombination processes. In the case of IBSC, there are electrons in IB. The electrostatic potential can be given by the Poisson equation [y is the direction of light emission and the along of the electrical field distribution, e is the elementary charge, ε is the dielectric constant of the material, p(y) is the hole density, nc(y) is electron density in CB, n1(y) is electron density in IB, Gij is the optical generation rate, Uij is the radiative recombination rate where subscript ij = ci, iv, and cv expresses CB-IB, IB-VB, and CB-VB transition respectively. Jc is the electron current density in CB and Jv is the hole current density in VB. Jc and Jv are given by drift–diffusion equations shown below:μe and μh are the carrier mobility of electrons in CB and holes in VB, De and Dh are the diffusion coefficients, respectively.To investigate the characteristics (equation –30.7\doc CB (Eq. ) and holx, y, and z dimensions, respectively, e.g.,  and . The bound state with the quantum number  is called the ground state and it constitutes the IB [Ec) is 0.33 eV.Figure s the IB . The gros the IB . As the k varies along the edges of first IBZ. As shown in Fig. Figure Jsc and G are estimated to be 16.9067 mA/cm2 and 1.48943 × 1028 m−3·s−1 for Si-based cell without AR layer and 21.1465 mA/cm2 and 3.16059 × 1028 m−3·s−1 for Si-based cell with AR layer, respectively. It is clear that the active layer with thickness of 3 µm has small light absorption. So the graphene/Si QD layers are embedded in the active layer of the Si-based solar cell in the simulation. Graphene/Si QD SL introduce intermediate states which enhance absorption of Si layer as is shown in Fig. Jsc = 24.5192 mA/cm2 and G = 7.79295 × 1028 m−3·s−1 when one layer of QD is embedded. Figure A Si-based solar cell with active layer thickness of 3 µm is simulated under illumination of a light source with spectral range of 0.3–5 µm. The G increases significantly. It means that the IB created by the graphene/Si QDs SL, splits the total bandgap of active layer (EG) into two sub-bandgaps. These sub-bandgaps absorb photons with energy less than EG. This process allows for increased G via a two-step photon absorption from the VB to the IB and from the IB to the CB. The absorption of sub-bandgap photons results in an additional photocurrent. The embedded graphene/Si quantum dots indeed help increase the photo-generated current as expected and thus improve the conversion efficiency of solar cell.When QD SL is embedded in the active layer of the Si-based solar cell, H) and the number of QD layers (L) on the graphene/Si QDIBSC performance, we design and simulate graphene/Si QDIBSC with different H and L. The characteristics of Jsc and G versus L (when H is fixed at 20 nm) and H (when L is fixed at 2) are reported in Tables The number of QD layers and shape of QDs strongly influence the quantized energy levels and optical transitions . In ordeJsc is achieved. Because as L increases, more bound states are introduced by additional QD layers. However, according to the results given in Table LAs the more layers are embedded higher H. As H increases, Jsc also increases. However, for HJsc becomes saturated due to overlapping of minibands. Because we fix the position of QD layers, when we increase H, the spacing between QD layers decreases. As a result, instead of formation of IB, the minibands, which are introduced by two QD layers, overlap.When two QD layers are embedded in the active layer of QDIBSC, we alter Jsc and G of this solar cell with and without QD SL were obtained by applying the 2D-FDTD method under illumination of a light source with spectral range of 0.3–5 µm. When the QD SL including one layer QD is embedded G was roughly tripled. Jsc was increased approximately 16% from 21.1468 to 24.5192 mA/cm2. Finally the dependence of IBSC performance on the important factors of QD SL, including L and H was investigated. For number of QD layers LH.A new type-I multilayer graphene/Si QD SL structure for IBSC applications was designed. Its ground energy state was calculated to be 0.6 eV above VB using the SK-TB method. This value of ground energy state provides a means to create an IB in the energy band structure of Si. The mini-band formation in a well-aligned and closely packed SL was observed. Then a Si-based solar cell was simulated and a closely packed SL of QDs was embedded in the active layer of this cell. The


A technique is implemented for trapping the bipolar electric charge on the graphene surface and arranged in a desired way to enhance the performance of a monolayer graphene metamaterial based tunable, ultrathin, dual narrow band terahertz (THz) absorber. A monolayer graphene sheet placed on the dielectric substrate can provide dual-band resonance by utilizing the surface plasmons of the fundamental and third order mode index and an absorption of more than 99% and 50% can be obtained in the lower and upper band, respectively. The absorption is further enhanced to the level of perfect-absorption by utilizing the charge trapping mechanism on the graphene and generating bipolar charged nodes to create higher order surface plasmons. The multiple interference and reflection theory proves that the destructive interference in the dielectric layer is the cause of perfect absorption. The applied technique in the dual-band absorber configuration provides a tunable response which remains insensitive to the polarization and incident angle of the electromagnetic wave. The proposed perfect absorber can be utilized as a biosensor for refractive index sensing and the detection of glucose in water and the malaria virus in blood. It can provide an ultrahigh sensitivity of 14.88 THz RIU Surface plasmons generated at the graphene dielectric interface can be altered by trapping the electric charge. The electromagnetic properties of such materials are not found in natural materials. Their extraordinary properties made the implementation of cloaks,2,3 an invisible carpet4 and a perfect lens5 possible. The current research trends are moving in the direction of implementing terahertz (THZ) devices like antennas,6 sensors,7–9 filters10 and absorbers.11 The purpose of implementing THz absorbers is enabling the technology in spectroscopy,12 detection and sensing13 and many more applications.14 Recently, the implementation of ultrathin,15 ultrasensitive8,13,16,17 absorption based sensors/biosensors with a narrow17,18 and ultra-narrowband19,20 response is being investigated. Recent implementations discuss the development of narrowband sensors with multi-layered media with complex structures with a large thickness.17,20,21 Another challenge in the implementation of sensors is making the response independent of the incident angle and polarization of the incident electromagnetic wave.7,11 This feature enables the sensor to be used in dynamic sensing systems which can be utilized in handheld devices.22 All these features of absorption-based sensors can be obtained by utilizing MM in THz implementations. In MM sensors, the localized surface plasmon resonance created due to free electrons at the highly conductive material and dielectric interface changes with the variation in the surroundings like the refractive index of the medium.23–25 This leads to a change in the spectral behaviour of the MM absorber and thus it can be utilized as a sensor.26 Specifically, biosensing applications require a narrowband sensor with perfect absorbance which can be possible with MM cell implementations due to the strong electric and magnetic resonance caused in the periodic structure.20,27–29 In the sequence of implementing the MM absorber, graphene has been introduced to obtain tunability and controllability in the frequency spectrum.8,30 The electrical behaviour of graphene for varying chemical doping and external electrostatic or magnetostatic field allows the impedance matching to free space which remains the primary requirement in mitigating the back reflections in the absorbers.6 The excitation of graphene surface plasmons (GSPs) causes a strong field confinement which results in a perfect absorption spectrum.8 In fact, the nanoscale fabrication can be miniaturized by the usage of graphene due to the strongly confined wave vector over the propagation in free space, which may help in providing ultrathin geometries.31–33Artificial materials with specific ranges of electrical parameters like permittivity and permeability have revolutionized high frequency applications.34–36 The frequency behaviour of the absorption spectra changes with the variation in the refractive index of the surroundings when a plane wave impinges on the graphene surface. Thus, the proposed narrow band absorber can be utilized in potential biosensing applications like in the detection of glucose in water and malaria with good performance indices like high sensitivity, figure-of-merits and quality factors. The absorber response remains independent of polarization and the incident angle of the electromagnetic wave shows the high degree of symmetry of the structure.37 The electrical bias voltage applied on graphene can provide the tunability and controllability of the absorption peaks. Moreover, the implemented absorbing unit behaves as a perfect wideband reflector in between the absorption peaks and thus can be utilized in the frequency selective THz sources. Generally, multiple or dual-band resonances are obtained in complex multi-layered structures.11,37–40 In comparison, the proposed ultrathin dual-band absorber can offer a geometry with less complexity. The experimental realization of metal-based nanoscale devices has already grown at a great level.24,25,28,29,41–43 However, the fabrication of graphene metamaterial based absorbers is still a challenging task and thus simple geometries are being implemented and investigated.30,44,45 This research work advances the literature and paves the way to implementing graphene metamaterial-based absorbers. The reported research work is mainly categorized by two outcomes; (i) implementation of a technique for alteration of surface plasmons on graphene and trapping the electric charge for the creation of bipolar charged nodes. This establishes the equality of the mode index of surface plasmons at the graphene-dielectric and graphene–air interface, which results in perfect absorption at the frequency of higher order resonance and (ii) the utilization of the proposed ultrathin, ultra-sensitive, tunable dual narrowband absorber as a biosensor for refractive index sensing and the detection of glucose in water and the malaria virus in blood.This work reports a MM absorber exploiting a graphene patch and providing dual-band resonance with perfect absorption. The structure offers an ultrathin geometry at the THz spectrum with a thickness of around thirty times scaled down of the free space wavelength. The monolayer graphene patch provides an absorption of more than 99% and 50% in the lower and upper band, respectively. A circular slot is inserted in the graphene sheet which traps the electric charge and hence bipolar charged nodes are created in the graphene sheet which enhances the impedance matching in the upper band and hence the absorption to more than 99%. The lower and upper band absorption peaks are the result of fundamental and higher order plasmonic resonance, respectively. The interference theory proves that absorption occurs due to multiple reflections caused in the dielectric substrate being utilized between the slotted graphene patch and metal layer.2) substrate with relative permittivity, εs = 2.25 and height h. A square-shaped graphene resonator of edge a is placed at the top of the substrate. This graphene resonator contains an annular circular slot of outer and inner radius ro and ri, respectively. This whole structure is placed at the top of the metallic sheet. In this structure, gold material is used as the metal plane or back reflector. The thickness of the metallic plane is kept such that it remains more than skin depth for proper reflection of the incident wave. The numerical analysis of the absorber is performed with the considerations of the periodic arrangement of the unit cells having periodicity w along the x and y-axis and Floquet port boundaries. The simulation is performed with 100 cells per wavelength and the total number of tetrahedrons as 733 917 along with the adaptive meshing.46 The incident electromagnetic wave from medium-2 (air) on the graphene sheet creates the p-polarized surface plasmons (SPs) with decaying electric field strength over the transverse distance.31,47 The dispersion relation of p-polarized surface plasmons (SPs) in a graphene patch placed on a substrate can be obtained from Fresnel's relations as given in 48, is the free space wave number, ω is the angular frequency and c is the speed of light. The electrostatic limits can be applied for obtaining the plasmons vectors as  under the condition ko ≪ |ksp|. Now, Drude's conductivity47 expression modifies the surface wave vector as  with τ as the relaxation time of graphene. This quadratic expression confirms the presence of 2-dimensional electron gas on the graphene-dielectric interface. The degree of confinement can be defined in terms of the surface plasmon wavelength λsp in respect to the free space wavelength λo as . Here, α ≈ 1/137 which is the fine-structure constant, h is the Plank's constant and EF is the fermi-energy.31,47 The edge length of the graphene patch is selected as a ≈ λsp/2 at frequency 4.4 THz for the value of graphene chemical potential as μc ≈ 0.3 eV, relaxation time τ = 0.1 ps at temperature T = 300 K. The minimum thickness of the substrate that provides the perfect absorption remains around h ≈ λsp/4.Here, 24,25,28,29,41–43 The fabrication of graphene-based absorbers is still a challenging task. There have been very few reports on the experimental validation of graphene-based absorbers.30,44,45 A method of fabrication of graphene-based absorbers is reported quoting the chemical vapour deposition (CVD) process and transfer approach.30 Monolayer graphene can be grown using the CVD process and then transferred on the SiO2 substrate. After that, the graphene sheet can be patterned using e-beam lithography. A detailed process of fabrication of the patterned graphene sheet is demonstrated in ref. The accurate fabrication methods of the micro/nanoscale graphene-based absorbers are currently being investigated. The fabrication of metal-based metamaterial implementation has already been reported frequently in the literature.x- and y-axis, respectively. The floquet ports are applied with the air spacing from the top and bottom surface of the absorber. E-field distribution shown in m = 1 and 3, respectively.31 This field distribution is reported for transverse electric (TE) polarization. The field distribution for transverse magnetic (TM) polarization becomes orthogonal phase shifted with similar characteristics and mode indices. The reflected wave from the graphene resonator must be as minimum as possible. This is confirmed by drawing the impedance plot as shown in A unit cell is analyzed with the plane wave incident at normal to the arrangement of electric and magnetic fields along the m = 1 and 3, respectively. This discontinuity results in a low value of absorption at the frequency of higher order resonance.31 It can be predicted in the field distribution that absorption can be enhanced at the frequency of the higher order resonance if an equal charge distribution is obtained along the graphene interfaces. This can be done by creating the electric charge storage geometry in the graphene sheet which has dimensions equivalent to the one half-wave variation of the surface plasmons wavelength. Also, the inserted geometry must be symmetrical to maintain the insensitivity to the polarization angle of the incident electromagnetic wave. The best way is the insertion of an annular circular slot of diameter equivalent to λsp/2 at the frequency of higher order resonance. The creation of a slot provides the capacitive effect with the capability of the storage of electric charge with opposite polarity along the orientation of electric field vectors.49 Thus, two extra nodes are created in the centre of the graphene sheet at both the ends of λsp/2 at a frequency around 9.85 THz which helps in maintaining the mode index as equal in both the sides of the graphene sheet. The creation of the charged nodes and their effect is illustrated in Two absorber structure configurations have been numerically analysed to understand the operation of the proposed dual-band absorber. The first structure (absorber-1) contains a graphene based rectangular resonator placed on the substrate and makes an interface with air providing two resonances at around 4.68 and 9.84 THz. This absorber provides an absorption peak with an absorptivity of more than 99% and 50% at the frequency of the first and second resonance, respectively. Absorber-1 offers a poor impedance matching in the upper band which results in the low value of absorption. For the enhancement of the absorption at a higher frequency, a circular annular slot is inserted in the rectangular graphene resonator. As a result, the absorption is enhanced to the level of more than 99% in the upper band, as shown in 34–36n1 and n2, respectively. Here, the graphene patch is considered as a partially reflecting surface (PRS). A fraction of the incident wave from medium-1 is transmitted into medium-2 and reflected back to medium-1 with the magnitude |S21| and |S11| and phase e21jθ and e11jθ, respectively. The metallic surface at the back provides the fully reflected wave with the addition of the phase factor ejπ−. This wave is again reflected back in medium-2 and transmitted in medium-1 with the expression as |S22|e22jθ and |S12|e12jθ. The magnitude and phase of all the transmitted and reflected waves are extracted from the full wave simulation using the CST microwave studio in the decoupled system, which is drawn in 34–36 The total reflection coefficient R(ω) in medium-1 is then calculated using 35The operation of the proposed absorber is verified with the help of the interference theory.β = kd is the propagation constant with k as the wave number in medium-2 and  is the thickness of medium-2 with ε1 and ε2 as the relative permittivity of medium-1 and 2, respectively and ϕ as the incident angle. The proposed model is passive in nature hence S12 = S21. Finally, the absorption is calculated as A(ω) = 1 − R(ω) − T(ω). Here, T(ω) is the transmission coefficient, which remains zero due to the presence of the ground plane. 35Here, h, the edge of the graphene patch, a, inner and outer radius of the inserted annular circular slot ri and ro, respectively is shown in h shows the perfect absorption in both the bands if its value is selected as h ≈ λsp/4(h = 2.5 μm and above), as shown in h is selected to maintain the ultrathin geometry. It can be noticed that a much smaller value of h can also be selected at the cost of nearly perfect absorption. There is a redshift in the response with a small shift in the lower and large shift in the upper band with the increment in a as shown in a can allow setting of the operating frequency. The insertion of the annular slot affects the absorption at the frequency of the higher order mode only. Similar results can be observed in ri. ro separates the resonant bands with a larger gap with the reduced value of absorption in the lower band.The absorber performance is analysed in terms of the variation in its physical parameters for the consideration of fabrication tolerances. One physical parameter is varied at a time and others are kept intact. The variation in the absorber response with the variation in substrate height θ. The absorption spectrum is approximately stable over the variation in θ in both the operating bands with slight deviation in the peak frequency of the upper band. The insensitivity to the angle of incidence makes the proposed absorber capable of being utilized in non-stationary handheld devices which generally remains quite difficult to implement.The symmetric structure of the absorber provides the insensitivity to the polarization angle. Moreover, εig = 1.82 is coated over the graphene patch so that all the periodically arranged unit cells can be biased together.37,45,50,51 The height of the substrate is reduced correspondingly to h = 2.43 μm so that resonant bands can be maintained at similar frequencies. μc. The increment in μc blueshifts the frequency response.52 There is a small and large shift in the lower and higher mode, respectively with the variation in μc. Kubo's formalism can be applied for defining the conductivity of graphene material with the selection of parameters as relaxation time τ = 0.1 ps and temperature T = 300 K with the single layer of graphene with thickness as tg = 0.34 nm.6,53 A number of research articles are available discussing graphene's conductivity, for more detail please consult ref. μc < 0.2 eV. Absorption peaks are obtained only when μc > 0.2 eV and the generated absorption peaks attain the value of more than 90% for μ > 0.3 eV.Once the dimensions are set for the desired frequency operation, the structure can be fabricated and a further variation in frequency response can be governed by the variation in the chemical potential of graphene. The chemical potential of graphene can be varied by applying a DC bias voltage on the graphene patch. An ion-gel layer of thickness 0.1 μm with permittivity A.μc = 0.5 eV for which the absorption peak touches the level of perfectness and hence can be selected for sensing applications keeping all other physical parameters similar as discussed earlier. For the analysis of the sensing performance, a layer of photoresist can be grown on the absorber and the effect of the fringing field is studied.24,25n = 2 and n = 1.6. The percentage of frequency shift (FS) is calculated using . Here, fta is peak absorption frequency with analyte thickness ta and fref is the peak absorption frequency without analyte.24 The percentage change in the frequency shift is reduced at the lower value of refractive index when thickness is varied. Moreover, the frequency shifting is saturated at the value of ta around 2 μm, which is selected for reporting the refractive index sensing performance of the proposed absorber in the next subsection.24,25ta with the analyte of refractive index n = 2. S), full-width half-maxima (FWHM), figure-of-merit (FOM), quality-factor (Q) and frequency shift Δf over the unit variation in the analyte thickness Δt. Here, Δf = f2 − f1, f1 is the initial frequency and f2 is the frequency after shifting when analyte thickness is varied from t1 to t2 and Δt = t1 − t2.17 The performance parameters are calculated as  (TU: thickness unit),  and Q = fp/FWHM. Here, fr is the peak absorption frequency. These parameters are calculated and plotted in ta. The proposed absorber provides high sensitivity, FOM and Q-factor at thickness ta ≈ 0.5 μm. The highest sensitivity obtained with the variation in the analyte thickness is 1.05 THz TU−1 and 2.2 THz TU−1 in the lower and upper band, respectively. The sensitivity and FOM are significantly reduced for the higher values of ta. It shows that the proposed absorber can be suitably fit for the biosensing application because the thickness of most of the viruses remains within ta < 1 μm.8B.td. The resonant frequencies of both the operating bands respond in the same manner and there is drastic variation till the value of td = 0.5 μm. For td > 0.5 μm, the shift in the peak resonant frequencies is saturated over the variations in td. In this exercise, the value of the refractive index of the analyte is selected as n = 1.2 with its thickness as ta = 2 μm.As stated earlier, the proposed biosensor is independent of the incident angle and hence its capability must be checked for its usage in dynamic systems by varying the spacing between the analyte and sensor. C.ta = 2 μm is placed at the top of the absorber. f is considered over the unit variation in refractive index Δn. Here, Δf = f2 − f1, f1 is the initial frequency and f2 is the frequency after shifting when the refractive index of analyte is varied from n1 to n2 and Δn = n1 − n2. The sensitivity is calculated as  (RIU-refractive index unit). It can be observed in μc = 0.5 eV. In this scenario, the lower and upper band provides the maximum sensitivity of 1.35 and 2.95 THz RIU−1, respectively. The maximum FOM is 4.67 and 8.8 (RIU−1) for the lower and upper band, respectively. Moreover, the proposed absorber provides the narrow linewidth being defined by FWHM. The intensity of the absorption peak remains more than 99% over the variation in the refractive index. The proposed absorber can be utilized in the sensing of water (n = 1.333), ethanol (n = 1.36), ethylene glycol (n = 1.41), glycerine (n = 1.47), benzene (n = 1.5), sodium chloride (n = 1.54) and carbon disulphide (n = 1.63) with high sensitivity and other improved performance parameters in comparison to recently reported graphene based sensors.55For the utilization of the proposed absorber in refractive index sensing (RIS) applications, an analyte of thickness D.n = 1.2 is placed at the top of the sensor and the chemical potential of graphene is varied. Tuning of the absorption spectrum is possible with variation in μc as shown in −1  with a high value of FOM around 23.7 and 53.09 with the lower and upper band, respectively. The absorber shows the spreading in linewidth with the increment in μc. Also, the absorber maintains a high Q-factor throughout the variation in μc. The high sensitivity of the absorber over the variation in μc represents the high tunability and controllability of sensor.An analyte with thickness 2 μm and refractive index, 8,56 The proposed absorber provides high sensitivity and FOM, as expected. Here, the thickness of the analyte being considered as blood with malaria virus is taken as 2 μm with the electrical characteristics of graphene as μc = 0.5 eV and τ = 0.1 ps at T = 300 K.8 The plots represent that there is a slightly increased linewidth but the absorber still offers a high FOM due to the high sensitivity in both cases. The absorber offers the sensitivity 5.1 and 12.7 THz RIU−1 with FOM as 21.73 and 41.1 RIU−1 in the lower and upper band, respectively in the case of pure water for μc = 0.4 eV and τ = 0.1 ps. The absorber offers the maximum sensitivity in the case of 25% glucose mixed water similar as in water with a little higher FOM of 21.86 and 43.212 RIU−1 in the lower and upper band, respectively. The other variations in the glucose concentration in water can also be detected using the proposed absorber with satisfactory performance parameters.57The performance of the proposed dual-band absorber is analysed in the water with refractive index 1.3198 and in water with 25% glucose with refractive index 1.3594, as illustrated in μc. The proposed absorber offers better performance in terms of sensitivity, FOM and Q-factor in comparison to recently reported other sensors. Also, the proposed tunable absorber offers a thin geometry with strong angular and polarization stability in comparison to others. Recently, some metamaterial based biosensors have been fabricated and reported which show a strong agreement in the simulated and measured results.24,25,58 This recent literature supports the hope that the absorber/sensor reported in this article will perform as expected if experimentally implemented in the future.A comparative analysis is reported in λsp/2. Consequently, the absorption in the upper band has been enhanced to more than 99%. The operation of the proposed absorber has been verified by interference theory confirming the cause of absorption as destructive interference in the dielectric being used as the substrate. The frequency response of the absorber remains insensitive to polarization and incidence angle. The performance of the proposed dual-band absorber has been analyzed as a refractive index sensor and different biomedical applications like the detection of glucose in water and detection of malaria virus in the blood. An ultrahigh sensitivity of 14.88 and 12.7 THz RIU−1 with FOM as 54 and 41.1 RIU−1 at the frequency of upper band has been obtained. The sensing performance in the upper band remains better in comparison to the lower band. The proposed absorber can potentially be utilized in dynamic hand held devices.A graphene based tunable ultrathin narrow dual-band absorber has been numerically analyzed and implemented. Fundamental and third order surface plasmon modes have been generated in the absorber geometry which provide an absorption of more than 99% and 50% in the lower and upper band, respectively. The technique has been implemented for electrostatic charge trapping and creation of the bipolar charged nodes on the graphene air interface by inserting an annular slot of dimensions equivalent to There are no conflicts to declare.