We integrated matched mRNA sequencing (mRNA-Seq), whole-genome bisulfite sequencing (WGBS), nucleosome occupancy methylome sequencing (NOMe-Seq) and chromatin immunoprecipitation sequencing (ChIP-Seq) data from primary human myeloid and lymphoid cells. Using these multi-omics data and machine learning, we trained two complementary models to determine the role of epigenetic factors in the regulation of IR in cells of the innate immune system. We show that increased chromatin accessibility, as revealed by nucleosome-free regions, contributes substantially to the retention of introns in a cell-specific manner. We also confirm that intrinsic characteristics of introns are key for them to evade splicing. This study suggests an important role for chromatin architecture in IR regulation. With an increasing appreciation that pathogenic alterations are linked to RNA processing, our findings may provide useful insights for the development of novel therapeutic approaches that target aberrant splicing.Dynamic intron retention (IR) in vertebrate cells is of widespread biological importance. Aberrant IR is associated with numerous human diseases including several cancers. Despite consistent reports demonstrating that intrinsic sequence features can help introns evade splicing, conflicting findings about cell type- or condition-specific IR regulation by   The role of introns in mammalian genomes remains largely unexplained. Given the time and energy required for the transcription and subsequent excision of introns from pre-mRNA, it was important to recognize in recent years that introns can be selectively retained in mature mRNA transcripts and thereby contribute significantly to transcriptomic complexity ,2. IntroIR is widespread across human tissues and affects >80% of protein-coding genes . For exatrans-acting splicing regulators interact with cis-acting regulatory elements; and (ii) globally, through the structure of chromatin, which is largely governed by epigenetic factors, including nucleosome assembly, histone modifications and CpG methylation  classifier and a conditional random forest (cRF) classifier with matched transcriptomic and epigenomic data from monocytes, macrophages, naïve T cells, central memory T cells and effector memory T cells Figure . Our res6 cells/ml in macrophage serum-free medium (Invitrogen) supplemented with 50 ng/ml recombinant human monocyte colony-stimulating factor . Cells were incubated at 37°C, 5% CO2 for 5 days before macrophage cells were collected. Cell isolation, differentiation, DNA/RNA extraction and library preparation for mRNA sequencing (mRNA-Seq), whole-genome bisulfite sequencing (WGBS), nucleosome occupancy methylome sequencing (NOMe-Seq) and chromatin immunoprecitiation sequencing (ChIP-Seq) experiments are described in detail in these articles . Primary monocytes and T cells  were retrieved from two healthy donors. Monocyte-derived macrophages were retrieved as follows: elutriated monocytes were seeded at 1 × 10articles ,29. DonoRNA-Seq reads (FASTQ format) of each technical replicate were tested for quality using FastQC v.0.11.5 (github.com/s-andrews/FastQC). Further processing, including adaptor trimming, was performed within the IRFinder algorithm for IR quantification . Sequenccriptome .et al.  as the region between two exons in any transcript. Regions covered by a gtf feature within an intron were excluded as they could confound an accurate measurement of IR. Introns that were present in at least 10% of a gene's mature mRNA transcripts (IRratio ≥0.1) with an overall intron depth ≥10 and ≥90% read coverage were considered retained. Retained introns were further filtered for those where the flanking exons had a percent spliced in index (PSI) ≥0.9. Non-retained introns were defined as those with an IRratio ≤0.01 and intron depth <10. Only introns from expressed host genes [fragments per kilobase per million (FPKM) ≥1] with a length <10 000 bp were selected for downstream analyses. For the intron classification system introduced by Braunschweig et al. , additioet al., we kept the 10 kb intron length filter for consistency. Our initial assessment indicated that >10 kb long introns are almost exclusively found in non-retained introns and often present the first intron in a transcript.In contrast to Braunschweig We used Cufflinks v2.1.1  to estimRaw WGBS FASTQ files were assessed for quality using FastQC v.0.11.5 (github.com/s-andrews/FastQC). Standard Illumina adaptors used for the library preparation were trimmed using cutadapt v.1.10  with a qq-value cut-off of 0.01. All histone modifications were processed in the ‘narrow peak’ mode to extract peak summit coordinates. Narrow peaks were used because wide peaks frequently tend to spread across retained and non-retained introns. For visualisation in Integrative Genomics Viewer  line plots, we subtracted ChIP-Seq input from respective HM ChIP-Seq read counts and normalised based on bins per million (BPM) mapped reads using bamCompare and parameters –binSize 1 –scaleFactorsMethod readCount –effectiveGenomeSize 2913022398 –operation subtract –normalizeUsing BPM.ChIP-Seq data for six histone modifications  were aligned to the human GRCh38 reference genome using STAR v2.7 . Duplicawer IGV; , we genecoverage2cytosine utility with –nome parameter.Raw FASTQ files were assessed for quality using FastQC v.0.11.5 (github.com/s-andrews/FastQC). Reads were mapped to the GRCh38 reference genome, duplicate reads removed and methylation calling performed using Bismark v.0.19.0 . GCH metNucleosome-free regions (NFRs) were predicted using the gNOMePeaks tool  with defnuc command. For splice site strength calculations, we used MaxEntScan (Model features were associated with three genomic regions around retained and non-retained introns: (i) ±100 bp from the 5′ splice site; (ii) ±100 bp from the 3′ splice site; and (iii) ±100 bp from the middle of an intron, each region being 200 bp long. GC content was extracted using bedtools v.2.26.0  nuc commxEntScan . CpG denxEntScan . The PSIxEntScan . Exons wxEntScan .trans-regulators of dynamic IR. We extracted RBP-binding motif data from the ATtRACT database (attract.cnic.es) (We considered RBPs as putative cnic.es)  and idenP-value ≤0.05 (Fisher test comparing CpG methylation in the NFR with the surrounding background). Presence or absence of an NFR was dichotomized as ‘yes’ = 1 and ‘no’ = 0. Information about nucleosome location was included in the model in a similar manner .To generate epigenetic features, we overlapped three regions of interest with the pre-processed epigenetic data. NFRs were defined as regions >40 bp in length with a The relationship between histone modification and IR was included in the model through the presence or absence of an overlap with a histone signal region. It was categorised as 0 = no overlap, 1 = overlap with a region of HM signal, 2 = overlap with a region of strong signal [strong signal = mean (HM pile-up) + SD (HM pile-up)]. The full list of features is presented in To identify features important for IR, we constructed a binary classification model using the EN algorithm. We approached the problem in a naïve manner, i.e. we did not impose any prior assumptions about the factors that might potentially play a role, and therefore an equal penalty factor was applied to all features. EN classification was performed in the caret R package  using thin silico analysis to validate our results using an independent machine learning algorithm, cRF. In cRF, unlike standard RF where the first split variable is randomly selected, an association test between the outcome and the model predictors is performed first. The ranked P-values are then used to identify the covariate with the strongest association with the outcome, which is later used for the first binary split at cutpoint c for a continuous covariate or at category C for a categorical covariate. cRF classification was also performed in caret using the cforest method as implemented in the party R package  affinity scores were calculated around the splicing sites of retained and non-retained introns using TEPIC Version 2.2 . We alsoP-values ≤ 0.05 were considered significant. Clustering was performed using unsupervised hierarchical clustering with complete linkage. Gene Ontology (GO) enrichment analysis on host genes of dynamic introns was performed using the R Bioconductor package enrichR  and not retained in one or more cell types . Differentially retained introns are determined based on pairwise comparisons (cell type A versus cell type B) with Audic and Claverie tests. They need to fulfil the retention criteria in at least one of the two cell types. Introns with a To investigate how IR is regulated in primary immune cells , we integrated transcriptomics (mRNA-Seq) data with epigenomics data including genome-wide CpG methylation (WGBS), histone modifications (ChIP-Seq) and nucleosome occupancy (NOMe-Seq) . The celWe identified a total of 26 147 retained introns in 12 379 genes, some of which were retained in both myeloid and lymphoid cells while others were cell type specific . The numP <0.05 Audic–Claverie test) between monocytes and macrophages (571/1425), T cells displayed greater stability regarding IR, with only 8% of introns classified as differentially retained . In contrast to the monocyte to macrophage differentiation, where we observed a reduction in IR events  located around their 5′ and 3′ splice sites (±100 bp) as well as the middle of an intron . InteresCpG methylation profiles (extracted from WGBS data) for retained and non-retained introns displayed a characteristic bimodal distribution, with two distinct peaks at 0% and 100%. Differential methylation was predominantly found at the splice sites when we compared regions of genomic DNA associated with IR and no IR. At the 5′ splice sites, we observed higher methylation levels in non-retained compared with retained introns in all five cell types. However, there was a cell type specificity in terms of CpG methylation within introns and 3′ splice sites .The M.CviPI enzyme, used in NOMe-seq experiments, methylates GpC sites that are not bound by nucleosomes. GCH methylation levels (where H is any nucleobase except guanine) provide information about chromatin accessibility. Unlike endogenous CpG methylation, GC dinucleotides are rarely fully methylated , therefon = 48) to train EN models for each cell type and predict whether introns are either retained or non-retained. The performance of our models was assessed based on the area under the receiver operating characteristic curve (AUC) values, which ranged between 0.87 and 0.95  sequence-based features: intron length, GC content, splice site strength, CpG density, branch point strength and distance ; (ii) transcriptomics features: PSI values of the flanking exons; and (iii) epigenomics features extracted from the WGBS, ChIP-Seq  and NOMe-Seq data . We then5 Figure  and valu5 Figure . The conThe EN model assumes a monotonic linear relationship between the class variable and the model features. To determine whether this assumption is adequate for IR classification, we also trained cRF models, which do not make any prior assumption about the relationship between the outcome of interest and the model features. Comparing the results from both types of models, we found that cRF performed slightly better than EN, with AUC values ranging between 0.91 and 0.98 Figure  and PR vNext, to evaluate whether the learned relationship between the model features and IR was generalisable across cell types, we trained our model with data from one cell type and tested it with data from another cell type. For all training/test data pairs, the AUC and accuracy metrics were comparable with those models that were trained and tested on the same cell type .To assess which features contribute most to the model performance (and thus the relevance of a feature to IR), we used variable-importance measures (VIMs). For EN, these are the regression coefficients ordered from lowest to highest, where parameters with larger values have a greater effect. For cRF, variable importance was calculated as the mean decrease in accuracy after permutation of each model feature. Given the known properties of retained introns, it was no surprise that intrinsic features, such as length, GC content and CpG density, were ranked as the top predictors, with a high level of agreement across all cell types analysed Figure . Again, Epigenetic features were also ranked among the top five predictors across all models and cell types; however, their nature and relative importance varied between cell types Figure . Overallet al. proposed three types of introns  that differ not only in their intrinsic sequence-based features but also in their relative levels of inclusion and in the impact their inclusion has on resulting transcripts  is known to contain dynamic introns starting from intron 5 and is important during granulopoiesis in mice  of trans-regulators of dynamic IR, can improve our model performance. We extracted RBP-binding motifs from the ATtRACT database . We incorporated this information as features in our classification models. The results show that RBP-related features improved the model performance marginally from AUC = 0.85 without RPB features to AUC = 0.882 (with RPB features). The best ranked RBP-related feature was for IGF2BP3 with binding sites at the centre of dynamic introns (rank #27).Finally, we tested whether RBPs, as putative database  and iden2FC FPKM ≤2); and (iii) host gene expression increased , whilst down- and up-regulated host genes were associated with 73 and 247 dynamically retained introns, respectively. Correlation analyses suggested that IR ratios of dynamic introns are on average slightly positively correlated with host gene expression  might regulate chromatin accessibility in dynamic introns. We analysed TF binding affinities in retained and non-retained introns using TEPIC . In totaAs chromatin accessibility was identified as the strongest predictive factor for dynamic IR, we closely examined its relationship with retained and non-retained introns. We identified five distinct GCH methylation profiles in the ±200 bp region around the 5′ splice site of retained introns Figure , left. SUpon visualising the intronic regions that changed their IR status between cell types, we observed greater chromatin accessibility levels in retained introns Figure . MoreoveBased on the observations concerning chromatin accessibility, we sought to assess the relationship between IR and epigenetic factors in the context of changing chromatin states, i.e. differential GCH methylation Figure , and staOne of the most interesting results of this analysis was that there are no differences in epigenetic marks between internal retained and non-retained introns when a stable chromatin state is maintained Figure , demandiet al. had previously assessed the importance of intrinsic features (length and GC content) of introns and neighbouring exons, as well as splice site strengths, for IR decisions. Using Kolmogorov–Smirnov statistics and a logistic regression model, they found that cis-acting features are predictive of IR in human neural tissues. However, this and other studies have used single or paired omics layers  only, missing out on important epigenetic factors. Moreover, they often used individual cell lines for their analyses, missing out on cell type-specific differences in epigenetic IR regulation.In this study, we have employed a machine learning approach to determine regulators of IR in primary haematopoietic cells. For the first time, we provide integrated matched transcriptomic, nucleosome occupancy, CpG methylation and six histone modification profiles from five primary human cell types representing two independent systems of haematopoietic cell differentiation. Previous studies have described features that are associated with retained introns, including a higher intronic GC content, shorter intron lengths, weaker 5′ and 3′ splice site strengths and some epigenetic marks ,14,17. BWe applied supervised machine learning using EN and cRF algorithms as well as a support vector machine. Unlike deep learning methods, which are very capable of identifying complex relationships but do not provide tools to determine how exactly an outcome was determined , these mIntrinsic features, such as length and GC content, have been consistently reported in association with IR across cell types ,4 and evet al. has shown that decoy exons interact with splice acceptor sites and thereby block intron excision, a phenomenon that seems widespread in terminal erythropoiesis  indicate a well-positioned nucleosome , while rIn conclusion, our results advance our understanding of alternative splicing regulation. We found an unanticipated strong contribution of chromatin organization in IR modulation where nucleosomes position upstream or downstream of retained introns (determined by the length of linker regions and NFRs) to facilitate acceleration of RNA Pol II elongation and increased IR. Furthermore, the models generated in this study can be adapted to study epigenetic gene expression and alternative splicing regulation in other cell systems, other species, in health or disease, and further our understanding of these essential biological mechanisms.https://github.com/combiomed/IR_code. Processed sequencing data used to train the models were deposited at Mendeley Data: http://dx.doi.org/10.17632/b6crxbxbk2.1.Sequencing data are deposited at the European Genome-Phenome Archive under the accession numbers EGAS00001001595 and EGAS00001001624. Access is subject to an application process as per the EGA requirements. R scripts developed for this study are available at gkac994_Supplemental_FilesClick here for additional data file.


H1/TH17 T‐cells and impairment of T‐reg cells may be responsible. Clinicians should be aware of the potential for exacerbation of sarcoidosis when transitioning from immune‐checkpoint inhibitors to these novel BRAF‐dimerisation inhibitors, particularly as their uptake in treating cancers increases beyond clinical trials. Further studies are required to assess whether these next‐generation agents can trigger sarcoidosis de‐novo, or simply exacerbate pre‐existing sarcoidosis.Sarcoidosis is a non‐infective granulomatous disorder of unknown aetiology, with cutaneous involvement affecting up to 30% of patients. Drug‐induced sarcoidosis has been reported secondary to modern melanoma therapies including immune‐checkpoint inhibitors and first generation BRAF inhibitors such as vemurafenib and dabrafenib. Herein, we report a case of cutaneous micropapular sarcoidosis that first developed on immune‐checkpoint inhibition with ipilimumab and nivolumab for metastatic melanoma, which was exacerbated and further complicated by pityriasis rubra pilaris‐like palmar plaques upon transition to a next‐generation BRAF‐dimerisation inhibitor. Both the micropapular eruption and palmar plaques rapidly resolved after cessation of the novel BRAF‐inhibitor and concurrent commencement of hydroxychloroquine. It is unclear how inhibition of BRAF‐dimerisation results in granuloma formation, though upregulation of T His medical history was notable for asthma and prior psoriasis limited to scalp and inguinal regions. After surgical resection (NRAS‐Q61K mutation confirmed on sequencing), adjuvant nivolumab was commenced. New inguinal lymph node disease in November 2019 required addition of ipilimumab with a complete response in the inguinal node, but no response in the cutaneous metastases . Immune hepatitis and hypophysitis required cessation of ipilimumab after three cycles, and addition of oral prednisolone.A 36‐year‐old man was diagnosed with acral lentiginous melanoma of his left 4BRAF‐dimerisation inhibitor in January 2021.In July 2020 he developed micropapules involving the axillae and inguinal creases, diagnosed as cutaneous sarcoidosis on biopsy. Serum angiotensin converting enzyme (ACE) was elevated 1.2 times the upper limit of normal, with multi‐system reviews negative for systemic sarcoidal involvement. As the cutaneous sarcoidosis was asymptomatic, nivolumab was continued. Progressive cutaneous metastases to his left leg and arm precipitated transition onto a clinical trial of a novel In April 2021 the micropapular eruption extended to involve his torso, limbs, and dorsal feet Figure . ConcurrBRAF inhibitor to another clinical trial of combined MEK/FAK inhibitors. On review two months later, the micropapular sarcoid and palmar plaques had completely resolved.Application of topical steroids was impractical for the patient, so hydroxychloroquine was initiated. In June 2021 progressive lower limb cutaneous metastases triggered change from the novel A timeline of medical issues and management changes are summarised in Figure 4H1 and TH17 pathways are hypothesised.Sarcoidosis is a non‐infectious granulomatous inflammatory disorder of unknown aetiology, although upregulation of T4 monoclonal antibody binding to and inhibiting programmed cell‐death 1 (PD‐1) receptors, while ipilimumab is an IgG1 antibody inhibiting cytotoxic T‐lymphocyte‐associated protein 4 (CTLA‐4) receptors. Nivolumab and ipilimumab are immune‐checkpoint inhibitors (ICI's) blocking inhibitory or exhaustion signals on cytotoxic CD8+ T‐cells to direct immune activity against cancer cells, with superior outcomes compared to chemotherapy.Nivolumab is an IgGH17 T‐cell activity. CTLA‐4 inhibitors are associated with expansion of TH17 cells, while PD‐1 inhibitors increase their production of TH17 cytokines.Mechanisms of granuloma formation on ICI's are unclear, but may involve up‐regulation of TBRAF‐inhibition.BRAF or NRAS, increase cellular proliferation and survival – promoting oncogenesis.NRAS‐mutant tumours, as in our case, are not amenable to first‐generation BRAF‐inhibitors (such as vemurafenib or dabrafenib) as these preferentially inhibit BRAF‐v600E mutant cells. With the exception of mutant BRAF‐v600E, dimerisation is required for RAF‐kinase activation.BRAF‐inhibitor capable of inhibiting both monomeric and dimeric BRAF‐mutant kinases, as well as RAF dimerisation itself. Therefore, by inhibiting RAF fusion, such next‐generation BRAF‐inhibitors function as ‘pan‐RAF’ inhibitors, and unlike first‐generation BRAF‐inhibitors can be used to treat MAPK‐mutant tumours other than BRAF‐v600E  with trials underway.Sarcoidosis has similarly been reported on BRAF‐inhibition results in granuloma formation, however insight can be gleaned from biochemical studies of first‐generation agents. Vemurafenib and dabrafenib increase serum interferon (IFN)‐γ and tumour necrosis factor (TNF)‐α, TH1 cytokines instrumental for T‐cell and macrophage activation, and thereby granuloma formation, in sarcoidosis.reg) function in the tumour microenvironment, with impaired Treg‐cells also implicated in the pathophysiology of sarcoidosis.BRAF‐dimerisation.It is unclear how BRAF‐inhibitor. Sarcoidosis can rarely develop spontaneously in melanoma patients, with an incidence of 0.42%,BRAF‐inhibitor that remained until it was ceased suggests it also contributed to the eruption – possibly ‘primed’ by the ICI's. It is unknown if the MEK/FAK inhibitors contributed to the resolution of his sarcoid, as this has not been reported.In this case, the sarcoidosis was likely triggered by the ICI's then exacerbated by the novel BRAF‐inhibition. Psoriasiform sarcoidosis is unlikely as no granulomas were evident on biopsy. An exacerbation of the patient's pre‐existing psoriasis is also unlikely as definitive histological features of psoriasis were not seen. Inhibition of TNF‐α and IL (interleukin)‐17 have shown efficacy in treating PRP, suggesting TH1/TH17 cytokines are implicated in its aetiology, as with sarcoidosis.PRP‐like palmar plaques have not been previously reported on At both episodes of his sarcoid, cancer treatment was continued as the metastatic melanoma was deemed the treatment priority. Systemic immunosuppressants, such as methotrexate or TNF‐α inhibitors, were avoided as treatment for the sarcoid given their potential to promote melanoma progression.5BRAF‐dimerisation inhibitors can exacerbate cutaneous sarcoidosis when primed by immune‐checkpoint inhibition. Dermatologists may encounter such reactions more frequently as uptake of these novel agents increases for treating cancers beyond clinical trials. Further studies are essential in determining whether BRAF‐dimerisation inhibition can trigger sarcoidosis de‐novo; as well as identifying therapeutic approaches for the sarcoid in patients with underlying cancers where immunosuppression is not ideal.Our case demonstrates that next‐generation A. M. Menzies has served on advisory boards for BMS, MSD, Novartis, Roche, Pierre‐Fabre, QBiotics. R. P. M. Saw has received honoraria for advisory board participation from MSD, Novartis and Qbiotics and speaking honoraria from BMS and Novartis.J. P. Pham: Data curation; Investigation; Writing – original draft; Writing – review & editing. P. Star: Conceptualization; Data curation; Investigation; Writing – original draft; Writing – review & editing. S. Wong: Conceptualization; Data curation; Investigation; Writing – original draft; Writing – review & editing. D. L. Damian: Conceptualization; Data curation; Investigation; Writing – original draft; Writing – review & editing. R. P. M. Saw: Conceptualization; Data curation; Investigation; Writing – original draft; Writing – review & editing. M. J. Whitfeld: Conceptualization; Data curation; Investigation; Writing – original draft; Writing – review & editing. A. M. Menzies: Conceptualization; Data curation; Investigation; Writing – original draft; Writing – review & editing. A. M. Joshua: Conceptualization; Data curation; Investigation; Writing – original draft; Writing – review & editing. A. Smith: Conceptualization; Formal analysis; Investigation; Supervision; Writing – original draft; Writing – review & editing.


Ce, the electron thermal coefficient of pressure, and the coefficients of electron compressibility and thermal expansion in graphene at the LTT. All the thermodynamic parameters possess the strongest singularities in graphene at the LTT near the saddle points. This opens exciting opportunities for inducing and exploring the Lifshitz topological transitions in graphene.The origin of the Lifshitz topological transition (LTT) and the 2D nature of the LTT in graphene has been established. The peculiarities of the Lifshitz topological transitions in graphene are described at the Brillouin zone centre Γ, the zone corners K in the vicinity of the Dirac points, and at the saddle point M. A general formulation of the thermodynamics at the LTT in graphene is given. The thermodynamic characteristics of graphene are investigated at the Lifshitz topological transitions. Anomalies are found in the electron specific heat  The origin of the Lifshitz topological transition (LTT) and the 2D nature of the LTT in graphene has been established. This leads to a change in the connectivity of the Fermi surface , and at absolute zero temperature T = 0 K, the grand thermodynamic potential Ω  acquires an irregular correction:Anomalies in the thermodynamic quantities of metals due to a change in the topology of the Fermi surface z = μ − εc = 0 ; therefore, this change in the topology of the Fermi surface is also called the 2½-order phase transition (FT2½) according to the Ehrenfest terminology.6,7It can be seen that the third derivatives of the thermodynamic potential become infinite at the point T ≪ εF not only in the thermodynamic characteristics of metals but also in other characteristics . It has been shown in 17 gave new inspiration to investigations of the Lifshitz transition properties. To date, numerous papers have been devoted to the Lifshitz transitions in bilayer (BLG) and multilayer (MLG) graphene.18–30 The results of these studies indicate that the effects of the LTT are appreciable and can be used to observe the 2½-order transitions as well as to investigate the degree of smearing of the Fermi surface in metals. In 31 theoretically and experimentally.The anomalies arising in the LTT manifest themselves at 32–45 Apparently, the thermodynamics of graphene has been characterized from many points of view; however, the role of the Lifshitz topological transitions in the thermodynamic properties of graphene has not been studied. This paper aims to close this gap. Because graphene is the first real two-dimensional solid, a general formulation of the thermodynamics at the LTT in graphene is given. The unusual thermodynamic properties of graphene stem from its 2D nature, forming a rich playground for new discoveries of heat flow physics and potentially leading to novel thermal management applications.The 21st century has brought many new results related to graphene thermodynamics.This paper is arranged as follows. In section 2, the origin of the Lifshitz topological transition and the 2D nature of the LTT in graphene are considered. Peculiarities of the Lifshitz topological transitions in graphene are then investigated in section 3. The thermodynamics of graphene at the Lifshitz topological transitions is proposed in section 4. Finally, conclusions are drawn in section 5.2εc in the critical point of the momentum space p = pc, where the electron energy as a function of quasimomentum ε = ε(p) has a minimum εmin or maximum εmax. In this case, the isoenergetic surfaces in the vicinity of p = pc are well described by the ellipsoid equations:mx, my, and mz are the main values of the effective mass tensor in the vicinity of εmin  = εc contains the peculiar point of another type, named the cone point, at p = pc. In this case, the isoenergetic surface in the vicinity of the cone point p = pc is described by the hyperboloid of two sheets at energy ε < εc and the hyperboloid of one sheet at energy ε > εc  asD0(ε) is the regular smooth function of the energy, and δD(ε) depends on the type of LTT. The latter is computed by the relation :ħ is the reduced Planck–Dirac constant, and Δ(ε) is volume of the ellipsoid Δ(ε) is the change of the volume enclosed by the plane p3 = p0 and the hyperboloid of one p = pc.At energies close to mi  are the positive values of the effective mass tensor, mi ≠0, and integers aj  are equal to ±1.One can join aj.Four types of singularities exist of the density of the electron states in three-dimensional space, and the singularity type depends on the signs of the coefficients 0 (min) corresponds to the case where all three coefficients aj = +1. This point corresponds to the minimum in the energy spectrum.The point M1 (saddle) corresponds to the case where two coefficients aj are positive and the third one is negative. This is the saddle point (The point Mle point .2 (saddle) is the case where two coefficients aj are negative and a third one is positive. This is the second saddle point (The point Mle point .3 (max) corresponds to the case where all three coefficients aj = −1. This point corresponds to the maximum in the energy spectrum.The point Maj .There are three types of singularities of the density of the electron states in two-dimensional space, and the singularity type depends on the signs of the coefficients 0 (min) corresponds to the case where both coefficients aj = +1. This point corresponds to the minimum in the energy spectrum.The point P1 (saddle) corresponds to the case where one coefficient aj is positive and another one is negative. This is the saddle point.The point P2 (max) corresponds to the case where both coefficients aj = −1. This point corresponds to the maximum in the energy spectrum.The point PThere are two types of singularities of the density of the electron states in one-dimensional space:0 (min) corresponds to the case where coefficient a = +1. This point corresponds to the minimum in the energy spectrum.• The point Q1 (max) corresponds to the case where coefficient a = −1. This point corresponds to the maximum in the energy spectrum.• The point QThe analytical behavior of the density of the electron states at LTT is given in εc that nature of the Lifshitz topological transition stems from the van Hove singularities (VHS) of the state density δD(ε).48–52 In this connection, the van Hove topological theorem48 states that the spectrum must contain at least one of the saddle-points S1 and S2 (D(ε) must tend to −∞ on the upper end.We can conclude based on the square root peculiarities of the density of the electron states in three dimensions  at εc th1 and S2 , and themi ≠ 0 of the effective mass tensor; however, it is not applied to the massless Dirac fermions in graphene. If the logarithmic singularity is a general property of 2D electronic systems in the saddle points, this statement should be valid for 2D graphene. However, the latter is in contradiction with  because the value of C6 must be zero for the massless fermions in graphene. Here, the discrepancy arises because the logarithmic singularity vanishes. We will resolve this contradiction in section 3.The two-dimensional nature of graphene should exhibit special types of van Hove singularities and LTTs. This statement is illustrated by the general argument that in two dimensions, the saddle-points produce logarithmic singularities , and the55 It has been demonstrated in55 theoretically that the characteristic feature of a 2D system undergoing N consequent Lifshitz topological transitions is the occurrence of spikes of entropy per particle s of a magnitude ± ln 2/(J − 1/2) with 2 ≤ J ≤ N at low temperatures.Therefore, the Lifshitz topological transitions in graphene require special investigation. The latter was also confirmed by recent work.3e1 and e2 form the rhombic unit cell. The hexagonal lattice consists of two trigonal sublattices AAA and BBB.56 There are four valence electrons (two 2s and two 2p electrons). Three of those participate in the chemical bonding and thus are in bands well below the Fermi energy. We therefore consider the bands formed by the one remaining electron. We assume a tight-binding model in which the electron hops between neighboring atoms. We denote the spacing between neighbouring atoms by a.A single layer of graphene consists of carbon atoms in the form of a honeycomb lattice . The priFrom b1 and b2, are defined such thatThe reciprocal Bravais lattices, The result is The distance ΓΚ is These basis vectors are of equal length and at 120°; therefore, the reciprocal lattice is a hexagonal lattice . The firΨR for the electron to be at the site labeled by R. We look for the wave functions with amplitudes which vary, such as eik·r. There will be different amplitudes ΨA and ΨB on sublattices A and B, so ΨR = ΨAeik·r (R ∈ A), and ΨR = ΨBeik·r (R ∈ B). An electron at site R can hop to any of the neighboring sites. An atom on sublattice AAA has neighboring atoms (a),  and  An atom on sublattice BBB has three neighbors on sublattice AAA at displacements ,  and  In the nearest-neighbour approximation, there are no hopping processes within the sublattices AAA and BBB; hopping only occurs between them. Hence, the eigenvalue ε and the amplitudes ΨA and ΨB are determined for each wavevector k from two equations:γ0 is the hopping parameter between nearest neighbors.Consider a state with amplitude ng atoms , all on k = p/ħ (where p is the electron quasimomentum), taking into account We write the Hamiltonian in the tight-binding approximation for the wave vector The electron energy eigenvalues of the Hamiltonian In expression kx, ky) plane for different positions of the wave vector k.To explore the possible Lifshitz topological transitions, consider the structure of the isoenergetic lines in the  in εc = −3γ0 corresponds to the minimum of energy in the valence band (the point Po (min) in kya|, |kxa| ≪ 1, from kya)2, (kxa)2:(i) The maximum and minimum energies are centre Γ  of the fk = 0. It follows from p-space:Thus, the isoenergetic lines are circles in the vicinity of the extrema of energy at εc = ±3γ0, where the cavity εc = +3γ0 in the conduction band or appears at εc = −3γ0 in the valence band.Consequently, there exist LTT at critical values of energy Δ(ε) is the area of the cavity in the momentum space.The number of the electron states inside the two-dimensional cavity (per spin direction and per unit area) is equal toεc = 3γ0.We obtain from (3.13)δD(ε) due to LTT asOne can represent the change of the density of states ε = ±3γ0 comes from a maximum or minimum of the dispersion relation in two dimensions. The analytic expression without derivation for the total DOS in graphene for model (3.7) was provided by Hobson and Nierenberg in 1953.53 In a recent paper,54 the expression for this model was derived for the total DOS  is the complete elliptic integral of the first kind, i.e.The discontinuity at the end points of area   and one ε| ≲ 3γ0 in the vicinity of the LTT points |εc| = 3γ0, one obtains (per spin direction and per unit area):Expanding of δD (ε) coincides with the total D(ε) given by ε| ≲ 3γ0 in the vicinity of the LTT points |εc| = 3γ0, where at |ε| ≲ 3γ0.The result C5 and C7 in As follows from C5 and C7 in γ0/VF2 instead of  respectively, and this substitution can be treated as the fermion effective mass in the vicinity of the point Γ:K is the wavevector at the zone corner,  for example, and we will assume that κ is small.Hence, in 2D graphene, the mass-factors of coefficients κ we have, from To the lowest order in Substitution of εc = 0 (for the conduction band) or in the vicinity of the maximum of energy εc = 0  at the corner of the zone. It follows from p-space  in εc = 0 corresponds to the maximum of energy in the valence band (the point P2 (max) in The value of εc = 0, where the new cavity (3.25) appears  in the vicinity of the zone corners K(K′):Expanding the expression C6 and C7 for graphene in e.g. near the middle M of the boundary of the first Brillouin zone. We writeK is the wavevector at point M of the zone boundary , we must make the following substitutions for the coefficients boundary . The disqya|, |qxa| ≪ 1, we have from qya), (qxa)Taking into account |1 (saddle) in p-space in the vicinity of these saddle points . One can say that middles of the edges of the first Brillouin zone are saddle points. We can consider the corresponding points similar to M (the middles of the edges of the first Brillouin zone)  as the se points :3.363.37ε < εc to ε > εc, and εc = γ0. In this transition, the isoenergetic lines in the vicinity of point M change from hyperbole Δ(ε) enclosed by hyperbole py = ħ/a, or px = ħ/a, one obtains:εc = γ0.The Lifshitz topological transition is realized in the saddle point M by the variation of energy from  used in εc) is equal toNow, we are able to resolve the contradiction with the coefficient ε| → εc = γ0:Also, the expansion of C6 for graphene in Therefore, in the saddle point M, the coefficient C6 in γ0/VF2 instead of, and this substitution can be treated as the graphene effective mass in the vicinity of the saddle point M:Thereby, in 2D graphene, the mass-factor 57 Estimation of the values of mΓeffand mMeffyields :3.44mΓe44.1.μ is close to a value of the critical energy εc, the grand thermodynamic potential Ω  = μ, or to a decrease of the line connectivity.Transition from region I into region II corresponds to the appearance of a new cavity of the isoenergetic line εin graphene, while only the third derivative of δΩ diverges at the point z = 0 as z−1/2 in three dimensions. As a result, completely different anomalies will be obtained for the thermodynamic parameters at the Lifshitz topological transitions in graphene.From comparison of T → 0:z = εc − μ, εc= 3γ0.When the electronic cavity disappears in the Brillouin zone centre Γ, one computes from T → 0:z = μ − εc, εc= 0.Considering the appearance of new cavities in the Brillouin zone corners K, we obtain from μ = εc), it is convenient to use the Helmholtz free energy potential F 2 instead of the grand thermodynamic potential Ω . We assume that area S is the parameter connected with applied pressure, tensile stress, or other mechanical action. The critical energy is the function of the area, i.e. εc = εc(S), and the chemical potential μ is also a function of S because of constancy of the carriers:Because the number of electrons in the conduction band is permanent .According to F can be written in the formF0 is the smooth part of the free energy.The Helmholtz free energy potential δF is quantitatively equal to the irregular contribution δΩ expressed in the variables S and T according to the Landau theorem5 about the small variations of the thermodynamic potentials due to small changes of some parameters of the solid state:One can readily be convinced that δΩ given by the relations T ≪ z in the vicinity of the Lifshitz electronic transition, where z → 0.One can see that variations of δF is given by z| = η|S − Sc|.Thus, T → 0:z| = ηγ0|S − Sc|, ηγ0 = η(μ→γ0).In the case of the hyperbolic changes of the Fermi lines at the saddle point M, we obtain from T → 0:z| = ηγ03|S − Sc|, ηγ03 = η(μ→3γ0).When the electronic cavity disappears in the Brillouin zone centre, one obtains from T → 0:z| = η0|S − Sc|, η0 = η(μ→0).Considering the appearance of new cavities in the Brillouin zone corners, one obtains from 4.2.C = Cph + Ce. However, phonons dominate the specific heat of graphene58 at all practical temperatures (>1 K),59,60, and the phonon specific heat increases with temperature.62 The electron specific heat Ce of monolayer graphene (MG) is given by the following relations:62S is the sample area and kB is the Boltzmann constant.The specific heat of graphene is stored in the lattice vibrations (phonons) and the free conduction electrons of graphene, We can explore the electron-specific heat peculiarities of monolayer graphene at the LTT based on expressions of the change of the Helmholtz free energy by T → 0:z = ηγ0|S − Sc|.In the case of the hyperbolic changes of the Fermi lines at the saddle point M, one obtains from T → 0:When the electronic cavity disappears in the Brillouin zone centre Γ, one computes from T → 0:z| = η0|S − Sc|, η0= η(μ → 0).Considering the appearance of new cavities in the Brillouin zone corners K, we obtain from Thus, the formulae MGeof the monolayer graphene (MG) obtained in paper.61 Indeed, substituting , and expressing T in Kelvins, one obtains from The results for the specific heat μ of graphene does not exceed 1 eV,63 and the estimated value of the overlap integral γ0 is between 2 and 4 eV.64–66 Tuning of the chemical activity of graphene in a wide range could be achieved by the formation of a Moiré superstructure between the graphene and transition metal substrate.67 Thus, to observe the LTT at the graphene saddle point (where |z| = |μ − γ0| → 0), we must increase the chemical potential μ or decrease the overlap integral γ0 due to strain. Increasing μ can be realized by electron doping due to renormalization of the electron spectrum.68 It has been demonstrated in μ at low temperature T ≪ μ, especially for high carrier concentrations of n0 > 1011 cm−2. The band structure of graphene has been determined under strain using density functional calculations.69 The ab initio band structure was then used to extract the best fit to the tight-binding hopping parameters used in a microscopic model of strained graphene.70 It was found that the hopping parameters may increase or decrease with increasing strain depending on the orientation of the applied stress. The fitted values were compared with an available parameterization for the dependence of the orbital overlap on the distance separating the two carbon atoms.Note that experimental observation of singularities 4.3.71,72The compressibility of graphene is an important object of study in condensed matter physics because it gives information about the intrinsic nature of the electron structure of graphene and its interactions with external fields.T → 0:z = ηγ0|S − Sc|.In case of the hyperbolic changes of the Fermi lines at the saddle point M, we obtain from T → 0:ηγ03= η (μ → 3γ0).When the electronic cavity disappears in the Brillouin zone centre, one obtains from T → 0:z| = η0|S − Sc|, η0= η(μ → 0).Considering the appearance of new cavities in the Brillouin zone corners, one obtains from As a result, the 4.4.T → 0:z = ηγ0|S − Sc|.In case of the hyperbolic changes of the Fermi lines at the saddle point A, we obtain the change of the electron thermal coefficient of pressure from T → 0:ηγ03= η(μ → 3γ0).When the electronic cavity disappears in the Brillouin zone centre, one obtains from T → 0:η0 = η(μ → 0).Considering the appearance of new cavities in the Brillouin zone corners, one obtains from The 4.5.e.g., specific heat and thermal expansion) are based on density-functional theory (DFT) calculations combined with a quantum quasi-harmonic approximation (QHA) for the vibrational modes.73,74 This is expected to yield reliable results at low temperature for the graphene lattice contribution to the thermal properties; however, it may be questioned with respect to the graphene electron part. The answer to the latter can give the Lifshitz topological transitions.The thermal properties of graphene have been investigated in recent years; in particular, its thermal expansion and heat conduction have been studied by various theoretical and experimental techniques in T → 0:z = ηγ0|S − Sc|.In the case of the hyperbolic changes of the Fermi lines at the saddle point M, we obtain the change of the electron thermal expansion coefficient from T → 0:ηγ03= η(μ → 3γ0).When the electronic cavity disappears in the Brillouin zone centre, one obtains from T → 0:z = η0|S − Sc|.Considering the appearance of new cavities in the Brillouin zone corners, one obtains from T ≪ |z|, like the lattice thermal expansion coefficient of graphene  corresponds to the minimum in the energy spectrum. The point P1 (saddle) corresponds to the case where the Lifshitz topological transitions are realized by variation of the energy from ε < εc to ε >εc. The point P2 (max) corresponds to the maximum in the energy spectrum.(i) Connection of the Lifshitz topological transition has been established with the van Hove singularities of the electron state density in graphene. There are three types of singularities of the density of the electron states in two dimensions. The point Pεc = 3γ0, where the cavity of the isoenergetic lines disappears. The existence of the LTT is shown at the critical energy value of εc = 0, where six pockets of low energy excitations appear, one for each of the two inequivalent Dirac points K and K′.(ii) Peculiarities of the Lifshitz topological transitions in graphene are described at the Brillouin zone centre Γ, at the zone corners K, in the vicinity of the Dirac points, and at the saddle point M. It is found that LTT can be realized in the centre Γ at the critical energy value ε < εc to ε > εc and at the critical value of energy εc = γ0. It is shown that the Dirac fermion slows down in the vicinities of the points Γ and M, becoming not massless but massive, and the values of the fermion effective mass in the vicinity of these points are mΓeff ≈ 0.1me, and mMeff ≈ 0.1me (where me is the free electron mass).The Lifshitz topological transition is realized in the saddle point M by variation of the energy from Ce, the electron compressibility , the electron thermal coefficient of pressure , and the electron thermal expansion coefficient . The anomalies are described in terms of the Lifshitz parameter z = μ − εc. The electron specific heat Ce diverges at the saddle point M as ln|z| and is proportional to |z| at points K and Γ of the first Brillouin zone. The electron compressibility  diverges at the saddle point M as ln|z|, is proportional to |z| at points K, and takes a constant value at point Γ of the first Brillouin zone. The electron thermal coefficient of pressure  diverges at the saddle point M as 1/|z|, and it becomes negative in the vicinities of points K and Γ of the first Brillouin zone. The electron thermal expansion coefficient  diverges at the saddle point M as 1/(|z| ln |z|) becoming negative in the vicinity of point Γ, and it diverges as 1/|z| at point K of the first Brillouin zone.(iii) The thermodynamic characteristics of graphene were investigated at the Lifshitz topological transitions. A general formulation of the thermodynamics at the LTT in graphene is given. The anomalies are found at the LTT of the electron specific heat μ does not exceed 1 eV.63 Therefore, it is essential to tune μ through the VHS by chemical doping76,77 or by gating.17,57,78–81 In recent work,82 a simple technique of doping graphene by manipulating adsorbed impurities was reported, and a change in the electron mobility of 650% was observed. Also, it is worth paying experimental attention to the tuning of μ through the VHS by the following two methods. The first method is connected with deformation of the graphene monolayer to mimic twisted graphene. Rotation between two stacked graphene monolayers in twisted graphene83 can generate van Hove singularities, which can be brought arbitrarily close to the chemical potential μ by varying the angle of rotation.84 The second method consists of investigating the LTT in graphene under 3D high pressure.84 This opens exciting opportunities for inducing and exploring the Lifshitz topological transitions in graphene.One can conclude that all the thermodynamic parameters possess the strongest singularities in graphene at the LTT near the saddle points M. In 2D graphene, a saddle point M in the electronic band structure leads to a divergence in the density of states of the logarithmic-type van Hove singularities (VHS). This implies the possibility of experimental observation of the LTT by bringing the chemical potential μ and the VHS together. However, one cannot change the position of the VHS in the band structure. It is pointed out in section 4.2 that the accessible experimental value of the graphene chemical potential This work includes theoretical investigations.The paper has been written without any assistance, and I gave final approval for publication.The work has no source of funding.This work did not involve any ethics statements.I have no competing interests.


In order to improve the corrosion resistance and conductivity of the ACF, graphene nanosheets were modified on the surface of the ACF by electrospraying for the first time. The results show that this graphene modification could be carried out continuously on a meter scale. With the modification of the graphene layer, the corrosion rate of graphene-decorated ACF (G/ACF) can be reduced by 74.56%, and after 72 h of salt spray test, the conductivity of ACF samples without modification of graphene can be reduced by 34.1%, while the conductivity of G/ACF samples with modification of graphene can be reduced by only 6.5%. This work proves the potential of graphene modified ACF to prepare robust large-area transparent conductive film.Transparent conductive films are widely used in electronic products and industrial fields. Ultra-thin Ag conductive nanofilm (ACF) was prepared on a soda lime silica glass  substrate with industrial magnetron sputtering equipment with AZO (Al Transparent conductive film is an important component of instrument panels, electronic touch screens, optoelectronic devices, modern wearable electronics, and other devices ,2,3. BecITO (indium tin oxide) is a typical representative of current high-performance transparent conductive films because of its excellent optoelectronic properties . HoweverIn order to replace ITO, Al-doped ZnO films (AZO) , metal m3, ITO, and MgF2 to realize composite Ag film with high conductivity [During the conventional film forming process, Ag atoms nucleate first, and then grow in the vertical and horizontal directions to form three-dimensional grains; in this way, only three-dimensional structure grain-like “islands” can be formed when the thickness of Ag film is 10–20 nm, with which it is difficult to form a continuous conductive silver film . Howeveructivity ,22,23. HHerein, we prepared an ACF on a soda lime silica glass  substrate with industrial magnetron sputtering equipment with AZO as the crystal bed and wetting layer. In order to improve the corrosion resistance and conductivity of the ACF, graphene nanosheets were modified on the surface of ACF by electrospraying. Moreover, this graphene modification could be carried out continuously on a meter scale. After modification, the corrosion rate of the ACF decreased by nearly an order of magnitude, which improved its durability significantly. Meanwhile, the ACF kept a low surface resistance of 11.1 Ω/sq and relatively high transmittance of 57.25% (weighted average of visible region). The method may also be used in flexible substrates such as polyethylene terephthalate to realize the preparation of large-area flexible transparent conductive films.x, AZO, Ag, NiCr, and SiNx layers were sequentially sputtered from Si, Al-ZnO, Ag, NiCr, and Si sputtering targets under the N2, O2-Ar, Ar, Ar, and N2 atmosphere, respectively. The initial vacuum of the sputtering chamber was 1 × 10−6 mbar, and the working pressure was maintained at 5 × 10−4 mbar. The SiNx layer was deposited with reactive sputtering, in which a Si target was sputtered by a medium frequency AC power supply, 34 kHz, 600 V, 80 A, and N2 was the reaction gas, with the volume flow ratio of N2: Ar = 40:60. The AZO layer deposition also used a medium frequency AC power supply, 24 kHz, 500 V, 10 A; the molar ratio of Zn: Al in the target was 95:5; and the working gas included O2 and Ar, of which the volume flow ratio was 5:95. Both Ag and NiCr layers were deposited with a DC power supply, 300–500 V, 5–8 A, and the working gas was Ar. The thickness for every layer was monitored with a digital thickness monitor connected with a dual quartz crystal microbalance inside the sputtering chamber. The thicknesses of SiNx, AZO, NiCr, and SiNx layers were 25 nm, 5 nm, 5 nm, and 48 nm, respectively. In order to study the effect of silver nanolayer thickness, we prepared intermediate ultra-thin silver nanolayer samples with the thickness of 3 nm, 6 nm, 9 nm, 12 nm, and 15 nm, respectively. The SiNx layer improves the surface smoothness of the soda lime silica glass, prevents the precipitation of sodium ions in the glass, and improves the surface activity of the glass to facilitate the adhesion of the AZO layer. As a wetting layer and crystal seed, the AZO layer can inhibit the island effect of Ag sputtering deposition and reduce the critical thickness and surface roughness of continuous Ag film. The NiCr layer and outer SiNx layer are protective layers to reduce the oxidation and vulcanization of Ag layer in atmospheric environment. The outer SiNx layer is also an antireflection layer to improve the transmittance of visible light.Ultra-thin Ag conductive films were prepared by an industry magnetron sputtering system  with the soda lime silica glass  as model substrates. After the cleaning of the substrate surfaces, SiNGraphene nanosheets were prepared by direct exfoliation of vermicular graphite particles dispersed in deionized water without the presence of a surfactant. Then, the as-prepared graphene nanosheets were dispersed in the deionized water with a volume ratio of 5% ethanol to form a suspension with a concentration of 20 ppm. A conventional electrospinning setup was refitted by increasing the single nozzle of electrospinning to 5 nozzles in a row (nozzle spacing was 2 cm) for electrostatic spraying experiments. Meanwhile, a stepping motor was used to control the moving speed and range of the nozzles (50 mm/min over a width of 100 mm), so as to realize the uniform spraying of the graphene nanosheets on the substrates surface. The conductive glass substrates were placed on the rotating table with a diameter of 10 cm to receive graphene nanosheet microdroplets. During electrospraying, graphene nanosheet suspension was injected through 5 nozzles with the rate of the 10 mL/h for each syringe, with the electrospraying voltage as 15 kV . The distance between the nozzle tip and the G/ACF substrate was kept as 5 cm. After electrospraying, the excess amount of water on the G/CAF was wiped away with filter paper. The thickness of the graphene-decorated films was adjusted by the electrospraying time.x/AZO/Ag/AZOII” samples, of which the AZOII layer was just used to prevent the oxidation of the silver. Its thickness was only about 3 nm, so that we could use an ordinary X-ray photoelectron spectroscopy  to detect the silver layer surface.The transparency and reflectivity of ultra-thin Ag conductive films and G/ACF films were measured using UV-Vis spectroscopy . The sheet resistance (Rs) was measured using a surface resistance meter . The morphology of graphene nanosheets and the ACF and G/ACF films after corrosion was evaluated with a field-emission scanning electron microscope . The salt spray test was carried out in the salt spray box  and the corrosion electrochemical experiment was tested by electrochemical workstation . Raman spectra and mapping , microscopic characterization , and a contact angle test  were also carried out. In order to determine the chemical state of the silver layer surface, we prepared “Glass/SiNIn a multilayer composite film, the interfacial stability between any two layers needs much attention. Herein, the state of interface between the metal Ag layer and oxide AZO layer in the ACF film is worthy of special research. The XPS full spectrum and Ag 3d5/2 peak fitting spectrum are shown as Graphene, which is composed of a densely packed sp2-honeycomb network of C, shows excellent chemical inertness and impermeability to molecules even as small as He, thus enabling it protect the underlying metal substrates from corrosion . Liquid −1) and a sharp G peak (~1548 cm−1) and 2D peak (~2680 cm−1), which confirmed the high quality of the as-prepared graphene nanosheets together with the morphology measurements [The homogeneous two-dimensional graphene nanosheets were firstly prepared by direct exfoliation. The continuity and wrinkles in the graphene nanosheets are obviously shown in the SEM b and TEMurements . Figure urements . As show2 as the working electrode, Ag/AgCl electrode as the reference electrode, and a Pt sheet as the counter electrode. Silicone rubber was used to expose the working electrodes with the desired area, and all measurements were conducted in 5% NaCl solution. The CHI 660E electrochemical workstation was used to provide the applied potential and to record data.The electrochemical method is considered to be a reliable method to evaluate the corrosion resistance of the protective layer . Figure −1, all samples showed typical Tafel polarization. Compared with the bare ACF samples (Sample 1 and 2), the graphene-decorated ACF samples  all displayed a decrease in corrosion current density (Icorr). Meanwhile, the corrosion potential (Ecorr) of all the graphene-decorated ACF samples was shifted to a more positive potential. The positively shifting Ecorr means that the G/ACF samples can only be corroded at a higher potential compared with their bare counterparts, which indicates that the graphene layer can provide protection to the underlying ACF. The experimental result in corrI (extracted from the Tafel plots) by the following formula [K is 3272 mm yr−1, the equivalent weight WE is 107.87 g for Ag, the material density ρ is 10.49 g/cm3, and A is 1 cm2 as the exposed area of the samples.Corrosion rate is an important indicator of corrosion resistance and can be calculated using the  formula ,28,29:. During the tests, the samples were exposed to a seawater analogue that was prepared by 5% NaCl solution adjusted to pH = 6.5–7.2 with HCl under the ISO 3768-1976 method. Moreover, the samples were tested with microscope, SEM, optical, and electrical spectra after a certain time of salt spray.It has been reported that graphene possesses a low surface energy that leads to inherent hydrophobicity . As showIn summary, we realized the preparation of large-area and high-quality ACF on soda lime silica glass by introducing an isolation layer and wetting layer in this work. Aiming at the problem that Ag nanofilm is unstable and easily corroded, we controllably modified the graphene layer on the surface of the ACF layer by electrospraying, and this graphene modification could be carried out continuously on a meter scale. The modified graphene layer has no adverse effect on the light transmittance and conductivity of the ACF layer, but shows obvious corrosion resistance, and has a more obvious protective effect on ACF samples with high conductivity. After modification of the graphene layer, the corrosion rate of G/ACF can be reduced by 74.56% compared with that of the bare ACF sample. The conductivity of ACF samples without modification of graphene can be reduced by 34.1% after 72 h of salt spray test, while the conductivity of G/ACF samples with modification of graphene can be reduced by only 6.5%, which demonstrates the anti-corrosion ability of the graphene layer. Therefore, a new method with industrial potential to prepare robust large-area transparent conductive film is proposed. This method can also be extended to flexible substrates to prepare flexible transparent conductive films, which can be applied to the field of large-scale flexible transparent electronic devices.


L1 and L2 containing electron-rich quinoline and anthracene rings were designed. L1 is AIEE active in a MeOH-H2O solvent system while formed aggregates as confirmed by the DLS measurements and fluorescence lifetime studies. The chemosensor L1 was used for the sensitive, selective, and reversible ‘turn-on’ detection of Al3+ and Ga3+ ions as well as Aspartic Acid (Asp). Chemosensor L2, an isomer of L1, was able to selectively detect Ga3+ ion even in the presence of Al3+ ions and thus was able to discriminate between the two ions. The binding mode of chemosensors with analytes was substantiated through a combination of 1H NMR spectra, mass spectra, and DFT studies. The ‘turn-on’ nature of fluorescence sensing by the two chemosensors enabled the development of colorimetric detection, filter-paper-based test strips, and polystyrene film-based detection techniques.In this work, two Schiff-base-based chemosensors  Kb was L1 or L2) versus the concentration of analytes  while σ is the standard deviation of ten blank replicate fluorescence measurements of chemosensors (L1 or L2) . In . In L1–A3+/Ga3+ ions to L1 and L2. Both chemosensors L1 and L2 offer three types of functional groups: phenolic-OR (R = -CH2- or -CH3), imine-N, and quinoline-N. Both Al3+ and Ga3+ ions are hard acids and are thus likely to interact and/or bind preferentially with the phenolic-OR followed by imine-N [L1 and L2, the position of the quinoline-N is likely to play a crucial role. In the case of L1, the binding of a metal ion through phenolic-OR (R = -CH2-), imine-N, and quinoline-N results in the formation of both six- and five-membered chelate rings and supports chelation-enhanced fluorescence. It is important to mention that a metal ion (Al3+/Ga3+) is situated significantly above (approx. 2.7–2.8 Å) the plane of L1 to facilitate the simultaneous coordination of phenolic-OR, imine-N, and quinoline groups, as depicted by the DFT studies (vide infra). Due to the formation of such chelate rings, L1 achieves structural rigidity while the intramolecular bond rotation of the imine-N group becomes restricted , and quinoline-N were shifted downfield, confirming their involvement in binding to the Al3+ ion. Moreover, the quinoline ring protons also shifted downfield, thus further confirming their role in binding. Importantly, both -CH2- and -CH3 protons were completely resolved, indicating a difference in their chemical environment after the binding of the Al3+ ion. Further, anthracene ring protons were also perturbed after the potential coordination of an Al3+ ion. Notably, various aromatic protons were found to split to give multiplets. We propose that imine-N, phenolic-OR, and quinoline-N form a pocket in which a metal ion nicely resides. Such a binding mode affects the chemical environment of nearby arene rings and hence multiplets were observed [All studies pointed to a similar mode of binding of both Alerformed . When seobserved .L2, the position of quinoline-N was changed, which is now anti to the imine-N group. As a result, the formation of a common binding pocket was not possible. It is therefore proposed that a larger Ga3+ ion is able to interact with both phenolic-OR  groups and imine-N. As the Al3+ ion is smaller in size, it could not interact with all three groups, and hence L2 did not show its recognition. The enhanced emission was observed due to the suppression of PET and ‘turn-on’ of CHEF. As the quinoline ring was not involved in binding to a Ga3+ ion, FRET was not operative [1H NMR spectral studies where protons of both phenolic-OR and imine-N displayed a downfield shift whereas both quinoline and anthracene rings remained unaffected 3, and a CH3OH solvent, respectively. It is important to note that, for both species, the isotopic distribution patterns nicely matched that of the simulated patterns. The mass spectra further asserted a 1:1 metal binding stoichiometry to L1 [3+ and Ga3+ ions .All chemical structures were optimized by the DFT using the suitable basis sets and functional  the plane of the chemosensor to facilitate the simultaneous coordination of all binding sites. The optimized structure of L2–Ga3+ confirmed the involvement of the phenolic-OCH3 group  in binding in addition to the phenolic-OCH2- group. In contrast, quinoline-N was situated farthest at 6.19 Å from the Ga3+ ion and thus remained uncoordinated. To better understand the electron density shifts, contour plots of the frontier molecular orbitals (FMOs) from HOMO-4 to LUMO+4 were visualized (L1 (3.42 eV) and L2 (3.64 eV) decreased to 2.42, 2.85, and 3.44 eV corresponding to L1–Al3+, L1–Ga3+, and L2–Ga3+, respectively  of 5.09 ns with a nearly 1.5-fold enhancement  protons displayed a downfield shift  with both Al3+ and Ga3+ ions and Asp when compared to other metals and amino acids [L1 . Such peelable polystyrene films displayed enhanced emission under UV light for the detection of both Al3+ and Ga3+ ions as well as Asp from their aqueous solutions. Similarly, filter paper test strips containing L1 were able to detect both Al3+ and Ga3+ ions  and Asp  from the aqueous solutions of different metal ions and amino acids [3+ ions , were able to detect concentrations as low as 5 μM by showing color change from blue to cyan under the UV lamp (3+ and Ga3+ ions as well as Asp for practical on-site detections.The ‘turn-on’ detection of Alensor L1 . The colno acids . Next, pno acids . Importa UV lamp . Hence, L1 and L2, decorated with electron-rich quinoline and anthracene rings. Chemosensor L1 displayed AIEE in a MeOH-H2O solvent system due to the suppression of PET. DLS measurements and fluorescence lifetime studies confirmed the aggregation of L1 in the presence of water. Chemosensor L1 was utilized for the sensitive, selective, and reversible detection of Al3+ and Ga3+ ions in the presence of other metal ions. L1 displayed ‘turn-on’ emission in the presence of both Al3+ and Ga3+ ions with high binding constants and low detection limits. Chemosensor L2, a structural isomer of L1, was able to discriminate between the Al3+ and Ga3+ ions and was exclusively selective for the Ga3+ ion with an impressive detection limit and a high binding constant. The discriminative sensing ability of L2 was due to the presence of different binding sites which was substantiated by the 1H NMR spectra, mass spectra, and DFT studies. The chemosensor L1 was further utilized for the selective and sensitive detection of Asp amongst all 20 amino acids. Chemosensor L1 exhibited a ‘turn-on’ fluorescence response in the presence of Asp with a remarkable detection limit and binding constant. The ‘turn-on’ nature of the fluorescence sensing by these chemosensors allowed for the fabrication of colorimetric detection, filter-paper-based test strips, and polystyrene-film-based detection strategies.This work illustrates two Schiff-base-based chemosensors,


Electron doping of graphene has been extensively studiedon graphene-supportedsurfaces, where the metallicity is influenced by the substrate. Herewithwe propose potassium adsorption on free-standing nanoporous graphene,thus eluding any effect due to the substrate. We monitor the electronmigration in the π* downward-shifted conduction band. In thisrigid band shift, we correlate the spectral density of the π*state in the upper Dirac cone with the associated plasmon, blue-shiftedwith increasing K dose, as deduced by electron energy loss spectroscopy.These results are confirmed by the Dirac plasmon activated by theC 1s emitted electrons, thanks to spatially resolved photoemission.This crosscheck constitutes a reference on the correlation betweenthe electronic π* states in the conduction band and the Diracplasmon evolution upon in situ electron doping of fully free-standinggraphene. An increase of electronic charge in the conduction bandcan significantly reduce the electrical resistivity, as observed alsoin graphite and carbon nanotubes.24 thanks to their simple electronic configurations, and the chemicaldoping can open new routes to explore the response of metallic Grat increasing electron charge transfer, up to a downshift of the π*conduction band (CB) with the Fermi level by more than 1 eV into theCB.25 In particular, AM doping significantly affects thelow-frequency dielectric response of graphene, which is determinedby the collective charge oscillation of the π* electron density n, i.e., the so-called Dirac plasmon (DP). Doping can alsobe obtained in electrostatically gated graphene transistors, wherethe applied gate voltage moves the Fermi level up to a position ofhigher π* state density,27 slightly modifyingthe vibrational and plasmonic response coupling.8 However, this method cannot be effectively employed infree-standing Gr as proposed here because of the low efficiency ofthe gate and the structural instability of suspended Gr under an appliedfield.Alkali metals (AMs) can act as electron donors on carbon-basedmaterials and organic systems,20 or a straightforward Dirac cone shift, with unperturbed band topology.25 As frequently interpreted alsofor electron-doped graphite,2 a rigid bandmodel shift induced by the charge migration can catch the salientphenomenology due to the AM doping in a low doping regime, where boththe band topology and the high group velocity are preserved. As faras plasmon excitation is concerned, it has been extensively investigatedwith high-resolution electron energy loss spectroscopy (HREELS) inthe case of substrate-supported30 graphene or by infrared/terahertzexcitation light in a gated graphene,32 while to thebest of our knowledge no detailed investigation has been yet reportedfor fully suspended graphene.Whereas theoretical calculations have often been carriedout forAM on ideal Gr, experimental studies have been performed only forAM adatoms deposited on supported Gr, unraveling discordant conclusions,like a gap opening irrespective of the AM and the substrateSupporting Information, SI), with a negligible defect density that presents the hallmarksof an ideal semimetallic Gr layer, as recently shown by Raman andphotoelectron spectroscopy studies.34 Thus, NPGcan mimic an ideal graphene particularly apt for doping with AMs,monitoring the occupation of the π* conduction band correlatedwith the Dirac plasmon evolution.We herewith propose a fine controlof the graphene metallicity,i.e., the doping level, giving insight into the interrelationshipbetween the electronic spectral density in the conduction band andthe plasmonic spectrum, by combining state of the art photoelectronspectromicroscopy and high-resolution electron energy loss spectroscopy.To circumvent the effects due to the substrate, we deposit potassiumon fully unsupported large size and free-standing nanoporous graphene(NPG). NPG is a high-quality single- or double-turbostratic and lowinteracting layer graphene, with a continuous surface in space (seemicroscopy images in the 34 A scanning electron microscopy (SEM) image of this NPG is reportedin SI).A pivotal challenge to finelycontrol the Fermi level positionand the metallic state of Gr is to employ fully free-standing Gr specimenswith high specific surface area, where alkali metals can homogeneouslyadsorb to form a thermodynamically stable arrangement. Nanoporousgraphene is an ideal candidate for this purpose. It is constitutedby a compact, bicontinuous interconnected three-dimensional (3D) arrangementof high-quality Gr veils, constituted by single or weakly interactingbilayer(s) of Gr, stacked in a twisted turbostratic arrangement, asrecently assessed by transmission electron microscopy and Raman measurements.35 is reported in SI. The average K:C core-level intensity ratio after normalizationto each core-level excitation cross section35 is shown in IK/IC ≃0.12, compatible with the predicted (2 × 2) phase with a KC8 stoichiometry with each K adatom expected in the hollow sitesat the center of one Gr honeycomb lattice every two lattices.25 This configuration is suggested by DFT-LDA predictionswith an energy landscape of the stable (2 × 2) structure computedfor K adsorbed on graphite,17 while potassium adsorbedon Gr supported on surfaces unravels a more complex phase diagramdriven by thermodynamic forces and adsorption architectures, inducedby the substrate.25To determine the adsorption process and to quantifythe potassiumcontent on NPG during the K deposition in an ultrahigh vacuum, weemploy X-ray photoelectron spectroscopy (XPS). The C 1s and K 2p core-levelphotoemission spectra for the clean NPG and for subsequent K exposuresup to saturation coverage are displayed in 2 planar configuration.The work function(WF) variation with respect to the pristine NPGas a function of the K evaporation time is reported in ED with respect to the Fermi level, i.e., (EF – ED) =ΔE, as can be verified in panel (c) of SI).A fine control of theevolution of the electronic structure closeto the Fermi level as a function of K doping is reported in the UVphotoemission valence band data shown in 36 with respect to thatof pristine free-standing graphene (vF = 1 × 106 m/s), and the estimated accumulated chargeis n = (3.4 ± 0.8) × 1013 cm–2 for the saturation coverage.From the VB shift, we can therefore approximatelycalculate theinjected charge density according to the formula: The electron chemicaldoping of free-standing Gr by K adsorptionprovides the opportunity to investigate the collective charge oscillationsof the electron density in the upper Dirac cone. Combining HREEL datawith complementary UPS measurements, we are able to follow the evolutionon the plasmon excitation as a function of K doping.E (asdetermined by UV photoemission and checked by XPS). In panel (a) thespectrum of the pristine NPG is compared with that corresponding toΔE = 0.28 ± 0.02 eV. While the formeris essentially featureless, displaying a Drude-like quasi-elastictail characterized by a power-law line shape, upon K doping we observethe growth of a clearly defined and asymmetric feature, related tothe plasmon excitation. SI)—for increasing valuesof ΔE and the Dirac cone energy shift. Theloss feature is quite asymmetric, showing a blue-shift and a markedbroadening upon increasing potassium doping. The energy value associatedwith the plasmon mode—corresponding to the loss feature maximum—isreported in the inset of 37 We observe a very notable increase in plasmon broadening vs K doping,corresponding to an increased damping due to an increased probabilityof e-h π–π* pair excitations.38 The nature of the band asymmetry and the possible presenceof more complex multiple modes39 are controversial andstill debated.A selectedset of HREELS spectra of K-NPG are reported in SI). We pick up two exemplary C 1s peaks with limiting K:C ratios,reported in panel (a) of 2 component), whose intensity is proportionalto the local coverage of K.Interestingly, the here reported evidence of adoping-dependentplasmonic feature helps to clarify the modification of the C 1s lineshape upon K adsorption, as shown in SI). In fact, the high-BE spectral tail cannot be merely explainedby an increasing metallic asymmetry.40 Thepresence of an additional high-BE feature is essential to reproducethe experimental results, which can be ascribed to the excitationof the Dirac plasmon by the outgoing photoelectrons. The plasmon energyincreases as a function of K doping , but no experimental investigation of the C 1s core level of AM-dopedGr has been taken into consideration the occurrence of an effectiveand distinct plasmon loss. From the theoretical point of view, Despojaet al.42 simulated the C 1s core levelof free-standing graphene for different levels of doping, enlighteningthe increasing probability of interband transitions from π toπ* bands as a function of doping, but also claimed the occurrenceof a π* plasmon due to the charge migration in the upper Diraccone, in agreement with our findings.Only few experimentalpapers have observed an unresolved shoulderon the high-BE side of the main C 1s peak in AM-doped supported Grand graphite,SI), andthe distinctive well-resolved π* plasmon peak due to the electronfluctuations in the conduction band, while the contamination givesonly a negligible residual (see SI). Itis worth noting that a rigid band model can explain the evolutionof the plasmon as a function of electron doping if the Dirac coneΔE is in an energy range comparable with thevan Hove singularity.42 The quasiparticle energy as afunction of K dose can be compared to the maximum of the plasmonicfeature measured by HREELS. In A key finding of our highenergy resolved micro-XPS experimentis that the C 1s core-level high-BE side can be interpreted as thesuperposition of the electron–hole pairs due to the interbandtransition from π to π* bands, giving rise to the asymmetrictail of the main peak graphene plasmonic excitation as a function of the K doping. Thesecorrelated experimental findings on the plasmonic response and Diraccone evolution in electron-doped free-standing graphene establisha reference point, though a careful theoretical investigation candistinctively clarify the evolution of the quasi-particle spectrumin the phase space.30Mn70 alloy were first synthesizedby melting pure Ni and Mn in an Ar-protected arc melting furnace,and then they were annealed to become microstructured and composition-homogeneousalloys and rolled to thin films. In order to obtain the nanoporousNi template, the NiMn alloy sheet was chemically dealloyed with 0.5M ammonium sulfate for nanoporous Ni. The nanoporous Ni was used asa CVD substrate, and benzene was then used as precursor for CVD graphenegrowth at 900 °C for 5 min. The graphene sheet covering nanoporousNi and presenting its same three-dimensional morphology was subsequentlyexfoliated by chemical dissolution of the Ni template by 1.0 M hydrochloricacid. The synthesis and preparation process are described in detailelsewhere.48Nanoporous graphene was grown througha nanoporous Ni template by means of chemical vapor deposition (CVD).Ingots of Ni49Prior to the spectroscopic data acquisition in each UHV apparatusin each laboratory, the NPG samples were degassed at 600–620°C for several hours to remove contaminants from air exposure.–10 mbar range) by using commercial SAES getterdispensers, after overnightdegassing at currents slightly below the sublimation onset. The sublimationrate was kept as constant as possible in each measurement set, andit was similar in the different UHV chambers, by using equivalentdispensers mounted in each apparatus.Potassium was sublimated in UHV (in the10–10 mbar), and the sample was kept cooled at a liquid nitrogen temperatureduring measurements, to avoid radiation damage.34The spectromicroscopy photoemissionexperiments were performed at the ANTARES beamline of the SOLEIL synchrotronradiation facility (France). The nano-X-ray photoelectron spectroscopy(XPS) microscope is equipped with two Fresnel zone plates for beamfocusing, ensuring spatial resolution in raster imaging down to the400–500 nm scale. The NPG sample was positioned at the commonfocus point of the hemispherical analyzer and the Fresnel zone plates,by mounting it onto a precision positioning stage. In the imagingmode the spectrum of photoelectrons in the desired energy range wascollected on the 2D detector at each point of the spatial raster havinga submicrometer step. Core-level spectra were taken with 350 eV photonenergy, to enhance the surface sensitivity, and the analyzer passenergy was set to 50 and 200 eV for the spatially integrated and resolvedmodes, respectively. Measurements were taken under UHV (10IIα radiation (40.814 eV). Photoelectronswere analyzed with an electrostatic hemisferical Scienta SES 200 analyzerequipped with a multichannel plate detector, operated with an overall20 meV energy resolution, analogous to the setup employed at the ANTARESbeamline. The work function has been determined through the measurementof the whole spectral width from the secondary electron cutoff tothe Fermi level, after biasing the sample by −3 V with respectto ground and using HeIα radiation(21.218 eV).The UPS valence band data have been taken at theLotus laboratory  by using a GammadataVUV 5000 microwave excited and monochromatized He source, with Hei = 52°. We remark that the NPG three-dimensional (3D)morphology is characterized by a rather broad distribution of surfaceorientations, thus hindering a precise determination of the exchangedmomentum q. Complementary XPS and UPS measurementswere also performed, to combine information on coverage and Fermienergy shift, respectively. XPS core-level spectra were taken usinga nonmonochromatic X-ray source (Al Kα 1486.7 eV) and acquiredwith an Omicron EA-125 hemispherical analyzer. The UPS valence banddata were taken using HeIα radiationwith the same hemispherical analyzer.HREELSmeasurements were performed at the SESAMO laboratory (University ofModena) with a LK 5000 spectrometer (3.5 meV resolution), with primarybeam energy of 9 eV and incident angle θ


In this paper, a graphene-based multi-functional anisotropic metamaterial composed of two finite parallel graphene ribbons in each unit cell is designed and proposed in the 0.1–5.5 terahertz (THz) region. Simulations are performed by the finite element method (FEM) in the frequency-domain solver of CST Software. An equivalent circuit modeling (ECM) as a simplified approach has been provided by a MATLAB code to model the performance of the metamaterial. The metastructure is polarization-sensitive because of the geometric non-symmetry. The absorption/reflection spectrum of the metamaterial is dynamically tunable by changing the Fermi energy level of the graphene. The introduced metamaterial can act as a THz switch and inverter at 1.23 and 4.21 THz. It acts as an ON state when the incident electric field is in the x-direction and acts as an OFF state when the incident electric field is in the y-direction. It can also act as a bi-functional mirror: a triple-band mirror for the incident electric field in the x-direction and an ultra-broadband mirror for the incident electric field in the y-direction. The proposed metamaterial has a maximum absorption of 100%, maximum linear dichroism (LD) of 100%, and a maximum switching extinction ratio of 33.01 dB. The metamaterial and its applications could be used as a potential platform in future THz devices and systems. CDchi ≠ 0 shows that the metamaterial is chiral. If CDchi = 0, the metamaterial is not chiral in most cases. CDani ≠ 0 proves that the metamaterial is anisotropic. Anisotropy is included in both CDchi and CDani definitions so we cannot conclude anything about the metamaterial anisotropy if only CDani = 0. A metamaterial can be anisotropic  while CDani = 0 but LD ≠ 0. Chirality can arise from chiral metamaterials or chiral molecules as sub-structures when anisotropy is introduced through metamaterials with anisotropic geometries, anisotropic material in the metamaterial structure, or applying a magnetic field. Metamaterials with anisotropic geometries do not superimpose on their mirror image at some degrees of rotation and can thus produce LD and/or CDani2.Chiral metamaterials do not superimpose on their mirror image at any degree of rotation and can exhibit responses such as circular dichroism (CD) and linear dichroism (LD). CD may be observed from anisotropic metamaterials as well. However, since the origin of CD of chiral and anisotropic metamaterials is not the same, we are referring to CDchi + CDani) and/or LD responses up to 99%12. The design and investigation of tunable graphene-based metamaterials for switching, inverting, modulating, sensing, and so on applications is a worthy and uninvestigated field of research.Graphene, a 2D layer of graphite, has excellent features which make it a promising candidate for optical devices and systems. Graphene-based chiral and anisotropic metamaterials have been proposed, analyzed, and investigated recently. They produce tunable CD , while the others are investigated and analyzed as a single purpose device like absorber. The tunability feature of these metamaterials widens their applicability making them the interesting possibility for future telecommunication technology or spectroscopic sensing for example. There is an urgent need for tunable multi-functional metamaterial in THz systems to minimize the size of the system greatly as the metamaterial can have more than two performances at the same time and extend their versatility. The multi-functional device can be switched into different applications which is very beneficial. Moreover, we could save material, cost, and time greatly. In these papers, the maximum dichroism responses reached 99%.The recently reported Graphene-based chiral and anisotropic metamaterials14. The metamaterial in Ref.14 contains ribbons that are infinite from one side and finite from another side. The metamaterials don’t contain metal layers beneath the structures to avoid transmission and they were analyzed from the transmission point of view. The considered frequency region for Ref.13 is 13–30 THz and for Ref.14 is 4–26 THz. The metamaterial in Ref.13 doesn’t contain any theoretical analysis and the structure in Ref.14 is analyzed based on coupled mode theory.Graphene-based metamaterials containing two parallel graphene ribbons in each unit cell were proposed and designed as filtering applications in Refs.10, we proposed single-function graphene-based multi-band metamaterial absorbers containing a single layer of graphene resonators in 0.5–4.5 and 1–5.5 THz, respectively. The maximum LD responses reached 94 and 99%, respectively. In our earlier paper8, we proposed dual-function (multiband and broadband) graphene-based metamirror containing two layers of graphene resonators in 0.3–4.5 THz with a maximum LD response of 96%. In this paper, we propose a multi-functional graphene-based anisotropic metamaterial composed of one layer of parallel graphene ribbon resonators in 0.1–5.5 THz. The metamaterial is designed to act as a triple-band and ultra-broadband mirrors, inverter, and switch. Compared to Ref.8, we need fewer resources and time to analyze and perform the simulations and ECM. The ECM and its procedure in this work differ from that reported in Refs.10 as the graphene resonators are modeled as an impedance circuit in the x-direction and an open circuit (OC) in the y-direction. In addition, the number of layers containing the metamaterial differs from that reported in Refs.10.In our earlier papers16. The substrate is made of quartz with a refractive index of 1.9617. A gold metal layer with a conductivity of 4.56 × 107 S/m18 is used beneath the metamaterial to avoid passing the electromagnetic waves from the other side of it. Simulations were done in the frequency domain solver of CST Microwave Studio by finite element method (FEM)10. Periodic boundary condition in the x- and y-directions, and absorbing boundary condition in the z-direction were used. The metamaterial was meshed by the tetrahedral mesh type. The device works as a tunable THz multi-functional metamaterial with four performances: switch, inverter, ultra-broadband mirror, and triple-band mirror. The dimensions and their optimized values are given in Table Periodic and unit cell views of the designed graphene-based multi-functional THz anisotropic metamaterial comprised of supercell each cell containing two finite parallel ribbon resonators are given in Fig. 19. The unit cell dimensions are assumed as Px = 21 μm and Py = 9 μm which are smaller than λmin = 54.55 μm if fmax = 5.5 THz (maximum frequency of the simulated frequency range) to prevent the propagation of the high order Floquet modes22.The metamaterial is optimized in CST by use of the genetic algorithm optimization techniqueλmin) in the considered frequency range. So, the thickness of the metamaterial has been relatively thin.The total thickness of the metamaterial (graphene/quartz/gold layers) is ~ 8.5 μm , and ζ is the integral variable. τ is the relaxation time26:vf = 106 m/s is the Fermi velocity and µ = 2 m2/(V s) is the carrier mobility of graphene. The propagation constant of the electromagnetic wave in a graphene-vacuum configuration is27:k0 and η0 are the wave vector of the incident wave and the vacuum impedance.The Fermi energy level of the graphene resonator layer Ef could be controlled by the applied external bias voltage. The relation between Ef and the applied bias voltage can be expressed as28:V0 is the offset voltage28 anda0 is the capacitive model of the structure, εd is the dielectric permittivity, and V is the externally applied bias voltage to the graphene resonator layer.The graphene Fermi energy level The multi-functional metamaterial in Fig. entclass1pt{minima10. Then, the equivalent conductivity in the x-direction 29:The reflection coefficient θin, θout, and Z0 are respectively the angle of the incident illuminated wave, the relative permittivity of the dielectric substrate (Quartz), the angle of the transmitted wave, and the vacuum impedance (377 Ω). The graphene resonator layer is modeled as an OC for the wave illumination in the y-direction. So:In which θin and θout is:The relation between The transfer matrices of the graphene resonator layer in the x- and y-directions are as follows:θsub and θsub is calculated by:c is the speed of the light. The transfer matrix of the dielectric substrate in the x- or y-direction is:So:So:The total transfer matrix of the designed multi-functional metamaterial is:The matrix elements for the incident E field in the x-direction are:The matrix elements for the incident E field in the y-direction are:The input impedance of the multi-functional metamaterial of Fig. ing Eqs.  and 25)30\documeing Eqs.  and 29)30\documeThe scattering parameter in the x-direction is:The scattering parameter in the y-direction is:The reflection coefficients in x- or y-directions are:The linear dichroism (LD) is calculated by:The extinction ratio (ER) of the multi-functional metamaterial in the switching performance in dB is calculated by:µc (eV) are obtained for the switching performance of the multi-functional metamaterial in Fig. µc = 0.6 eV.The absorption spectra of the multi-functional metamaterial of Fig. µc (eV) are obtained for the anisotropic metamaterial by Eq. (µc = 0.6 eV. CDani = 0 (based on Eq. (2).The maximum linear dichroisms (LDs) vs l by Eq.  and the d on Eq.  in Ref.2The E field distributions of the multi-functional metamaterial of Fig. The surface current distributions of the proposed multi-functional metamaterial of Fig. µc of the graphene resonator layer as the input and the reflection value of the metamaterial as the output of the inverter. The reflection spectra of the metamaterial as an inverter are shown in Fig. The designed multi-functional metamaterial in Fig. Moreover, the designed multi-functional metamaterial works as a triple-band mirror when the incident E field is in the x-direction. The metamaterial works as an ultra-broadband mirror when the incident E field is in the y-direction.The structure containing the graphene resonator layer on the Quartz dielectric half-space (with a thickness of 500 µm) is simulated in CST and the reflection coefficients for this configuration are obtained. Then, the real and the imaginary parts of the equivalent conductivities in the x- and y-directions for the graphene resonator layer are obtained by Eqs.  and 10)10). The µc and the results are given in Fig. µc, the resonance frequencies increase which exhibits a blueshift.Absorption spectra of the multi-functional metamaterial in Fig. chi + CDani) in the reported references of Table 30. The metamaterial is also compared with previously proposed switches in Table The designed multi-functional metamaterial is compared with previously published absorbers/mirrors including chiral absorbers/mirrors and anisotropic absorbers/mirrors in Table 7.The fabrication procedure of the designed metamaterial is not in the scope of this paper, but it can have the same procedure as explained in our previously published workIn summary, we introduce and design a multi-functional anisotropic metamaterial containing two parallel graphene ribbons in each unit cell in the 0.1–5.5 terahertz (THz) region. The maximum absorption and linear dichroism of the metamaterial reached 100% and 100%, respectively. The metamaterial has a non-symmetric geometry, and it is polarization sensitive. The absorption/reflection spectrum of the metamaterial is obtained by use of the finite element method (FEM) in CST Software. The spectrum is dynamically tunable by the alternation of the applied bias voltage to graphene. Moreover, applications of the proposed metamaterial as a switch, an inverter, and a bi-functional mirror are studied. The maximum switching extinction ratio of the metamaterial reached 33.01 dB. It acts as a triple-band mirror for the incident electric field in the x-direction and an ultra-broadband mirror for the incident electric field in the y-direction. Using one device to reach four different functions  can greatly reduce the size of the future THz systems saving material, time, and cost. An equivalent circuit modeling (ECM) approach by a simple MATLAB code has been presented to model the performance of the metamaterial. The FEM and ECM results are well-matched. The proposed metamaterial and its applications could be used in future THz devices and systems.