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Scanning microwave impedance microscopy (sMIM) is a near‐field technique that enables the characterization of conductive materials with a resolution down to 1 nm. In hexagonal boron nitride (hBN)‐encapsulated devices, microwaves emitted from the sMIM tip penetrate and reach with the underlying 2D materials, allowing for the mapping of local conductivity variations. Using twisted bilayer graphene, it is demonstrated that this technique can characterize moiré patterns through hBN flakes up to 2.5 nm thick. Additionally, it is showed that sMIM can distinguish between conductive and insulating materials in samples encapsulated by hBN layers exceeding 15 nm. A key finding is that signal decay due to encapsulation is intrinsically linked to the tip's condition. This work overcomes limitations in the application of twistronics, enabling the verification of the periodicity of moiré patterns in high‐quality encapsulated devices between electrical contacts. [ABSTRACT FROM AUTHOR]

ABSTRACT In this paper, we investigate a twisted bilayer graphene on an h‐BN substrate. The graphene is grown using high‐quality chemical vapor deposition (CVD) and subsequently transferred onto the h‐BN substrate. Our focus is on the stacking transition within the bilayer system, based on fluctuations in both intralayer and interlayer processes. Our findings reveal that post‐annealing induces alterations in the electron–phonon interaction, corresponding to the spatially dependent stacking changes in the bilayer structure. This makes it possible to modify the electronic band structure of graphene and subsequently all its optoelectronic properties. [ABSTRACT FROM AUTHOR]

Interlayer twist evokes revolutionary changes to the optical and electronic properties of twisted bilayer graphene (TBG) for electronics, photonics and optoelectronics. Although the ground state responses in TBG have been vastly and clearly studied, the dynamic process of its photoexcited carrier states mainly remains elusive. Here, we unveil the photoexcited hot carrier dynamics in TBG by time-resolved ultrafast photoluminescence (PL) autocorrelation spectroscopy. We demonstrate the unconventional ultrafast PL emission between the van Hove singularities (VHSs) with a ∼4 times prolonged relaxation lifetime. This intriguing photoexcited carrier behavior is ascribed to the abnormal hot carrier thermalization brought by bottleneck effects at VHSs and interlayer charge distribution process. Our study on hot carrier dynamics in TBG offers new insights into the excited states and correlated physics of graphene twistronics systems. [ABSTRACT FROM AUTHOR]

Near the magic angle, strong correlations drive many intriguing phases in twisted bilayer graphene (tBG) including unconventional superconductivity and chern insulation. Whether correlations can tune symmetry breaking phases in tBG at intermediate (≳ 2°) twist angles remains an open fundamental question. Here, using ARPES, we study the effects of many-body interactions and displacement field on the band structure of tBG devices at an intermediate (3°) twist angle. We observe a layer- and doping-dependent renormalization of bands at the K points that is qualitatively consistent with moiré models of the Hartree-Fock interaction. We provide evidence of correlation-enhanced inversion symmetry-breaking, manifested by gaps at the Dirac points that are tunable with doping. These results suggest that electronic interactions play a significant role in the physics of tBG even at intermediate twist angles and present a new pathway toward engineering band structure and symmetry-breaking phases in moiré heterostructures.

Twisted bilayer graphene (TBG) has been extensively studied because of its novel physical properties and potential application in electronic devices. Here we report the synthesis and characterization of 30° TBG naturally grown on Cu0.75Ni0.25 (111) film and investigate the electronic structure by angle-resolved photoemission spectroscopy. Compared with other substrates, our TBG with a wafer scale is acquired with a shorter growth time. The Fermi velocity and energy gap of Dirac cones of TBG are comparable with those of a monolayer on Cu0.85Ni0.15 (111). The signature of moiré lattices has not been observed in either the low-energy electron diffraction patterns or the Fermi surface map within experimental resolution, possibly due to different Cu and Ni contents in the substrates enhancing the different couplings between the substrate and the first/second layers and hindering the formation of a quasiperiodic structure. [ABSTRACT FROM AUTHOR]

We consider the problem of numerically computing the quantum dynamics of an electron in twisted bilayer graphene. The challenge is that atomic-scale models of the dynamics are aperiodic for generic twist angles because of the incommensurability of the layers. The Bistritzer--MacDonald PDE model, which is periodic with respect to the bilayer's moir\'e pattern, has recently been shown to rigorously describe these dynamics in a parameter regime. In this work, we first prove that the dynamics of the tight-binding model of incommensurate twisted bilayer graphene can be approximated by computations on finite domains. The main ingredient of this proof is a speed of propagation estimate proved using Combes--Thomas estimates. We then provide extensive numerical computations, which clarify the range of validity of the Bistritzer--MacDonald model. [ABSTRACT FROM AUTHOR]

The optical properties and Landau quantisations in twisted bilayer graphene are investigated using a generalised tight-binding model that takes into account all interlayer and intralayer atomic interactions in the Moire superlattice. The system is a zero-gap semiconductor with double-degenerate Dirac-cone structures, and saddle-point energy dispersions appear at low energies for small twisting angles. The magnetic quantisation phenomena in this system are rich and unique, with Landau-level subgroups specified owing to specific Moire zone folding through modulation of the stacking angles. The Landau-level spectrum shows hybridised characteristics associated with those in monolayer, as well as AA and AB stackings. The detailed analysis explores the complex relations among the different sublattices on the same and different graphene layers. [ABSTRACT FROM AUTHOR]

Twisted bilayer graphene (TBG) has emerged as a fascinating research frontier in condensed matter physics and materials science. This review article comprehensively overviews recent advances and future perspectives in studying TBG. The challenges associated with fabricating and characterizing TBG structures, including precise control of the twist angle and accurate determination of electronic properties, are discussed. Furthermore, the intriguing phenomena observed in TBG, such as superconductivity, insulating phases, and correlated electron states, shedding light on their underlying mechanisms, are explored. Scalability and device integration of TBG are explored, along with potential engineering strategies to tailor its properties for specific applications. By synthesizing and analyzing the latest scientific reports, a roadmap for further research is provided and the promising prospects for TBG are highlighted. [ABSTRACT FROM AUTHOR]

Flat band has attracted more and more interest in recent years, motivated by its discovery in twisted bilayer graphene (TBG). In this work, we report our study of the impurity effect on this flat band system, which is an important issue for real materials. Employing the Lanczos recursive method, we solve the local density of states (LDOS) around a potential impurity. We find for large impurity size, a series of bound states are formed inside the impurity, and the flat band peak in LDOS is suppressed near the impurity boundary and shifted by the impurity potential deep inside the impurity. As the impurity size becomes smaller, the effect on the flat band becomes weaker, as anticipated from the large scale of the underlying Wannier function. This property distinguishes with the usual flat band systems with small localized Wannier orbitals, and indicates the flat band in TBG is more stable against small-size impurities. [ABSTRACT FROM AUTHOR]

The full optical response of twisted bilayer graphene at the neutrality point close to the magic angle within the continuum model (CM) is discussed. First, three different channels consistent with the underlying D3 symmetry are identified, yielding the total, magnetic, and chiral response. Second, the full optical response in the immediate vicinity of the magic angle θm is numerically calculated, which provides a direct mapping of the CM onto an effective two‐band model. It is, further, shown that the ground state of the CM in the immediate vicinity of θm is unstable toward transverse current fluctuations, a so‐called Condon instability. Third, due to the large counterflow, the acoustic plasmonic excitations with typical wave numbers have larger energies than the optical ones and their energy density may be largely enhanced at certain frequencies which are denominated as chiral resonances. Finally, symmetry relations for the optical response and their consequences for the chiral response are discussed. [ABSTRACT FROM AUTHOR]

The recently-introduced topological heavy fermion (THF) model [1] of twisted bilayer graphene (TBG) aims to reconcile the quantum-dot-like electronic structure of the latter observed by scanning tunneling microscopy, with its electron delocalization seen in transport measurements. The THF model achieves this by coupling localized (heavy) fermions with anomalous conduction electrons. Originally, the parameters of the THF model were obtained numerically from the Bistritzer–Macdonald (BM) model of TBG [1]. In this work, we derive analytical expressions for the THF model parameters as a function of the twist angle, the ratio between the tunneling amplitudes at the AA and AB regions (w0/w1), and the screening length of the interaction potential. By numerically computing the THF model parameters across an extensive experimentally-relevant parameter space, we show that the resulting approximations are remarkably good, i.e., within the 30% relative error for almost the entire parameter space. At the single-particle level, the THF model accurately captures the energy spectrum of the BM model over a large phase space of angles and tunneling amplitude ratios. When interactions are included, we also show that the THF description of TBG is good around the magic angle for realistic values of the tunneling amplitude ratios (0.6 ≤ w0/w1 ≤ 1.0), for which the hybridization between the localized and conduction fermions γ is smaller than the onsite repulsion of the heavy fermions U1 (i.e., |γ| < U1). [ABSTRACT FROM AUTHOR]

Graphene is the first experimentally discovered two‐dimensional material. This article reviews the unique properties of the so‐called twisted bilayer graphene (TBG), which can be considered a superstructure formed by stacking two graphene layers with a specific twisting angle. The main topics covered by this review include the correlated insulating phase, superconducting phase, quantum anomalous Hall effect, and the corresponding theoretical analysis. In addition, the twisted multilayer graphene, considered to have better tunability than the TBG, is discussed, followed by our conclusions and proposed research fields. [ABSTRACT FROM AUTHOR]

Twisted bilayer graphene can demonstrate extraordinary optical and electrical characteristics due to its interlayer interactions. The strong coupling of normal and tangential van der Waals interactions at the interface results in inhomogeneous interlayer deformations and further changes the bilayer graphene's physical properties. Herein, theoretical and numerical models are established to study the torsional deformation behaviour of twisting a graphene flake over a rigid graphene substrate. It is found that in-plane deformations have significant influences on the interlayer potential energy density of AA stacking, but seldom affect other stacked domains. The deformation process is thus approximated by first twisting the graphene flake rigidly, and then relaxing the rigid constraints. The bilayer graphene system minimizes its energy by reducing (enlarging) the size of high-energy (low-energy) domains through additional rotations. The additional angles of the graphene flake are derived analytically based on a mechanical model following the principle of minimum potential energy. Results show that the influences of graphene film deformations get significant at small-twist-angles (typically less than 2∘). This work reveals the torsional deformation evolution mechanism of bilayer graphene and provides beneficial guidance on achieving intriguing physical properties. [ABSTRACT FROM AUTHOR]

We report the existence of moiré patterns and magic angle physics in all families of chiral collapsed carbon nanotubes. A detailed study of the electronic structure of all types of chiral nanotubes, previously collapsed via molecular dynamics, has been performed. We find that each family possesses a unique geometry and moiré disposition, as well as a characteristic number of flat bands. Remarkably, all kinds of nanotubes behave the same with respect to magic angle tuning, showing a monotonic behavior that gives rise to magic angles in full agreement with those of twisted bilayer graphene. Therefore, magic angle behavior is universally found in chiral collapsed nanotubes with a small chiral angle, giving rise to moiré patterns. Our approach comprises first-principles and semi-empirical calculations of the band structure, density of states and spatial distribution of the localized states signaled by flat bands. [Display omitted] [ABSTRACT FROM AUTHOR]

Twisted bilayer graphene (TBLG) has emerged as an exciting new material with tunable electronic properties, but current methods of fabrication and identification of TBLG are painstaking and laborious. We combine Raman spectroscopy with Gaussian mixture model (GMM) data clustering to identify areas with particular twist angles, from a TBLG sample with a mixture of orientations. We present two approaches: training the GMM on Raman parameters returned by peak fits, and on full spectra with dimensionality reduced by principal component analysis. In both cases, GMM identifies regions of distinct twist angle from within Raman datacubes. We also show that once a model has been trained, and the identified clusters labelled, it can be reapplied to new scans to assess the similarity between the materials in the new region and the testing region. This could enable high-throughput fabrication of TBLG, by allowing computerized detection of particular twist angles from automated large-area scans. [Display omitted] [ABSTRACT FROM AUTHOR]

This study has investigated the adsorption of phosphine toxic gas molecule on monolayer graphene, bilayer graphene and twisted bilayer graphene with, and without Magnesium impurity. The results of absorption energy studies using density functional theory (DFT) showed that bilayer graphene provides better adsorption than monolayer graphene and a difference in adsorption energy will be observed for twisted bilayer graphene with a rotation angle of 21.78°. By adding Mg impurity to the configurations, the sensitivity, and working temperature of the twisted bilayer graphene with Mg impurity increase compared to twisted bilayer graphene. Also, working temperature, and value of adsorption energy were calculated for bilayer graphene with Mg impurity less than Mg-doped twisted bilayer graphene, and monolayer graphene with Mg impurity. [ABSTRACT FROM AUTHOR]

Graphene has demonstrated great potential in new-generation electronic applications due to its unique electronic properties such as large carrier Fermi velocity, ultrahigh carrier mobility, and high material stability. Interestingly, the electronic structures can be further engineered in multilayer graphene by the introduction of a twist angle between different layers to create van Hove singularities (vHSs) at adjustable binding energy. In this work, using angle-resolved photoemission spectroscopy with sub-micrometer spatial resolution, the band structures and their evolution are systematically studied with twist angle in bilayer and trilayer graphene sheets. A doping effect is directly observed in graphene multilayer system as well as vHSs in bilayer graphene over a wide range of twist angles (from 5° to 31°) with wide tunable energy range over 2 eV. In addition, the formation of multiple vHSs (at different binding energies) is also observed in trilayer graphene. The large tuning range of vHS binding energy in twisted multilayer graphene provides a promising material base for optoelectrical applications with broadband wavelength selectivity from the infrared to the ultraviolet regime, as demonstrated by an example application of wavelength selective photodetector.

We present transport measurements of bilayer graphene with a 1.38? interlayer twist. As with other devices with twist angles substantially larger than the magic angle of 1.1?, we do not observe correlated insulating states or band reorganization. However, we do observe several highly unusual behaviors in magnetotransport. For a large range of densities around half filling of the moir'e bands, magnetoresistance is large and quadratic. Over these same densities, the magnetoresistance minima corresponding to gaps between Landau levels split and bend as a function of density and field. We reproduce the same splitting and bending behavior in a simple tight-binding model of Hofstadter's butterfly on a triangular lattice with anisotropic hopping terms. These features appear to be a generic class of experimental manifestations of Hofstadter's butterfly and may provide insight into the emergent states of twisted bilayer graphene. [ABSTRACT FROM AUTHOR]

Few atom thick, twisted bilayer graphene (tBLG) possesses a rotation angle (θ) dependent van Hove singularity (vHs). Fine-tuning vHs serves a potential method to enhance charge transfer (CT) in surface enhanced Raman spectroscopy. This study shows that tBLG having a specific θ promotes as high as a 1.7 times enhancement of the Raman signals of copper phthalocyanine (CuPc) as compared to that caused by single layer graphene (SLG). The results of a combination of reflection imaging spectroscopy and widefield Raman provide spatial and spectral information about both tBLG with θ ranging from 10.9 to 13.7° and the corresponding vHs. Comparison of Raman spectra of CuPc in presence and absence of tBLG demonstrates that a significant enhancement of certain CuPc vibrational modes occurs when the underlying tBLG possesses a θ = 12.2°, showing as high as 6.8 and 1.7 times enhancements of certain vibrational mode as compared to those of CuPc on bare and SLG substrates, respectively. Theoretical calculations indicate that a match between the energies of vHs of tBLG with those of frontier orbitals of CuPc facilitates CT from the distant SLG to CuPc. [Display omitted] [ABSTRACT FROM AUTHOR]

Theory of superconductivity in twisted bilayer graphene (tBLG) is presented, based on the fact that Dirac fermions are pairing creating the topological bosons as consequence of topologically protected Lifshitz topological transition (TPLTT). We have shown that multiple TPLTTs are realised at low twisting angles in tBLG. At TPLTT the Berry phase changes from 2π in bilayer graphene to π in tBLG. It is favourable to form the Bardeen Cooper Schrieffer – Bose Einstein unconventional crossover (BCS-BEUC) when the attractive interaction for pairing dominates the repulsive screened Coulomb interaction. The theory yields a second-order phase transition for BCS-BEUC, and values of specific heat and the Ginzburg−Landau coherence length are calculated. The problem has been solved of emergent mystery in the magic angles at which there exists possibility for observation of BCS-BEUC. The solution is connected with the Umklapp processes when the quasiwave vector of the superconducting carriers is shifted from the Brillouin zone to other cell of the reciprocal space. The table is given of the allowed magic angles which include the corresponding effective masses of the pairing Dirac fermions. [ABSTRACT FROM AUTHOR]

Raman spectroscopy is an extremely useful tool to characterize graphene systems. The strongest Raman features are the first-order G band and the second-order 2D and 2D′ bands, which are the overtones of the double resonance D and D' bands. However, the 2G band, which is the overtone of the G band, is not usually observed in the spectra of monolayer graphene and of crystalline graphite. In this work, we present an experimental and theoretical investigation of the resonance Raman spectra in twisted bilayer graphene (TBG) with different twisting angles and using several laser excitation energies in the NIR and visible ranges. We observed that the 2G band is enhanced when the incident photons are in resonance with the transition between the van Hove singularities in the density of states of the TBG. We show that the 2G band has three contributions (2G 1 , 2G 2 and 2G 3), that are not dispersive by changing the laser excitation energy. We also present theoretical calculations showing that the 2G 1 and 2G 2 bands are related to combinations of the in-phase (IP) and out-of-phase (OP) vibrations of the atoms in the different layers. The Raman excitation profiles (REPs) of the 2G peaks are upshifted in comparison with the REP of the G band. This behavior was confirmed theoretically using a graphene tight binding model. We conclude that the different resonance behavior comes from the fact that the G band is a first-order process whereas the 2G band is second-order processes giving rise to overall different resonance conditions. [Display omitted] • Resonant Raman study of the overtone 2G band in twisted bilayer graphene samples. • 2G band is composed of three individual peaks corresponding to different processes. • Theoretical calculations show that twisted bilayer graphene presents two vibrational modes at the zone-center. • Placzek's approximation shows that one mode is the main contribution to the G band in resonance with the van Hove singularities. • The overtone 2G band is mainly composed by the combination of the two zone-center phonons. [ABSTRACT FROM AUTHOR]

To pinpoint the electronic and structural mechanisms that affect intrinsic and extrinsic performance limits of 2D material devices, it is of critical importance to resolve the electronic properties on the mesoscopic length scale of such devices under operating conditions. Herein, angle‐resolved photoemission spectroscopy with nanoscale spatial resolution (nanoARPES) is used to map the quasiparticle electronic structure of a twisted bilayer graphene device. The dispersion and linewidth of the Dirac cones associated with top and bottom graphene layers are determined as a function of spatial position on the device under both static and operating conditions. The analysis reveals that microscopic rotational domains in the two graphene layers establish a range of twist angles from 9.8° to 12.7°. Application of current and electrostatic gating lead to strong electric fields with peak strengths of 0.75 V/μm at the rotational domain boundaries in the device. These proof‐of‐principle results demonstrate the potential of nanoARPES to link mesoscale structural variations with electronic states in operating device conditions and to disentangle such extrinsic factors from the intrinsic quasiparticle dispersion. [ABSTRACT FROM AUTHOR]

Higher-order topological insulator is a newly discovered topological material, characterized by the topological corner states. In this work, we propose quantum oscillation that identifies the two-dimensional higher-order topological phase in twisted bilayer graphene systems. We use an instanton approach to argue that the tunneling of electrons between the topological corner states of the higher-order topological insulator generally causes the gate-tunable oscillation in the energy spectra. The oscillatory nodes signal the perfect suppression of the tunneling, which features the topological nature of the corner states. In the view of experimental realization, we propose the transport experiment that can readily observe the oscillation. Our work provides a feasible route to identify higher-order topological materials in twisted bilayer graphenes. Image 1 • Novel transport signature of higher-order topological insulator phase in twisted bilayer graphene. • Detecting the topological corner states through quantum tunneling. • Engineering topological bound states in twisted bilayer graphene. [ABSTRACT FROM AUTHOR]

Recent experiments on twisted bilayer graphene have shown a high-temperature parent state with massless Dirac fermions and broken electronic flavor symmetry; superconductivity and correlated insulators emerge from this parent state at lower temperatures. We propose that the superconducting and correlated insulating orders are connected by Wess-Zumino-Witten terms, so that defects of one order contain quanta of another order and skyrmion fluctuations of the correlated insulator are a "mechanism" for superconductivity. We present a comprehensive listing of plausible low-temperature orders and the parent flavor symmetry-breaking orders. The previously characterized topological nature of the band structure of twisted bilayer graphene plays an important role in this analysis. [ABSTRACT FROM AUTHOR]

The vibrational properties of twisted bilayer graphene (tBLG) show complex features, due to the intricate energy landscape of its low-symmetry configurations. A machine learning-based approach is developed to provide a continuous model between the twist angle and the simulated Raman spectra of tBLGs. Extracting the structural information of the twist angle from Raman spectra corresponds to solving a complicated inverse problem. Once trained, the machine learning regressors (MLRs) quickly provide predictions without human bias and with an average 98% of the data variance being explained by the model. The significant spectral features learned by MLRs are analyzed revealing the intensity profile near the calculated G-band to be the most important feature. The trained models are tested on noise-containing test data demonstrating their robustness. The transferability of the present models to experimental Raman spectra is discussed in the context of validation of the level of theory used for construction of the analyzed database. This work serves as a proof of concept that machine-learning analysis is a potentially powerful tool for interpretation of Raman spectra of tBLG and other 2D materials. Image 1 [ABSTRACT FROM AUTHOR]

Unconventional superconductivity in bilayer graphene has been reported for twist angles θ near the first magic angle and charged electrostatically with holes near half filling of the lower flat bands. A maximum superconducting transition temperature TC ≈ 1.7 K was reported for a device with θ = 1.05° at ambient pressure and a maximum TC ≈ 3.1 K for a device with θ = 1.27° under 1.33 GPa hydrostatic pressure. A high-TC model for the superconductivity is proposed herein, where pairing is mediated by Coulomb coupling between charges in the two graphene sheets. The expression derived for the optimal transition temperature, TC0 = kB−1Λ(|nopt − n0|/2)1/2e2/ζ, is a function of mean bilayer separation distance ζ, measured gated charge areal densities nopt and n0 corresponding to maximum TC and superconductivity onset, respectively, and the length constant Λ = 0.00747(2) Å. Based on existing experimental carrier densities and theoretical estimates for ζ, TC0 = 1.94(4) K is calculated for the θ = 1.05° ambient-pressure device and TC0 = 3.02(3) K for the θ = 1.27° pressurized device. Experimental mean-field transition temperatures TCmf = 1.83(5) K and TCmf = 2.86(5) K are determined by fitting superconducting fluctuation theory to resistance transition data for the ambient-pressure and pressurized devices, respectively; the theoretical results for TC0 are in remarkable agreement with these experimental values. Corresponding Berezinskii-Kosterlitz-Thouless temperatures TBKT of 0.96(3) K and 2.2(2) K are also determined and interpreted. [ABSTRACT FROM AUTHOR]

Twisted multi-layer heterostructures have been considered a platform for studying highly correlated many-particle systems, hosting the emerging phenomena of correlation physics. Electronic structure calculations of such materials which mainly focused on Twisted Bilayer Graphene (TBG) in the framework of the independent-electron approximation, despite the complexity, accurately match the experimental results around the Fermi level. Here, we present a convenient real space π -bands tight-binding model to calculate the band structure of TBG based on the Wannier interlayer hopping parameters obtained from non-twisted bilayer graphene. Our approach is based on mapping hopping parameters onto the real space TBG interlayer couplings, using Radial Basis Function (RBF) interpolation method. This accurate mapping, naturally, transfers all the symmetries and orbital shape features of the bilayer graphene lattice to the TBG lattice and preserves coupling orientation dependencies in addition to distance dependencies. The importance of this fact is explained by showing the effect of the threefold rotation symmetry of AB ′ interlayer coupling on the flat band of the TBG band structure. In addition, due to real space study, the model gives us a comprehensive and intuitive view of the role of each interlayer orbital coupling in the TBG band structure and the structural variation relative to twisting. • A real space tight-binding model for twisted bilayer graphene (TBG) based on Wannier hopping parameters. • π -band ab-initio tight-binding model of twisted bilayer graphene. • Wannier hopping mapping on twisted bilayer graphene structure using RBF interpolation. • Studying the flat band in the band structure based on sublattice couplings in twisted bilayer graphene. • The effect of the threefold rotation symmetry of AB interlayer coupling on the flat band of the TBG band structure. [ABSTRACT FROM AUTHOR]

In this paper we explore the properties of optical conductivity of twisted bilayer graphene (TBG) for small twist angles based on the continuum model. It is found that the spectrum structure of optical conductivity exhibits the characteristic of the "redshift" with the reduction of twist angle. The redshift of the spectrum structure for TBG can be understood and analyzed with a picture of an effective quantum well with the variable well width. There arises a quasi plateau for the conductivity in the low frequency range the height of which descends as the twist angle reduces. We present a quantitative explanation which is based on the linear dispersion of the connected Dirac cones and the Kubo formula. It is also demonstrated that the quasi plateau can be destroyed due to the Pauli blocking when the Fermi energy moves up away from the neutrality point. Moreover, we find that the van Hove singularities (VHS's) which possess the geometry of the saddle surface do not cause the peak for the interband conductivity at the neutrality point, which is supposed to originates from the negative Gaussian curvature and the symmetry of the local surface of energy band around VHS's. • In comparison with the common models describing the TBG we used a model that takes the two nonvanishing transferred crystal momentums into account. • In the low frequency range there exists a quasi plateau in the conductivity spectrum, which results from the Dirac cones in the energy band of the superlattice. We present a quantitative analysis on the occurrence and height of the quasi plateau based on the linear dispersion relation of the Dirac cone and Kubo formula. It is also noted that the length of the quasi plateau can be destroyed by the mechanism of the Paul Blocking. • The Van Hove singularities (VHS's) of the TBG has been verified by experiment and it can result in two peaks of the difference conductance under a DC bias when the Fermi levels approach the Van Hove singularities. However, our calculation about the conductivity and the density of the states shows that the Van Hove singularities with the saddle geometry do not lead to the peaks in the interband conductivity at the frequency equal to the difference of the two VHS's, which seems a bit of counterintuitive. It may be attributed to the negative Gaussian curvature. [ABSTRACT FROM AUTHOR]

• Four-point bending method is applied to reproduce the pure bending behavior of diamane. • Tension-induced bending failure is observed when the carbon layer number increases. • Bending limit is slightly larger than the ultimate tensile strain. • Twisted bilayer graphene with interlayer-bonding experiences structural failures under pure bending. The intriguing physical properties of two-dimensional (2D) nanomaterials make them promising building blocks for flexible electronics. Using a four-point bending approach, this work establishes a comprehensive understanding of the bending behavior of diamane – a 2D diamond nanostructure, from elastic deformation to structural failure through atomistic simulations. The four-point bending method accurately reproduces the pure bending of the sample, and the obtained force-displacement curve fit well with the classical Euler beam theory. Structural failure is observed from diamane under bending when its thickness or the number of layers increases. Atomic insights reveal that the crack initiates from the tension side of the sample, resulting in a tension-induced bending failure. Specifically, the bending limit is found to be slightly larger than the fracture strain under tensile deformation. Additionally, the bending behaviour of the diamane analogous – twisted bilayer graphene with interlayer-bonding (TBGIB), has been investigated. Different from diamane, TBGIB bends elastically at the initial stage and then experiences structural failures with increasing bending strain. Higher interlayer bonding density is observed to result in a higher bending stiffness. Meanwhile, significant interlayer shear strain is detected during bending, which leads to interlayer bond breakage, rippling, and buckling of the graphene layer. This work provides a full description of the pure bending behavior of diamane and its analogous structure, which could be beneficial for their applications in flexible electronics. Tension-induced failure of three- or four-layer diamane nanoribbon is revealed by four-point bending simulation. [Display omitted] [ABSTRACT FROM AUTHOR]

Motivated by the recent novel electronic features extracted from the magic-angle graphene superlattices, we studied the ground state superconducting pairing correlations within the Hubbard model on a twisted bilayer honeycomb lattice. Using Constrained-Path Quantum Monte Carlo method, we found that the d + i d pairing correlation dominates over other pairing patterns among various electron fillings and interaction strengths, and the effective pairing interaction was enhanced as the on-site Coulomb interaction increased. We further examined the effect of the nearest neighbor interaction V , and the effective pairing interaction with d + i d pairing symmetry was also enhanced by either a repulsive or attractive interaction. Our intensive numerical results confirm the interaction driven superconductivity with a dominant d + i d pairing symmetry in twisted bilayer graphene. [ABSTRACT FROM AUTHOR]

Graphene is perhaps the most studied material around the globe in recent years. It has served as a classic example of 2D material not just because of the historical reasons, but importantly, due to distinctly observable dimensional crossover in it, from 2D to 3D, via Bernal stacked (AB) bilayer to multilayer finally culminating in graphite. The interlayer interactions that are thus responsible, however, tend to differ vastly in presence of defects or disorders. Of particular interest is the angular disorder causing the layers to stack in a manner away from the conventional AB packing. The new class of graphene systems involving an angular twist among otherwise highly crystalline 2D layers, is often termed as twisted graphene. Among these, twisted bilayer graphene, tBLG, has become archetypical. The twist as a new degree of freedom induces several angle dependent properties in tBLG, from visible absorption to superconductivity, unheard of in the case of graphene itself. This article overviews the recent developments in twisted graphene covering aspects related to its synthesis, the twist dependent properties and potential applications. Image 1 [ABSTRACT FROM AUTHOR]

Highlights: This article presents an overview of twisted bilayer graphene (tBLG) on their fabrication techniques and twisting angle-dependent properties. The properties of tBLG can be controlled by controlling the twisting angle between two graphene sheets.Two-dimensional (2D) materials exhibit enhanced physical, chemical, electronic, and optical properties when compared to those of bulk materials. Graphene demands significant attention due to its superior physical and electronic characteristics among different types of 2D materials. The bilayer graphene is fabricated by the stacking of the two monolayers of graphene. The twisted bilayer graphene (tBLG) superlattice is formed when these layers are twisted at a small angle. The presence of disorders and interlayer interactions in tBLG enhances several characteristics, including the optical and electrical properties. The studies on twisted bilayer graphene have been exciting and challenging thus far, especially after superconductivity was reported in tBLG at the magic angle. This article reviews the current progress in the fabrication techniques of twisted bilayer graphene and its twisting angle-dependent properties. [ABSTRACT FROM AUTHOR]

Surface plasmons in 2-dimensional electron systems with narrow Bloch bands feature an interesting regime in which Landau damping (dissipation via electron-hole pair excitation) is completely quenched. This surprising behavior is made possible by strong coupling in narrow-band systems characterized by large values of the "fine structure" constant α=e²/ℏκvF. Dissipation quenching occurs when dispersing plasmon modes rise above the particle-hole continuum, extending into the forbidden energy gap that is free from particle-hole excitations. The effect is predicted to be prominent in moiré graphene, where at magic twist-angle values, flat bands feature α≫1. The extinction of Landau damping enhances spatial optical coherence. Speckle-like interference, arising in the presence of disorder scattering, can serve as a telltale signature of undamped plasmons directly accessible in near-field imaging experiments. [ABSTRACT FROM AUTHOR]

Abstract Using exact quantum Monte Carlo method, we examine the recent novel electronic states seen in magic-angle graphene superlattices. From the Hubbard model on a double-layer honeycomb lattice with a rotation angle θ = 1.08 ° , we reveal that an antiferromagnetically ordered Mott insulator emerges beyond a critical U c at half filling, and with a small doping, the pairing with d + i d symmetry dominates over other pairings at low temperature. The effective d + i d pairing interaction strongly increases as the on-site Coulomb interaction increases, indicating that the superconductivity is driven by electron-electron correlation. Our non-biased numerical results demonstrate that the twisted bilayer graphene shares the similar superconducting mechanism of high temperature superconductors, which is a new and ideal platform for further investigating the strongly correlated phenomena. [ABSTRACT FROM AUTHOR]

Misorientation of two layers of bilayer graphene leaves distinct signatures in the electronic properties and the phonon modes. The effect on the thermal conductivity has received the least attention and is the least well understood. In this work, the in-plane thermal conductivity of misoriented bilayer graphene (m-BLG) is investigated as a function of temperature and interlayer misorientation angle using nonequilibrium molecular dynamics (NEMD). The central result is that the calculated thermal conductivities decrease approximately linearly with the increasing lattice constant of the commensurate m-BLG unit cell. Comparisons of the phonon dispersions show that misorientation has negligible affect on the low-energy phonon frequencies and velocities. However, the larger periodicity of m-BLG reduces the Brillouin zone size to the extent that the zone edge acoustic phonons are thermally populated. This allows Umklapp scattering to reduce the lifetimes of the phonons contributing to the thermal transport, and consequently, to reduce the thermal conductivity. This explanation is supported by direct calculation of reduced phonon lifetimes in m-BLG based on density functional theory (DFT). [ABSTRACT FROM AUTHOR]

The interlayer coupling can be used to engineer the electronic structure of van der Waals heterostructures (superlattices) to obtain properties that are not possible in a single material. So far research in heterostructures has been focused on commensurate superlattices with a long-ranged Moiré period. Incommensurate heterostructures with rotational symmetry but not translational symmetry (in analogy to quasicrystals) are not only rare in nature, but also the interlayer interaction has often been assumed to be negligible due to the lack of phase coherence. Here we report the successful growth of quasicrystalline 30° twisted bilayer graphene (30°-tBLG), which is stabilized by the Pt(111) substrate, and reveal its electronic structure. The 30°-tBLG is confirmed by low energy electron diffraction and the intervalley double-resonance Raman mode at 1383 cm-1. Moreover, the emergence of mirrored Dirac cones inside the Brillouin zone of each graphene layer and a gap opening at the zone boundary suggest that these two graphene layers are coupled via a generalized Umklapp scattering mechanism--that is, scattering of a Dirac cone in one graphene layer by the reciprocal lattice vector of the other graphene layer. Our work highlights the important role of interlayer coupling in incommensurate quasicrystalline superlattices, thereby extending band structure engineering to incommensurate superstructures. [ABSTRACT FROM AUTHOR]

We study the effects of pressure and uniaxial heterostrain on the energy bands and density of states in twisted bilayer graphene based on the effective continuum model. We find that extremely flat bands (one tenth of the bandwidth at magic angle 1.05°) can be achieved under pressure for a wide range of twist angles due to the enhancement of interlayer coupling strength. Under strain, pressure dramatically reduces the separation and widths of the flatband van Hove singularities at angles beyond the magic angle. Strain direction provides an addition parameter for tuning the flat bands to realize narrow bandwidth. Moreover, high-order van Hove singularities favoring strong electron correlations can be managed by applying pressure and strain. These effects may promote correlated electron phenomena at a broad range of twist angles. • The extremely narrow flat bands are achieved under pressure for a wide range of twist angles. • Pressure could be a factor that reverses partial effects of strain on twisted bilayer graphene system. • The evolutions of the van Hove singularities in density of states under both pressure and strain are presented. • High-order van Hove singularities are managed by applying pressure and strain. [ABSTRACT FROM AUTHOR]

In this paper we explore in detail the symmetry of the effective non-Abelian gauge field model that characterize the system of twisted bilayer graphene (TBG). It is found that the total Lagrangian including the term of pseudo Rashba effect and the magnetic-like term is continuous locally U(1) invariant up to a total derivative term. The magnetic-like term is found that it is actually of the spin-orbit-interaction-like form which happens in the vector space of Lie algebra of the gauge transformation. The effective non-Abelian gauge fields are generalized as the time-dependent fields and the motion equation, which is analogous to the Yang-Mills equation except three extra current interaction terms, is achieved. • The symmetry of the effective non-Abelian fields model of the twisted bilayer graphene is identified to be locally U(1) invariant. • The physical meaning and the symmetry of the magnetic-like term in the model is explicitly identified as the spin-orbit-interaction-like. • The non-Abelian gauge fields is generalised in the presence of the time-dependent fields, which is analogous to the Yang-Mills equation. [ABSTRACT FROM AUTHOR]

Owing to its excellent properties in optical and electronic applications, twisted bilayer graphene (TBG) has attracted extensive research attention. As an encapsulation layer, hexagonal boron nitride (h -BN) is indispensable for fabricating TBG devices. Because h -BN and graphene exhibit similar lattice structures, TBG on h -BN exhibits periodic moiré patterns, which enable interlayer orientations to be revealed for bilayer graphene on h -BN. Herein, we used two-step chemical vapor deposition to synthesize TBG exhibiting multiple twist angles on h -BN. Conductive atomic force microscopy measurements revealed that the conductivity distribution was different for the graphene/ h -BN and TBG moiré patterns. Using the characteristics of the moiré patterns formed by these layers, h -BN and graphene interlayer orientations were precisely determined. This provides a feasible method for investigating the turbostratic arrangement of few-layer van der Waals heterostructures. [Display omitted] [ABSTRACT FROM AUTHOR]