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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.

The recently synthesized 30° twisted bilayer graphene (30°-TBG) systems are unique quasicrystal systems possessing dodecagonal symmetry with graphene’s relativistic properties. We employ a real-space numerical atomistic framework that respects both the dodecagonal rotational symmetry and the massless Dirac nature of the electrons to describe the local density of states of the system. The approach we employ is very efficiency for systems with very large unit cells and does not rely on periodic boundary conditions. These features allow us to address a broad class of multilayer two-dimensional crystal with incommensurate configurations, particularly TBGs. Our results reveal that the 30°-TBG electronic spectrum consist of extended states together with a set of localized wave functions. The localized states exhibit fractal patterns consistent with the quasicrystal tiling.

The study of twisted bilayer graphene (TBG) is a hot topic in condensed matter physics with special focus on magic angles of twisting at which TBG acquires unusual properties. Mathematically, topologically non-trivial flat bands appear at those special angles. The chiral model of TBG pioneered by Tarnopolsky, Kruchkov, and Vishwanath (2019) has particularly nice mathematical properties and we survey, and in some cases, clarify, recent rigorous results which exploit them. [ABSTRACT FROM AUTHOR]

We study Dirac points of the chiral model of twisted bilayer graphene (TBG) with constant in-plane magnetic field. The striking feature of the chiral model is the presence of perfectly flat bands at magic angles of twisting. The Dirac points for zero magnetic field and non-magic angles of twisting are fixed at high symmetry points K and K' in the Brillouin zone, with r denoting the remaining high symmetry point. For a fixed small constant in-plane magnetic field, we show that as the angle of twisting varies between magic angles, the Dirac points move between K, K' points and the r point. In particular, near magic angles, the Dirac points are located near the Γ point. For special directions of the magnetic field, we show that the Dirac points move, as the twisting angle varies, along straight lines and bifurcate orthogonally at distinguished points. At the bifurcation points, the linear dispersion relation of the merging Dirac points disappears and exhibit a quadratic band crossing point (QBCP). The results are illustrated by links to animations suggesting interesting additional structure. [ABSTRACT FROM AUTHOR]

Graphene has nearly become an area that is experiencing rapid growth. The observation of moiré patterns in mechanically stacked graphene layers has triggered rapid progress in graphene research. These moiré patterns arise due to the relative difference in the orientation of the mechanically stacked graphene layers. Since their first appearance, moiré superlattices have become a platform for advanced materials and different quantum phenomena. Graphene bilayer, obtained from the mechanical stacking of two decoupled graphene layers, has become archetypal. Weak inter-layer forces can sometimes induce angular disorder in the array that causes unconventional stacking of layers. This unconventional stacking induces several angle-dependent properties in twisted bilayer graphene (t-BLG) which are unprecedented for graphene itself. This review examines recent advances in t-BLG covering aspects of its electronic structure, fabrication, angle-dependent properties and the spectroscopic signatures.

Abstract This study discusses the effect of long‐range interactions within the self‐consistent Hartree‐Fock (HF) approximation in comparison to short‐range atomic Hubbard interactions on the band structure of twisted bilayer graphene (TBG) at charge neutrality for various twist angles. Starting from atomistic calculations, it determines the quasi‐particle band structure of TBG with Hubbard interactions for three magnetic orderings: modulated anti‐ferromagnetic (MAFM), (NAFM) and hexagonal anti‐ferromagnetic (HAFM). Then, it develops an approach to incorporate these magnetic orderings along with the HF potential in the continuum approximation. Away from the magic angle, it observes a drastic effect of the magnetic order on the band structure of TBG compared to the influence of the HF potential. Near the magic angle, the HF potential plays a major role in the band structure, with HAFM and MAFM being secondary effects, but NAFM appears to still significantly distort the electronic structure at the magic angle. These findings suggest that the spin‐valley degenerate broken symmetry state often found in HF calculations of charge neutral TBG near the magic angle should favor magnetic order, since the atomistic Hubbard interaction will break this symmetry in favor of spin polarization.

Advanced two-dimensional spin-polarized heterostructures based on twisted (TBG) and nanoporous (NPBG) bilayer graphenes doped with Eu ions were theoretically proposed and studied using Periodic Boundary Conditions Density Functional theory electronic structure calculations. The significant polarization of the electronic states at the Fermi level was discovered for both Eu/NPBG(AA) and Eu/TBG lattices. Eu ions' chemi- and physisorption to both graphenes may lead to structural deformations, drop of symmetry of low-dimensional lattices, interlayer fusion, and mutual slides of TBG graphene fragments. The frontier bands in the valence region at the vicinity of the Fermi level of both spin-polarized 2D Eu/NPBG(AA) and Eu/TBG lattices clearly demonstrate flat dispersion laws caused by localized electronic states formed by TBG Moiré patterns, which could lead to strong electron correlations and the formation of exotic quantum phases. [ABSTRACT FROM AUTHOR]

Cryogenic compute in- memory (CiM) is a promising alternative to room temperature von-Neumann technologies since cryogenic electronics can provide high speed and energy efficiency while CiM can solve the von-Neumann and memory wall bottlenecks. Moreover, CiM can reduce the energy requirement which can solve the cooling issues associated with the cryogenic systems. Here, we demonstrate a cryogenic in- memory full adder using Majority logic implemented in quantum anomalous Hall effect (QAHE)-based memory system. The utilization of QAHE-based memory enables a number of unique advantages for Majority logic– (i) Majority outputs correspond to voltages with two opposite polarities irrespective of the number of inputs and hence, only a simple voltage comparator can be used, (ii) in- memory Majority logic (and hence, full adder) does not require any modification in the peripheral circuitry, and (iii) the topologically protected Hall resistance states provide robustness against external variations. This work makes the first attempt to harness the unique advantages of QAHE phenomenon in implementing complex operations beyond the primitive bitwise Boolean operations.

The electron valley pseudospin in two-dimensional hexagonal materials is a crucial degree of freedom for achieving their potential application in valleytronic devices. Here, bringing valleytronics to layered van der Waals materials, we theoretically investigate lightwave-controlled valley-selective excitation in twisted bilayer graphene (tBLG) with a large twist angle. It is demonstrated that the counter-rotating bicircular light field, consisting of a fundamental circularly-polarized pulse and its counter-rotating second harmonic, can manipulate the sub-cycle valley transport dynamics by controlling the relative phase between two colors. In comparison with monolayer graphene, the unique interlayer coupling of tBLG renders its valley selectivity highly sensitive to duration, leading to a noticeable valley asymmetry that is excited by single-cycle pulses. We also describe the distinct signatures of the valley pseudospin change in terms of observing the valley-selective circularly-polarized high-harmonic generation. The results show that the valley pseudospin dynamics can still leave visible fingerprints in the modulation of harmonic signals with a two-color relative phase. This work could assist experimental researchers in selecting the appropriate protocols and parameters to obtain ideal control and characterization of valley polarization in tBLG. [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 D 3 symmetry are identified, yielding the total, magnetic, and chiral response. Second, the full optical response in the immediate vicinity of the magic angle θ m 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 θ m 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.

Twisted bilayer graphene (TBG) has attracted great interest in the last decade due to the novel properties it exhibited. It was revealed that e–phonon interaction plays an important role in a variety of phenomena in this system, such as superconductivity and exotic phases. However, due to its complexity, the e–phonon interaction in TBG is not well studied yet. In this work, we study the electron interaction with the acoustic phonon mode in TBG and one of its consequences, i.e. the Kohn anomaly. The Kohn anomaly in ordinary metals usually happens at phonon momentum $q = 2k_\textrm{F}$ as a dramatic modification of the phonon frequency when the phonon wave vector nests the electron Fermi surface. However, novel Kohn anomaly can happen in topological semimetals, such as graphene and Weyl semimetals. In this work, we show that the novel dynamic Kohn anomaly can also take place in TBG due to the nesting of two different Moire Dirac points by the phonon wave vector. Moreover, by tuning the twist angle, the dynamic Kohn anomaly in TBG shows different features. Particularly, at magic angle when the electron bandwidth is almost flat, the dynamic Kohn anomalies of acoustic phonons disappear. We also studied the effects of finite temperature and doping on the dynamic Kohn anomaly in TBG and discussed the experimental methods to observe the Kohn anomaly in such system.

Band flattening has been observed in various materials with twisted bilayer structures, such as graphene, MoS _2 , and hexagonal boron nitride (hBN). However, the unique phenomenon of magic-angle has only been reported in the twisted bilayer graphene (tBG) and not in the twisted bilayer semiconductors or insulators. We aim to investigate the impact of gap opening and interlayer coupling strength on the magic-angle in the tBG. Our results based on the continuum model Hamiltonian with mass term indicate that the presence of a band gap hinders the occurrence of the magic-angle, but strengthening the interlayer coupling tends to restore it. By introducing layer asymmetry, such as interlayer bias or mass difference between layers, the flat bands become more dispersive. Furthermore, we have explored the influence of the Moiré’s potential due to the hBN substrate by calculating the quasi-band-structure of the hetero-structure tBG/hBN. Our findings indicate that the conclusions drawn from using the mass term remain valid despite the presence of the Moiré’s potential due to the hBN substrate.

The symmetry of twisted bilayer graphene (tBG) has been extensively studied in the continuum model but somewhat overlooked in the tight-binding (TB) framework. In contrast to the continuum model, which requires operators for both sublattice and layer spaces, the TB framework relies solely on operators in real space. This paper begins by discussing the symmetries of the TB Hamiltonian and the single-valley TB Hamiltonian of tBG. Subsequently, the band structures with specific irreducible representations (irreps) are obtained by diagonalizing the irrep-dependent Hamiltonian constructed through projection operators. We also investigate the impact of symmetry on intervalley coupling and the influence of a non-zero mass term on the $C_{2z}T$ symmetry of the single-valley Hamiltonian. To understand the irrep change as the wavevector moves inside the Brillouin zone and the irrep change after considering the intervalley coupling or introducing a non-zero mass term at a fixed wavevector, we derive two kinds of compatibility relationships. The methodology presented here can be applied to other layered materials because the basis functions we employ are generic and unique to twisted bilayers.

Abstract Twisted bilayer graphene (tBLG) possesses various novel physical properties. Most of tBLG are fabricated by using artificial methods of stacking or folding single‐layer graphene. Chemical vapor deposition (CVD) has been verified that it holds great potential for preparation of large‐size high‐quality graphene. Therefore, it is significant for preparing tBLG in situ by using CVD technology. In this work, a novel approach is developed to directly prepare tBLGs on liquid Cu substrate. When the growth temperature exceeds a certain critical value, the state of aligned high‐quality single‐layer graphene domains grown on liquid Cu will be broken. Then, tBLG with twisted double‐layer regions is prepared in situ by rotating and intercalating between graphene domains. Experimental observations suggest that the liquid phase of Cu substrate and gas flow play a crucial role for the formation of tBLGs. These results demonstrate that the liquid Cu is an ideal potential substrate for preparing tBLGs with a full range of twisted angles and studying the formation mechanism of layer‐stacked materials.

Advanced two-dimensional spin-polarized heterostructures based on twisted (TBG) and nanoporous (NPBG) bilayer graphenes doped with Eu ions were theoretically proposed and studied using Periodic Boundary Conditions Density Functional theory electronic structure calculations. The significant polarization of the electronic states at the Fermi level was discovered for both Eu/NPBG(AA) and Eu/TBG lattices. Eu ions’ chemi- and physisorption to both graphenes may lead to structural deformations, drop of symmetry of low-dimensional lattices, interlayer fusion, and mutual slides of TBG graphene fragments. The frontier bands in the valence region at the vicinity of the Fermi level of both spin-polarized 2D Eu/NPBG(AA) and Eu/TBG lattices clearly demonstrate flat dispersion laws caused by localized electronic states formed by TBG Moiré patterns, which could lead to strong electron correlations and the formation of exotic quantum phases.

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.

The electron valley pseudospin in two-dimensional hexagonal materials is a crucial degree of freedom for achieving their potential application in valleytronic devices. Here, bringing valleytronics to layered van der Waals materials, we theoretically investigate lightwave-controlled valley-selective excitation in twisted bilayer graphene (tBLG) with a large twist angle. It is demonstrated that the counter-rotating bicircular light field, consisting of a fundamental circularly-polarized pulse and its counter-rotating second harmonic, can manipulate the sub-cycle valley transport dynamics by controlling the relative phase between two colors. In comparison with monolayer graphene, the unique interlayer coupling of tBLG renders its valley selectivity highly sensitive to duration, leading to a noticeable valley asymmetry that is excited by single-cycle pulses. We also describe the distinct signatures of the valley pseudospin change in terms of observing the valley-selective circularly-polarized high-harmonic generation. The results show that the valley pseudospin dynamics can still leave visible fingerprints in the modulation of harmonic signals with a two-color relative phase. This work could assist experimental researchers in selecting the appropriate protocols and parameters to obtain ideal control and characterization of valley polarization in tBLG.

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]

Abstract 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.

Graphene/silicon hybrid photodetector operating at communication wavelength has attracted enormous attention recently due to its potential to realize bandwidth larger than 100 GHz. However, the responsivity is intrinsically limited by the low absorption from the atomic-thick graphene monolayer, which imposes significant obstacles towards its practical application. Although plasmonic structures has been widely applied to enhance the responsivity, it may induce the metallic absorption thus limit the responsivity lower than 0.6 A/W. Twisted bilayer graphene (TBG) has been reported to hold the ability to dramatically enhance the optical absorption due to the unique twist-angle-dependent van Hove singularities. In this article, we present a design of a silicon/TBG hybrid photodetector with a responsivity higher than 1 A/W and bandwidth exceeding 100 GHz. The enhanced responsivity is achieved by tuning the twisted angle of TBG to increase the absorption within the 1550 nm as well as utilizing the silicon slot waveguide to boost the mode overlap with TBG. The fabrication process of proposed design is also discussed demonstrating the advantages of low fabrication complexity. The proposed silicon/TBG photodetector could not only exhibit superior performance compared to previously reported silicon/monolayer graphene photodetector, but also pave the way for the practical application of graphene-based silicon optoelectronic devices.

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.

Summary: Twisted bilayer graphene (TBG) exhibits fascinating correlation-driven phenomena like the superconductivity and Mott insulating state, with flat bands and a chiral lattice structure. We find by quantum-transport calculations that the chirality leads to a giant unidirectional magnetoresistance (UMR) in TBG, where the unidirectionality refers to the resistance change under the reversal of the direction of current or magnetic field. We point out that flat bands significantly enhance this effect. The UMR increases quickly upon reducing the twist angle, and reaches about 20% for an angle of 1.5° in a 10 T in-plane magnetic field. We propose the band structure topology (asymmetry), which leads to a direction-sensitive mean free path, as a useful way to anticipate the UMR effect. The UMR provides a probe for chirality and band flatness in the twisted bilayers.

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 twistronics, which is arising from the moiré superlattice of the small angle between twisted bilayers of 2D materials like graphene, has attracted much attention in the field of 2D materials and condensed matter physics. The novel physical properties in such systems, like unconventional superconductivity, come from the dispersionless flat band that appears when the twist reaches some magic angles. By tuning the filling of the fourfold degeneracy flat bands, the desired effects are induced due to the strong correlation of the degenerated Bloch electrons. In this article, we review the twistronics in twisted bi- and multi-layer graphene (TBG and TMG), which is formed both by transfer assembly of exfoliated monolayer graphene and epitaxial growth of multilayer graphene on SiC substrates. Starting from a brief history, we then introduce the theory of flat band in TBG. In the following, we focus on the major achievements in this field: (a) van Hove singularities and charge order; (b) superconductivity and Mott insulator in TBG and (c) transport properties in TBG. In the end, we give the perspective of the rising materials system of twistronics, epitaxial multilayer graphene on the SiC. [ABSTRACT FROM AUTHOR]

We argue that the unusually strong electron–electron interactions in the narrow bands in moiré superlattices originate from compact Wannier orbitals. Enhanced overlaps of electronic wavefunctions, enabled by such orbitals, result in a strong el–el superlattice umklapp scattering. We identify the umklapp scattering processes as a source of the strong temperature-dependent resistivity observed in these systems. In a simple model, the umklapp scattering predicts a T -dependent resistivity that grows as T ^2 with a numerical prefactor that grows as the Wannier orbital radius decreases. We quantify the enhancement in el–el scattering by the Kadowaki–Woods (KW) ratio, a quantity that is sensitive to umklapp scattering but, helpfully, insensitive to the effects due to the high density of electronic states. Our analysis predicts anomalously large KW ratio values that clearly indicate the importance of the umklapp el–el processes and their impact on the T -dependent resistivity.

We theoretically study Floquet band structures and transport properties of twisted bilayer graphene at the magic-angle under the irradiation of variously polarized light. The magic-angle bilayer graphene is depicted by the newly proposed ten-band tight-binding model and the iterative continued fraction method is adopted to facilitate the calculations of electronic properties in the low-frequency regime. The transitions between Floquet sidebands induce discontinuous electronic bands and energy gaps which further give rise to the antiresonances in longitudinal conductivity calculated by the Kubo formula. Furthermore, significant Hall conductivity is generated by circularly polarized light and its magnitude and sign are sensitive to light polarization as well as photoinduced bandgap-opening, offering a feasible way to tune Hall conductivity by manipulating light polarization. We finally take into account the interplay between light irradiation and short-range disorder, and reveal that disorder scattering remarkably enhances the photoinduced Hall conductivity and can be viewed as an extrinsic source to Hall conductivity.

In this work, we investigate the role of an external electric field in modulating the spectrum and electronic structure behavior of twisted bilayer graphene (TBG) and its physical mechanisms. Through theoretical studies, it is found that the external electric field can drive the relative positions of the conduction band and valence band to some extent. The difference of electric field strength and direction can reduce the original conduction band, and through the Fermi energy level, the band is significantly influenced by the tunable electric field and also increases the density of states of the valence band passing through the Fermi level. Under these two effects, the valence and conduction bands can alternately fold, causing drastic changes in spectrum behavior. In turn, the plasmon spectrum of TBG varies from semiconductor to metal. The dielectric function of TBG can exhibit plasmon resonance in a certain range of infrared.

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]

Graphene is a good candidate for protective material owing to its extremely high stiffness and high strength-to-weight ratio. However, the impact performance of twisted bilayer graphene is still obscure. Herein we have investigated the ballistic resistance capacity of twisted bilayer graphene compared to that of AA-stacked bilayer graphene using molecular dynamic simulations. The energy propagation processes are identical, while the ballistic resistance capacity of the twisted bilayer graphene is almost two times larger than the AA-bilayer graphene. The enhanced capacity of the twisted bilayer graphene is assumed to be caused by the mismatch between the two sheets of graphene, which results in earlier fracture of the first graphene layer and reduces the possibility of penetration.

The twistronics, which is arising from the moiré superlattice of the small angle between twisted bilayers of 2D materials like graphene, has attracted much attention in the field of 2D materials and condensed matter physics. The novel physical properties in such systems, like unconventional superconductivity, come from the dispersionless flat band that appears when the twist reaches some magic angles. By tuning the filling of the fourfold degeneracy flat bands, the desired effects are induced due to the strong correlation of the degenerated Bloch electrons. In this article, we review the twistronics in twisted bi- and multi-layer graphene (TBG and TMG), which is formed both by transfer assembly of exfoliated monolayer graphene and epitaxial growth of multilayer graphene on SiC substrates. Starting from a brief history, we then introduce the theory of flat band in TBG. In the following, we focus on the major achievements in this field: (a) van Hove singularities and charge order; (b) superconductivity and Mott insulator in TBG and (c) transport properties in TBG. In the end, we give the perspective of the rising materials system of twistronics, epitaxial multilayer graphene on the SiC.

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]