Twisted bilayer graphene (TBG) features strongly correlated and topological phases due to its flat bands emerging near the magic angle. However, the effects of the non-Hermiticity, arising from the coupling to the environment and dissipation, have remained unexplored. We here develop a simple non-Hermitian (NH) version of twisted bilayer graphene (TBG) by considering relative twisting of two NH graphene monolayers with non-Hermiticity encoded in the imbalance of in-plane nearest-neighbor hopping amplitudes. Remarkably, by generalizing the Bistritzer-MacDonald approach to NH systems, we discover exceptional magic angles where the band structure changes from purely real to purely imaginary thus featuring flat bands with infinite lifetime. Between them, the bands remain flattened, and a Hermitian magic angle emerges at which the imaginary part of energy is maximal, and corresponds to the usual magic angle in non-dissipative, purely Hermitian TBG. We propose an optical lattice setup with gain and loss where our theoretical predictions can be verified. These results suggest the robustness of the flat bands in open systems, paving the way for the further studies on the interplay of dissipative effects, electronic topology, and interactions in such NH moiré bands.
Twist bilayer graphenes with magical angle have nearly flat band, which become strongly correlated electron systems. Herein, we propose another system based on strained bilayer graphene that have flat band at the intrinsic Fermi level. The top and bottom layers are uniaxially stretched along different directions. When the strength and directions of the strain satisfy certain condition, the periodical lattices of the two layers are commensurate to each other. The regions with AA, AB and BA stacking arrange in a triangular lattice. With magical strain, the bands around the intrinsic Fermi level …
Twisted bilayer graphene with tiny rotation angles have drawn significant attention due to the observation of the unconventional superconducting and correlated insulating behaviors. In this paper, we employ a full tight-binding model to investigate collective excitations in twisted bilayer graphene near magic angle. The polarization function is obtained from the tight-binding propagation method without diagonalization of the Hamiltonian matrix. With the atomic relaxation considered in the simulation, damped and undamped interband plasmon modes are discovered near magic angle under both room te…
We derive a simple formula for the real-space chirality of twisted bilayer graphene that can be related to the cross-product of its sheet currents. This quantity shows well-defined plateaus for the first remote band as function of the gate voltage which are approximately quantized for commensurate twist angles. The zeroth plateau corresponds to the first magic angle where a sign change occurs due to an emergent $C_6$-symmetry. Our observation offers a new definition of the magic angle based on a macroscopic observable which is accessible in typical transport experiments.
At certain angles of rotation called `magic angles' twisted bilayer graphene features almost flat bands. The resulting strong correlations drive the system to novel phases which have been observed in experiments recently. A complete understanding of the `magic' angle physics---both at the single-particle as well as the many-particle level---is still missing, and the search is ongoing. Here, we identify a new set of `magic' angles, where locally flat bands with a variety of possible many-body instabilities arise, but where the single-particle problem admits an exact solution. This occurs in the…
We combine state-of-the-art large-scale first principles calculations with a low-energy continuum model to describe the nearly flat bands of twisted bilayer graphene at the first magic angle $θ=1.08^\circ$. We show that the energy width of the flat band manifold, as well as the energy gap separating it from the valence and conduction bands, can be obtained only if the out-of-plane relaxations are fully taken into account. The results agree both qualitatively and quantitatively with recent experimental outcomes.
This comment pertains the recent manuscript by Morissette {\it et al.} [arXiv:2206.08354v1]. The authors claim to have found signatures of collective excitations in electron spin resonance experiments that would be linked to the correlated structure of magic angle bilayer graphene. However, identical resonance features have already been reported in previous works on mono- and few-layer graphene, voiding their theoretical framework. A straight forward theoretical picture within the single-particle topologically non-trivial band structure of graphene delivers satisfactory explanations for the ob…
In this work, we study the Raman spectra of twisted bilayer graphene samples as a function of their twist-angles ($θ$), ranging from 0.03$^\circ$ to 3.40$^\circ$, where local $θ$ are determined by analysis of their associated moire superlattices, as imaged by scanning microwave impedance microscopy. Three standard excitation laser lines are used (457, 532, and 633 nm wavelengths), and the main Raman active graphene bands (G and 2D) are considered. Our results reveal that electron-phonon interaction influences the G band's linewidth close to the magic angle regardless of laser excitation wavele…
We introduce a new approach that allows one complete control over the modulation of the effective twist angle change in few-layer van der Waals heterostructures by irradiating them with longitudinal waves of light at the end of a waveguide. As a specific application, we consider twisted bilayer graphene and show that one can tune the magic angles to be either larger or smaller, allowing in-situ experimental control of the phase diagram of this and other related materials. A waveguide allows one to circumvent the free-space constraints on the absence of longitudinal electric field components of…
Twisted bilayer graphene (TBLG) has recently emerged as a versatile platform for studying a variety of exotic transport phenomena. Here, we present a theoretical study of near-field thermal radiation between suspended TBLG with a focus on the magic angle. Within the chirally symmetric continuum model, we observe a suppressed heat flow when approaching the magic angle owing to a reduced Drude weight, with greater suppressions at lower temperatures and larger gap sizes. When the chemical potential lies in the energy gap near the charge neutrality point, more than 100-fold heat-flow variation can…
The discovery of correlated electronic phases, including Mott-like insulators and superconductivity, in twisted bilayer graphene (TBLG) near the magic angle, and the intriguing similarity of their phenomenology to that of the high-temperature superconductors, has spurred a surge of research to uncover the underlying physical mechanism. Local spectroscopy, which is capable of accessing the symmetry and spatial distribution of the spectral function, can provide essential clues towards unraveling this puzzle. Here we use scanning tunneling microscopy (STM) and spectroscopy (STS) in magic angle TB…
We consider twisted bilayer and trilayer graphene in the presence of Rashba spin-orbit coupling and explore the physics of Moiré spintronics. The electronic charge density has a sharp step right at the magic angles $θ_m$. As a result, local spin observables (polarization and equilibrium spin currents) have sharp peaks (of width about a small fraction of 1$^\circ$) as a function of the twist angle $θ$, and abrupt sign reversals at $θ_m$. Thereby, the magic angle can be determined in an unprecedented accuracy. In the first chiral limit, the spin currents vanish, but the peculiar pattern of the p…
Near a magic twist angle, bilayer graphene transforms from a weakly correlated Fermi liquid to a strongly correlated two-dimensional electron system with properties that are extraordinarily sensitive to carrier density and to controllable environmental factors such as the proximity of nearby gates and twist-angle variation. Among other phenomena magic-angle twisted bilayer graphene hosts superconductivity, interaction induced insulating states, magnetism, electronic nematicity, linear-in-T low-temperature resistivity, and quantized anomalous Hall states. We highlight some key research results …
Bilayer graphene was theorized to host a moire miniband with flat dispersion if the layers are stacked at specific twist angles known as the magic angles. Recently, such twisted bilayer graphene (tBLG) with the first magic angle twist was reported to exhibit correlated insulating state and superconductivity, where the presence of the flat miniband in the system is thought to be essential for the emergence of these ordered phases in the transport measurements. Tunneling spectroscopy and electronic compressibility measurements in tBLG have revealed a van Hove singularity that is consistent with …
The emergence of flat bands and correlated behaviors in 'magic angle' twisted bilayer graphene (tBLG) has sparked tremendous interest, though many aspects of the system are under intense debate. Here we report observation of both superconductivity and the Mott-like insulating state in a tBLG device with a twist angle of approximately 0.93, which is smaller than the magic angle by 15%. At an electron concentration of +/-5 electrons per moire unit cell, we observe a narrow resistance peak with an activation energy gap of approximately 0.1 meV, indicating the existence of an additional correlated…
Thanks to the recent discovery on the magic-angle bilayer graphene, twistronics is quickly becom11 ing a burgeoning field in condensed matter physics. This letter expands the realm of twistronics to acoustics by introducing twisted bilayer phononic graphene, which remarkably also harbors the magic angle, evidenced by the associated ultra-flat bands. Beyond mimicking quantum mechanical behaviors of twisted bilayer graphene, we show that their acoustic counterpart offers a considerably more straightforward and robust way to alter the interlayer hopping strength, enabling us to unlock magic angle…
When two graphene layers are rotated from AA or AB configuration by a small angle, the band structure changes dramatically. Numerical calculations have shown that, at certain discrete angles called magic angles, the low energy bands become flat leading to localization of electrons. The origin of this strange behavior, however, is not well understood. Here, I propose a theory that offers an understanding of the phenomenon, focusing on the first magic angle. It is shown that coupling between the layers, in addition to renormalizing the Dirac velocity, introduces higher order momentum terms in th…
Magic angle twisted bilayer graphene has emerged as a powerful platform for studying strongly correlated electron physics, owing to its almost dispersionless low-energy bands and the ability to tune the band filling by electrostatic gating. Techniques to control the twist angle between graphene layers have led to rapid experimental progress but improving sample quality is essential for separating the delicate correlated-electron physics from disorder effects. Owing to the 2D nature of the system and the relatively low carrier density, the samples are highly susceptible to small doping inhomoge…
Using the semiclassical quantum Boltzmann theory and employing the Dirac model with twist angle-dependent Fermi velocity we obtain results for the electrical resistivity, the electronic thermal resistivity, the Seebeck coefficient, and the Wiedemann-Franz ratio in near magic angle twisted bilayer graphene, as functions of doping density (around the charge-neutrality-point) and modified Fermi velocity $\tilde v$. The $\tilde v$-dependence of the relevant scattering mechanisms, i.e. electron-hole Coulomb, long-ranged impurities, and acoustic gauge phonons, is considered in detail. We find a rang…
Magic-angle twisted bilayer graphene (MA-TBG) exhibits intriguing quantum phase transitions triggered by enhanced electron-electron interactions when its flat-bands are partially filled. However, the phases themselves and their connection to the putative non-trivial topology of the flat bands are largely unexplored. Here we report transport measurements revealing a succession of doping-induced Lifshitz transitions that are accompanied by van Hove singularities (VHS) which facilitate the emergence of correlation-induced gaps and topologically non-trivial sub-bands. In the presence of a magnetic…
The chiral Hamiltonian for twisted graphene bilayers is analyzed in terms of its squared Hamiltonian which removes the particle-hole symmetry and thus one bipartite lattice, allowing to write the Hamiltonian in terms of a $2\times 2$ matrix. This brings to the front the three main physical actors of twisted systems: kinetic energy, confinement potential and an interlayer interaction operator which is divided in two parts: a non-Abelian interlayer operator and an operator which contains an interaction energy between layers. Here, each of these components is analyzed as a function of the angle o…
At a discrete set of magic angles, twisted bilayer graphene has been shown to host extraordinarily flat bands, correlated insulating states, unconventional superconductivity, and distinct Landau level degeneracies. In this work, we design a highly efficient quantum Otto engine using a twisted bilayer graphene sample. Flat bands, which occur at magic angles, make the prospect of extracting useful work from our Otto engine lucrative. We use an eight-band continuum model of twisted bilayer graphene to compute efficiencies and work outputs for magic and non-magic angle twists, and compare the resu…
We report strong electron-phonon coupling in magic-angle twisted bilayer graphene (MA-TBG) obtained from atomistic description of the system including more than 10000 atoms in the moire supercell. Electronic structure, phonon spectrum, and electron-phonon coupling strength lambda are obtained before and after atomic-position relaxation both in and out of plane. Obtained lambda is very large for MA-TBG, with lambda > 1 near the half-filling energies of the flat bands, while it is small (lambda ~ 0.1) for monolayer and unrotated bilayer graphene. Significant electron-hole asymmetry occurs in the…
Twisted bilayer graphene (TBG) hosts nearly flat bands with narrow bandwidths of a few meV at certain {\em magic} twist angles. Here we show that in twisted gapped Dirac material bilayers, or massive twisted bilayer graphenes (MTBG), isolated nearly flat bands below a threshold bandwidth $W_c$ are expected for continuous small twist angles up to a critical $θ_c$ depending on the flatness of the original bands and the interlayer coupling strength. Narrow bandwidths of $W \lesssim $30 meV are expected for $θ\lesssim 3^{\circ} $ for twisted Dirac materials with intrinsic gaps of $\sim 2$ eV that …
Although much progress has been made on the physics of magic angle twisted bilayer graphene at integer fillings, little attention has been given to fractional fillings. Here we show that the three-peak structure of Wannier orbitals, dictated by the symmetry and topology of flat bands, facilitates the emergence of a novel state at commensurate fractional filling of $ν= n \pm 1/3$. We dub this state a "fractional correlated insulator". Specifically for the filling of $\pm 1/3$ electrons per moiré unit cell, we show that short-range interactions alone imply an approximate extensive entropy due to…
Recent experiments on twisted bilayer graphene (tBG) close to magic angle show that a small relative rotation in a van der Waals heterostructure greatly alters its electronic properties. We consider various scattering mechanisms and show that the carrier transport in tBG is dominated by a combination of charged impurities and acoustic gauge phonons. Charged impurities still dominate at low temperature and densities because of the inability of Dirac fermions to screen long-range Coulomb potentials at charge neutrality; however, the gauge phonons dominate for most of the experimental regime beca…
Bismuth consist of bismuth bilayers that are two-dimensional topological insulators and correspondingly, the surface is an array of edge states. Moreover, topological models, including second order topologic order, predict an interlayer electrical coupling mediated by hinge states. Here we report that angle dependent magnetoresistance measurements of small diameter single-crystal bismuth nanowires exhibit the sequence of magnetoresistance (MR) peaks at Yamaji magic angles and a peak for B//bilayer, indicating coherent transport between layers, and showing that the Fermi surface of surface elec…
The electronic properties of junctions defined electrostatically on twisted bilayer graphene can be addressed theoretically using lattice models. Recent works have introduced minimal local orbital models to describe twisted bilayer graphene at the magic angle (MATBLG) with different degrees of approximation and accounting for fragile topology. In the present work we use a Green's function formalism to obtain the spectral and transport properties for MATBLG junctions based on these models. We introduce different symmetry breaking perturbations to simulate the effect of interactions and characte…
Low-energy moiré flat bands in magic-angle twisted bilayer graphene (tBG) have demonstrated incredible potentials to exhibit rich exotic quantum phenomena. Theoretically, the moiré flat bands of tBG are based on the extended structures, i.e., the moiré patterns with periodic boundary conditions. However, a fundamental question of whether the flat bands can exist in the graphene moiré patterns with a reduced structure symmetry, such as sample edges, remains unanswered. Here, via scanning tunneling microscopy and spectroscopy, we study the local electronic properties of a magic-angle tBG near th…
We uncover a new type of magic-angle phenomena when an AA-stacked graphene bilayer is twisted relative to another graphene system with band touching. In the simplest case this constitutes a trilayer system formed by an AA-stacked bilayer twisted relative to a single layer of graphene. We find multiple anisotropic Dirac cones coexisting in such twisted multilayer structures at certain angles, which we call "Dirac magic." We trace the origin of Dirac magic angles to the geometric structure of the twisted AA-bilayer Dirac cones relative to the other band-touching spectrum in the moiré reciprocal …
Magic-angle twisted bilayer graphene (TBG) has attracted significant interest recently due to the discoveries of diverse correlated and topological states in this system. Despite the extensive research on the electron-electron interaction effects and topological properties of the electrons, the phonons of magic-angle TBG are relatively less explored. In this work, we study the phonon properties in magic-angle TBG based on \textit{ab} \textit{initio} deep potential molecular dynamics. We have calculated phonon band structures and density of states at the magic angle, and have systematically ana…
We study the effect of electron-acoustic phonon interactions in twisted bilayer graphene on resistivity in the high-temperature transport and superconductivity in the low-temperature phase diagram. We theoretically show that twisted bilayer graphene should have an enhanced and strongly twist-angle dependent linear-in-temperature resistivity in the metallic regime with the resistivity magnitude increasing as the twist angle approaches the magic angle. The slope of the resistivity versus temperature could approach one hundred ohms per kelvin with a strong angle dependence, but with a rather weak…
Direct observation of flat bands in near-magic-angle twisted bilayer CVD graphene
Istituto Italiano di Tecnologia（意大利理工大学）；Scuola Normale Superiore（比萨高等师范学院）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）；National Institute for Materials Science（国立材料研究所）；Università di Pisa（比萨大学）；Istituto Nanoscienze - CNR（纳米科学研究所-国家研究委员会）
We theoretically study the band structure and optical conductivity of twisted bilayer graphene (TBG) near the magic angle considering the effects of lattice relaxation. We show that the optical conductivity spectrum is characterized by a series of peaks associated with the van Hove singularities in the band structure, and the peak energies evolve systematically with the twist angle. Lattice relaxation effects in TBG modify its band structure, especially the flat bands, which lead to significant shifts of the peaks in optical conductivity. These results demonstrate that spectroscopic features i…
Studies of twisted moiré systems have been mainly focused on two-dimensional (2D) materials such as graphene with Dirac points and transition-metal-dichalcogenide so far. Here we propose a twisted bilayer of 2D systems which feature stable quadratic-band-touching points and find exotic physics different from previously studied twisted moiré systems. Specifically, we show that exactly flat bands can emerge at magic angles and, more interestingly, each flat band exhibits a high Chern number ($C=\pm 2$). We further consider the effect of Coulomb interactions in such magic-angle twisted systems an…
Kitaev quantum spin liquids have been the focus of intense research effort thanks to the discovery of various materials (e.g., RuCl3) that approximate their intriguing physics. In this paper we construct a mean-field approximation for a moir`e superlattice emerging in twisted Kitaev bilayers in terms of solutions of commensurate bilayers. We show that the band structure of deconfined spinons, defined on the mini-Brillouin zone of the superlattice, is greatly modified. The system exhibits a hyper-magic manifold: a series of nearly perfectly-flat bands appear at energies above the lowest gap, ex…
Topological phases, van Hove singularities, and spin texture in magic-angle twisted bilayer graphene in the presence of proximity-induced spin-orbit couplings
Near a magic twist angle, the lowest energy conduction and valence bands of bilayer graphene moiré superlattices become extremely narrow. The band dispersion that remains is sensitive to the moiré's strain pattern, nonlocal tunneling between layers, and filling-factor dependent Hartree and exchange band renormalizations. In this article we analyze the influence of these band-structure details on the pattern of flavor-symmetry-breaking observed in this narrow band system, and on the associated pattern of Fermi surface reconstructions revealed by weak-field-Hall and Schubnikov-de Haas magneto-tr…
The Bistritzer-MacDonald continuum model (BM model) describes the low-energy moiré bands for twisted bilayer graphene (TBG) at small twist angles. We derive a generalized continuum model for TBG near any commensurate twist angle, which is characterized by complex interlayer hoppings at commensurate $AA$ stackings (rather than the real hoppings in the BM model), a real interlayer hopping at commensurate $AB/BA$ stackings, and a global energy shift. The complex phases of the $AA$ stacking hoppings and the twist angle together define a single angle parameter $ϕ_0$. We compute the model parameters…
Very recently, twisted graphene bilayer (TGB) around the first magic angle 1.1° has attracted much attention for the realization of exotic quantum states, such as correlated insulator behavior and unconventional superconductivity. Here we elaborately studied a series of TGBs around the first magic angle engineered by heterostrain, where each layer is strained independently. Our experiment indicated that a moderate heterostrain enables the structural evolution from the small-angle TGB ( ~ 1.5°) to the strained magic-angle TGB (θ ~ 1.1°), exhibiting the characteristic low-energy flat bands. The …
Carrier relaxation measurements in moiré materials offer a unique probe of the microscopic interactions, in particular the ones that are not easily measured by transport. Umklapp scattering between phonons is a ubiquitous momentum-nonconserving process that governs the thermal conductivity of semiconductors and insulators. In contrast, Umklapp scattering between electrons and phonons has not been demonstrated experimentally. Here, we study the cooling of hot electrons in moiré graphene using time- and frequency-resolved photovoltage measurements as a direct probe of its complex energy pathways…
The ability to control the strength of interaction is essential for studying quantum phenomena emerging from a system of correlated fermions. For example, the isotope effect illustrates the effect of electron-phonon coupling on superconductivity, providing an important experimental support for the BCS theory. In this work, we report a new device geometry where the magic-angle twisted bilayer graphene (tBLG) is placed in close proximity to a Bernal bilayer graphene (BLG) separated by a 3 nm thick barrier. Using charge screening from the Bernal bilayer, the strength of electron-electron Coulomb …
The interplay between interlayer van der Waals interaction and intralayer lattice distortion can lead to structural reconstruction in slightly twisted bilayer graphene (TBG) with the twist angle being smaller than a characteristic angle θc. Experimentally, the θc is demonstrated to be very close to the magic angle (θ ~ 1.05°). In this work, we address the transition between reconstructed and unreconstructed structures of the TBG across the magic angle by using scanning tunnelling microscopy (STM). Our experiment demonstrates that both the two structures are stable in the TBG around the magic a…
Twistronics is currently one of the most active research fields in condensed matter physics, following the discovery of correlated insulating and superconducting phases in twisted bilayer graphene (tBLG). Here, we present a magnonic analogue of tBLG. We study magnons in twisted ferromagnetic bilayers (tFBL), including exchange and Dzyaloshinskii-Moriya interactions (DMI). For negligible DMI, tFBL presents discrete magnon magic angles and flat moiré minibands analogous to tBLG. The DMI, however, changes the picture and renders the system much more exotic. The DMI in tFBL induces a rich topologi…
