When light is incident on a medium with spatially disordered index of refraction, interference effects lead to near-perfect reflection when the number of dielectric interfaces is large, so that the medium becomes a "transparent mirror." We investigate the analog of this effect for electrons in twisted bilayer graphene (TBG), for which local fluctuations of the twist angle give rise to a spatially random Fermi velocity. In a description that includes only spatial variation of Fermi velocity, we derive the incident-angle-dependent localization length for the case of quasi-one-dimensional disorder by mapping this problem onto one dimensional Anderson localization. The localization length diverges at normal incidence as a consequence of Klein tunneling, leading to a power-law decay of the transmission when averaged over incidence angle. In a minimal model of TBG, the modulation of twist angle also shifts the location of the Dirac cones in momentum space in a way that can be described by a random gauge field, and thus Klein tunneling is inexact. However, when the Dirac electron's incident momentum is large compared to these shifts, the primary effect of twist disorder is only to shift the incident angle associated with perfect transmission away from zero. These results suggest a mechanism for disorder-induced collimation, valley filtration, and energy filtration of Dirac electron beams, so that TBG offers a promising new platform for Dirac fermion optics.
We develop a theory for a qualitatively new type of disorder in condensed matter systems arising from local twist-angle fluctuations in two strongly coupled van der Waals monolayers twisted with respect to each other to create a flat band moiré superlattice. The new paradigm of 'twist angle disorder' arises from the currently ongoing intense research activity in the physics of twisted bilayer graphene. In experimental samples of pristine twisted bilayer graphene, which are nominally free of impurities and defects, the main source of disorder is believed to arise from the unavoidable and uncont…
We present a simple derivation of a continuum Hamiltonian for bilayer graphene with an arbitrary smooth lattice deformation -- technically in a fashion parametrized by displacement fields with small gradients. We show that this subsumes the continuum model of Bistritzer and Macdonald for twisted bilayer grapheneas well as many generalizations and extensions of it. The derivation is carried out entirely in real space.
Graphene is considered a promising candidate to replace conventional transparent conductors due to its low opacity, high carrier mobility and flexible structure. Multi-layer graphene or stacked single layer graphenes have been investigated in the past but both have their drawbacks. The uniformity of multi-layer graphene is still questionable, and single layer graphene stacks require many transfer processes to achieve sufficiently low sheet resistance. In this work, bilayer graphene film grown with low pressure chemical vapor deposition was used as a transparent conductor for the first time. Th…
Moiré patterns are known to confine electronic states in transition metal dichalcogenide bilayers, thus generalizing the notion of magic angles discovered in twisted bilayer graphene to semiconductors. Here, we present a revised Slater-Koster tight-binding model that facilitates the first reliable and systematic studies of such states in twisted bilayer MoS$_2$ for the whole range of rotation angles $θ$. We show that isolated bands appear at low energy for $θ\lesssim 5 - 6^\circ$. Moreover, these bands become "flatbands", characterized by a vanishing average velocity, for the smallest angles $…
The recent discovery of correlated insulator states and superconductivity in magic-angle twisted bilayer graphene has paved the way to the experimental investigation of electronic correlations in tunable flat band systems realized in twisted van der Waals heterostructures. This novel twist angle degree of freedom and control should be generalizable to other 2D systems, which may exhibit similar correlated physics behavior while at the same time enabling new techniques to tune and control the strength of electron-electron interactions. Here, we report on a new highly tunable correlated system b…
We study the localization properties of electrons in incommensurate twisted bilayer graphene for small angles, encompassing the narrow-band regime, by numerically exact means. Sub-ballistic states are found within the narrow-band region around the magic angle. Such states are delocalized in momentum-space and follow non-Poissonian level statistics, in contrast with their ballistic counterparts found for close commensurate angles. Transport results corroborate this picture: for large enough systems, the conductance decreases with system size for incommensurate angles within the sub-ballistic re…
The effect of an hexagonal boron nitride (hBN) layer close aligned with twisted bilayer graphene (TBG) is studied. At sufficiently low angles between twisted bilayer graphene and hBN, $θ_{hBN} \lesssim 2^\circ$, the graphene electronic structure is strongly disturbed. The width of the low energy peak in the density of states changes from $W \sim 5 - 10$ meV for a decoupled system to $\sim 20 - 30$ meV. Spikes in the density of states due to van Hove singularities are smoothed out. We find that for a realistic combination of the twist angle in the TBG and the twist angle between the hBN and the…
The effects of the long range electrostatic interaction in twisted bilayer graphene are described using the Hartree-Fock approximation. The results show a significant dependence of the band widths and shapes on electron filling, and the existence of broken symmetry phases at many densities, either valley/spin polarized, with broken sublattice symmetry, or both.
Twisted bilayer graphene (TBG) near "magic angles" has emerged as a rich platform for strongly correlated states of two-dimensional Dirac semimetals. Here we show that twisted bilayers of thin-film magnetic topological insulators (MTI) with large in-plane magnetization can realize flat bands near 2D Dirac nodes. Using a simple model for thin films of MTIs, we derive a continuum model for two such MTIs, twisted by a small angle with respect to each other. When the magnetization is in-plane, we show that interlayer tunneling terms act as effective $SU(2)$ vector potentials, which are known to le…
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…
Twisted bilayer graphene with a twist angle of around 1.1° features a pair of isolated flat electronic bands and forms a strongly correlated electronic platform. Here, we use scanning tunneling microscopy to probe local properties of highly tunable twisted bilayer graphene devices and show that the flat bands strongly deform when aligned with the Fermi level. At half filling of the bands, we observe the development of gaps originating from correlated insulating states. Near charge neutrality, we find a previously unidentified correlated regime featuring a substantially enhanced flat band split…
We compute the phase diagram of twisted bilayer graphene near the magic angle where the occurrence of flat bands enhances the effects of electron-electron interactions and thus unleashes strongly-correlated phenomena. Most importantly, we find a crossover between d+id superconductivity and Mott insulating behavior near half-filling of the lowest electron band when the temperature is increased. This is consistent with recent experiments. Our results are obtained using unbiased many-body renormalization group techniques combined with a mean-field analysis of the effective couplings.
In this work we carry out a theoretical study of the phonon-induced resistivity in twisted double bilayer graphene (TDBG), in which two Bernal-stacked bilayer graphene devices are rotated relative to each other by a small angle $θ$. We show that at small twist angles ($θ\sim 1^\circ$) the effective mass of the TDBG system is greatly enhanced, leading to a drastically increased phonon-induced resistivity in the high-temperature limit where phonon scattering leads to a linearly increasing resistivity with increasing temperature. We also discuss possible implications of our theory on superconduct…
We predict twisted double bilayer graphene to be a versatile platform for the realization of fractional Chern insulators readily targeted by tuning the gate potential and the twist angle. Remarkably, these topologically ordered states of matter, including spin singlet Halperin states and spin polarized states in Chern number $\mathcal C=1$ and $\mathcal{C}= 2$ bands, occur at high temperatures and without the need for an external magnetic field.
By using the first-principles method based on density of functional theory, we study the electronic properties of twisted bilayer graphene with some specific twist angles and interlayer spacings. With the decrease of the twist angle(the unit cell becomes larger), the energy band becomes narrower and Coulomb repulsion increases, leading to the enhancement of electronic correlation; On the other hand, as the interlayer spacing decreases and the interlayer coupling becomes stronger, the correlation becomes stronger. By tuning the interlayer coupling, we can realize the strongly correlated state w…
Twisted bilayer graphenes with magical angle exhibit strongly correlated electronic properties because of the isolated flat band at the Fermi level. We studied the twisted bilayer graphene with substrates on both layers. The substrate induce Kekul$\acute{e}$ distortion for each graphene layer. The systems are investigated by both continuous Dirac Fermion model and tight binding model. The two investigations give similar conclusion that isolated flat band with ultra-narrow bandwidth could appear.
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 …
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 …
Focusing on the twist angle for the minimal commensurate structure, we perform nonperturbative calculations of electron dynamics in the twisted bilayer graphene (TBG) under intense laser fields. We show that the TBG exhibits enriched high-harmonic generation that cannot occur in monolayer or conventional bilayers. We elucidate the mechanism of these nonlinear responses by analyzing dynamical symmetries, momentum-resolved dynamics, and roles of interlayer coupling. Our results imply nonlinear "optotwistronics," or controlling optical properties of layered materials by artificial twists.
The degeneracy of Landau levels flanking charge neutrality in twisted bilayer graphene is known to change from eight-fold to four-fold when the twist angle is reduced to values near the magic angle of $\approx 1.05^\circ$. This degeneracy lifting has been reproduced in experiments by multiple groups, and is known to occur even in devices which do not harbor the correlated insulators and superconductors. We propose $C_3$ symmetry breaking as an explanation of such robust degeneracy lifting, and support our proposal by numerical results on the Landau level spectrum in near-magic-angle twisted bi…
Experiments on bilayer graphene unveiled a fascinating realization of stacking disorder where triangular domains with well-defined Bernal stacking are delimited by a hexagonal network of strain solitons. Here we show by means of numerical simulations that this is a consequence of a structural transformation of the moiré pattern inherent of twisted bilayer graphene taking place at twist angles $θ$ below a crossover angle $θ^{\star}=1.2^{\circ}$. The transformation is governed by the interplay between the interlayer van der Waals interaction and the in-plane strain field, and is revealed by a ch…
The recent discovery of superconductivity in magic-angle twisted bilayer graphene has sparked a renewed interest in the strongly-correlated physics of $sp^2$ carbons, in stark contrast to preliminary investigations which were dominated by the one-body physics of the massless Dirac fermions. We thus provide a self-contained, theoretical perspective of the journey of graphene from its single-particle physics-dominated regime to the strongly-correlated physics of the flat bands. Beginning from the origin of the Dirac points in condensed matter systems, we discuss the effect of the superlattice on…
Currently there is a lively discussion concerning Fermi velocity renormalization in twisted bilayers and several contradicted experimental results are reported. Here we study electronic structures of the twisted bilayers by scanning tunneling microscopy (STM) and spectroscopy (STS). The interlayer coupling strengths between the adjacent bilayers are measured according to energy separations of two pronounced low-energy van Hove singularities (VHSs) in the STS spectra. We demonstrate that there is a large range of values for the interlayer interaction in different twisted bilayers. Below the VHS…
We have studied the phonon specific heat in single-layer, bilayer and twisted bilayer graphene. The calculations were performed using the Born-von Karman model of lattice dynamics for intralayer atomic interactions and spherically symmetric interatomic potential for interlayer interactions. We found that at temperature T<15 K, specific heat varies with temperature as T^n, where n = 1 for graphene, n = 1.6 for bilayer graphene and n = 1.3 for the twisted bilayer graphene. The phonon specific heat reveals an intriguing dependence on the twist angle in bilayer graphene, which is particularly pron…
We report scanning tunneling microscopy (STM) and spectroscopy (STS) of twisted graphene bilayer on SiC substrate. For twist angle ~ 4.5o the Dirac point ED is located about 0.40 eV below the Fermi level EF due to the electron doping at the graphene/SiC interface. We observed an unexpected result that the local Dirac point around a nanoscaled defect shifts towards the Fermi energy during the STS measurements (with a time scale about 100 seconds). This behavior was attributed to the decoupling between the twisted graphene and the substrate during the measurements, which lowers the carrier densi…
Twistronic has recently attracted tremendous attention because the twisting can engineer the bilayer graphene-like materials into varying types of strongly correlated phases. In this paper, we study the twisting of bilayer graphene (BLG) quantum dots (QDs) with hexagonal shape and zigzag edges. In the untwisted BLG-QDs, the zigzag edges of graphene host spontaneous magnetism with varying magnetic configurations. As a BLG-QD being adiabatically twisted, the quantum state evolves as a function of the twisting angle. If the twisting angle changes across certain critical value, the magnetic config…
We investigate twisted double bilayer graphene (TDBG), a four-layer system composed of two AB-stacked graphene bilayers rotated with respect to each other by a small angle. Our ab initio band structure calculations reveal a considerable energy gap at the charge point neutrality that we assign to the intrinsic symmetric polarization (ISP). We then introduce the ISP effect into the tight-binding parameterization and perform calculations on TDBG models that include lattice relaxation effects down to very small twist angles. We identify a narrow region around the magic angle $θ^\circ = 1.3^{\circ}…
Twisted Bilayer Graphene at the magic twist angle features flat energy bands, which lead to superconductivity and strong correlation physics. These unique properties are typically limited to a narrow range of twist angles around the magic angle with a small allowed tolerance. Here we report on a mechanism that enables flattening of the band-structure using coherent optical illumination, leading to emergence of flat isolated Floquet-Bloch bands. We show that the effect can be realized with relatively weak optical beams at the visible-infrared range (below the material bandwidth) and persist for…
Twisted bilayer systems with discrete magic angles, such as twisted bilayer graphene featuring moiré superlattices, provide a versatile platform for exploring novel physical properties. Here, we discover a class of superflat bands in general twisted bilayer systems beyond the low-energy physics of magic-angle twisted counterparts. By considering continuous lattice dislocation, we obtain intrinsic localized states, which are spectrally isolated at lowest and highest energies and spatially centered around the AA stacked region, governed by the macroscopic effective energy potential well. Such lo…
Angle disorder is an intrinsic feature of twisted bilayer graphene and other moiré materials. Here, we discuss electron transport in twisted bilayer graphene in the presence of angle disorder. We compute the local density of states and the Landauer-Büttiker transmission through an angle disorder barrier of width comparable to the moiré period, using a decimation technique based on a real space description. We find that barriers which separate regions where the width of the bands differ by 50% or more lead to a minor suppression of the transmission, and that the transmission is close to one for…
We study the edge states of twisted bilayer graphene and their topological origin. We show that the twisted bilayer graphene has special edge states associated with the moiré pattern, and the emergence of these moiré edge states is linked with the sliding Chern number, which describes topological charge pumping caused by relative interlayer sliding. When one layer of the twisted bilayer is relatively slid with respect to the other layer, the edge states are transferred from a single band to another across the band gap, and the number of the edge states pumped in a sliding cycle is shown to be …
We show that the twisted graphene bilayer can reveal unusual topological properties at low energies, as a consequence of a Dirac-point splitting. These features rely on a symmetry analysis of the electron hopping between the two layers of graphene and we derive a simplified effective low-energy Hamiltonian which captures the essential topological properties of twisted bilayer graphene. The corresponding Landau levels peculiarly reveal a degenerate zero-energy mode which cannot be lifted by strong magnetic fields.
Electronic structures and their Landau quantizations in twisted graphene bilayer and trilayer are investigated using scanning tunnelling microscopy and spectroscopy. In the twisted trilayer, the top graphene layer and second layer are AB (Bernal) stacking and there is a stacking misorientation between the second layer and third layer. Both the twisted bilayer and trilayer exhibit two pronounced low-energy van Hove singularities (VHSs) in their spectra. Below the VHSs, the observed Landau level quantization in the twisted bilayer is identical to that of massless Dirac fermion in graphene monola…
Twisted bilayer graphene provides a new two-dimensional platform for studying electron interaction phenomena and flat band properties such as correlated insulator transition, superconductivity and ferromagnetism at certain magic angles. Here, we present strong evidence of correlated insulator states and superconductivity signatures in p-type twisted double-bilayer WSe$_2$. Enhanced interlayer interactions are observed when the twist angle decreases to a few degrees as reflected by the high-order satellites in the electron diffraction patterns taken from the 2H/3R-stacked domains reconstructed …
We introduce a minimum tight-binding model with only three parameters extracted from graphene and untwisted bilayer graphene. This model reproduces quantitatively the electronic structure of not only these two systems and bulk graphite near the Fermi level, but also that of twisted bilayer graphene including the value of the magic angle, at which bands at $E_F$ flatten without overlap and two gaps open, one above and one below $E_F$. The Hamiltonian is sufficiently transparent and flexible to be adopted to other twisted layered systems.
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…
Inter-twisted bilayers of two-dimensional (2D) materials can host low-energy flat bands, which offer opportunity to investigate many intriguing physics associated with strong electron correlations. In the existing systems, ultra-flat bands only emerge at very small twist angles less than a few degrees, which poses challenge for experimental study and practical applications. Here, we propose a new design principle to achieve low-energy ultra-flat bands with increased twist angles. The key condition is to have a 2D semiconducting material with large energy difference of band edges controlled by …
Flatbands with extremely narrow bandwidths on the order of a few mili-electron volts can appear in twisted multilayer graphene systems for appropriate system parameters. Here we investigate the electronic structure of a twisted bi-bilayer graphene, or twisted double bilayer graphene, to find the parameter space where isolated flatbands can emerge as a function of twist angle, vertical pressure, and interlayer potential differences. We find that in twisted bi-bilayer graphene the bandwidth is generally flatter than in twisted bilayer graphene by roughly up to a factor of two in the same paramet…
We numerically calculate the optical conductivity of twisted graphene bilayers within the continuum model. To obtain the imaginary part, we employ the regularized Kramers-Kronig relation allowing us to discuss arbitrary twist angles, chemical potential and temperature. We find that the Drude weight $D$ as function of the chemical potential $μ$ closely follows the shell structure of twisted bilayer displayed by the density of states. For certain angles, this results in a transport gap D=0 at finite $μ$. We also discuss the loss function which, for low doping, is characterized by acoustic interb…
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 investigate the gap in the single-electron spectrum of twisted bilayer graphene. In a perfect infinite lattice of a twisted bilayer, the gap varies exponentially in response to weak changes of the twist angle. Such a large sensitivity makes theoretical predictions of the gap nearly impossible, since experimentally the twist angle is always known with finite accuracy. To address this issue, we numerically study finite clusters of twisted bilayer graphene. For finite systems, changing the twist angle causes a gradual crossover between gapless and gapped regimes. The crossover occurs when the …
We investigate the band structure of twisted monolayer-bilayer graphene (tMBG), or twisted graphene on bilayer graphene (tGBG), as a function of twist angles and perpendicular electric fields in search of optimum conditions for achieving isolated nearly flat bands. Narrow bandwidths comparable or smaller than the effective Coulomb energies satisfying $U_{\textrm{eff}} /W \gtrsim 1$ are expected for twist angles in the range of $0.3^{\circ} \sim 1.5^{\circ}$, more specifically in islands around $θ\sim 0.5^{\circ}, \, 0.85^{\circ}, \,1.3^{\circ}$ for appropriate perpendicular electric field magn…
Moiré superlattice created by twist stacking has multiple physical properties. These physical properties depend on the twist angle, hence investigation of the twist angle dependency is important for the deep understanding of physical phenomena in moiré superlattice. In this work, negative magnetoresistance owing to weak localization (WL) was investigated in twisted double bilayer graphene (TDBG) as a function of the twist angle. The ratio of the intervalley scattering time to the intravalley scattering time, estimated using the WL formula for bilayer graphene, tended to decrease as the twist a…
Theory predicts that the application of an electric field breaks the inversion symmetry of AB and BA stacked domains in twisted bilayer graphene, resulting in the formation of a triangular network of one-dimensional valley-protected helical states. This two-dimensional network of one-dimensional states has been observed in several studies, but direct experimental evidence that the electronic transport in these one-dimensional states is valley-protected is still lacking. In this study, we report the existence of the network in small-angle twisted bilayer graphene at room temperature. Moreover, …
We theoretically investigated phonon dispersion in AA-stacked, AB-stacked and twisted bilayer graphene with various rotation angles. The calculations were performed using the Born-von-Karman model for the intra-layer atomic interactions and the Lennard-Jones potential for the inter-layer interactions. It was found that the stacking order affects the out-of-plane acoustic phonon modes the most. The difference in the phonon densities of states in the twisted bilayer graphene and in AA- or AB-stacked bilayer graphene appears in the phonon frequencies range 90 - 110 1/cm. Twisting bilayer graphene…
The experimental control over the twist angle in twisted bilayer graphene has not been reported and its realistic structure is most likely incommensurate. In this paper, we develop a tight-binding virtual crystal approximation theory to study the electronic properties in incommensurate twisted bilayer graphene. The theory yields the electronic band structure and the local density of states for any incommensurate twist angle θ between the graphene sheets. Angle dependent Van Hove singularities are observed in the numerically calculated local density of states. In accord with observations in sca…
The transport properties of a twisted bilayer graphene barrier are investigated for various twist angles. Remarkably, for small twist angles around the magic angle $θ_m \sim 1.05^{\circ}$, the local currents around the AA-stacked regions are strongly enhanced compared to the injected electron rate. Furthermore, the total and counterflow (magnetic) current patterns show high correlations in these regions, given rise to well-defined magnetic moments that form a magnetic Moiré superlattice. The orientation and magnitude of these magnetic moments changes as function of the gate voltage and possibl…
Twisting in bilayers introduces structural chirality with two enantiomers, i.e., left- and right-hand bilayers, depending on the oriented twist angle. The interplay between this global chirality and additional degrees of freedom, such as magnetic ordering and the local octahedral chirality arising from the geometry of the bonds, can yield striking phenomena. In this work, we focus on collinear antiferromagnetic CrI$_3$ twisted homo-bilayers, which are characterized by a staggered octahedral chirality in each monolayer. Using symmetry analysis, density functional theory and tight-binding model …
Twisted van der Waals bilayers provide an ideal platform to study the electron correlation in solids. Of particular interest is the 30 degree twisted bilayer honeycomb lattice system, which possesses an incommensurate Moire pattern and uncommon electronic behaviors may appear due to the absence of phase coherence. Such system is extremely sensitive to further twist and many intriguing phenomena will occur. In this work, we show that due to the twist induced spatial inhomogeneity of interlayer coupling, there emerges an U(1) gauge field in magnetic transition-metal dichalcogenides (TMD) bilayer…
We examine the quantum Hall effect in bilayer graphene grown on Cu substrates by chemical vapor deposition. Spatially resolved Raman spectroscopy suggests a mixture of Bernal (A-B) stacked and rotationally faulted (twisted) domains. Magnetotransport measurements performed on bilayer domains with a wide 2D band reveal quantum Hall states (QHSs) at filling factors $ν=4, 8, 12$ consistent with a Bernal stacked bilayer, while magnetotransport measurements in bilayer domains defined by a narrow 2D band show a superposition of QHSs of two independent monolayers. The analysis of the Shubnikov-de Haas…
