The in-plane phonon-drag thermopower $S^g$, diffusion thermopower $S^d$ and the power factor $PF$ are theoretically investigated in twisted bilayer graphene (tBLG) as a function of twist angle $θ$, temperature $T$ and electron density $n_s$ in the region of low $T$ (1-20 K). As $θ$ approaches magic angle $θ_m$, the $S^g$ and $S^d$ are found to be strongly enhanced, which is manifestation of great suppression of Fermi velocity ${ν_F}^*$ of electrons in moire flat band near $θ_m$. This enhancement decreases with increasing $θ$ and $T$. In the Bloch- Gruneisen (BG) regime, it is found that $S^g \sim {ν_F}^{* -2}$, $T^3$ and ${n_s}^{-1/2}$. As $T$ increases, the exponent $δ$ in $S^g \sim T^δ$, changes from 3 to nearly zero and a maximum $S^g$ value of $\sim$ 10 mV/K at $\sim$ 20 K is estimated. $S^g$ is larger (smaller) for smaller $n_s$ in low (high) temperature region. On the other hand, $S^d$, taken to be governed by Mott formula, $\sim {ν_F}^{* -1}$, $T$ and ${n_s}^{-1/2}$ and $S^d<<S^g$ for $T > \sim$ 2 K. The power factor $PF$ is also found to be strongly $θ$ dependent and very much enhanced. Consequently, possibility of a giant figure of merit is discussed.In tBLG, $θ$ acts as a strong tuning parameter of both $S^g$ and $S^d$ and $PF$ in addition to $T$ and $n_s$. Our results are qualitatively compared with the measured out-of-plane thermopower in tBLG.
We report thermopower measurements of interacting GaAs bilayer hole systems. When the carrier densities in the two layers are equal, these systems exhibit a reentrant insulating phase near the quantum Hall state at total filling factor $ν=1$. Our data show that as the temperature is decreased, the thermopower diverges in the insulating phase. This behavior indicates the opening of an energy gap at low temperature, consistent with the formation of a pinned Wigner solid. We extract an energy gap and a Wigner solid melting phase diagram.
Magic-angle twisted bilayer graphene (MtBLG) has proven to be an extremely promising new platform to realize and study a host of emergent quantum phases arising from the strong correlations in its narrow bandwidth flat band. In this regard, thermal transport phenomena like thermopower, in addition to being coveted technologically, is also sensitive to the particle-hole (PH) asymmetry, making it a crucial tool to probe the underlying electronic structure of this material. We have carried out thermopower measurements of MtBLG as a function of carrier density, temperature and magnetic field, and …
Thermopower probing emergent local moments in magic-angle twisted bilayer graphene
Indian Institute of Science（印度科学学院）；Indian Institute of Technology Kanpur（坎普尔印度理工学院）；National Institute for Materials Science（物质材料研究机构）；The Ohio State University（俄亥俄州立大学）
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…
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 …
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…
Graphene bilayers exhibit zero-energy flat bands at a discrete series of magic twist angles. In the absence of intra-sublattice inter-layer hopping, zero-energy states satisfy a Dirac equation with a non-abelian SU(2) gauge potential that cannot be diagonalized globally. We develop a semiclassical WKB approximation scheme for this Dirac equation by introducing a dimensionless Planck's constant proportional to the twist angle, solving the linearized Dirac equation around AB and BA turning points, and connecting Airy function solutions via bulk WKB wavefunctions. We find zero energy solutions at…
Proximity Effects Between the Graphene Quasicrystal and Magic-Angle Twisted Bilayer Graphene
Catalan Institute of Nanoscience and Nanotechnology (ICN2), CSIC and BIST（加泰罗尼亚纳米科学技术研究所（ICN2），西班牙国家研究委员会和巴塞罗那高等研究院）；Department of Physics, Campus UAB（巴塞罗那自治大学物理系）；Institute of Condensed Matter and Nanosciences, Université catholique de Louvain (UCLouvain)（天主教鲁汶大学凝聚态与纳米科学研究所）；ICREA–Institució Catalana de Recerca i Estudis Avançats（加泰罗尼亚研究与高级研究所（ICREA））
The First Magic Angle Beyond the Chiral Limit in Twisted Bilayer Graphene
Universidad Nacional Autónoma de México (UNAM)（墨西哥国立自治大学）；NYU Shanghai（纽约大学上海分校）；NYU-ECNU Institute of Physics at NYU Shanghai（纽约大学上海纽约大学物理研究所）；Hainan University（海南大学）；IMDEA Nanoscience（IMDEA纳米科学研究所）；Donostia International Physics Center（圣塞巴斯蒂安国际物理中心）
In graphene, charged defects break the electron-hole symmetry and can even give rise to exotic collapse states when the defect charge exceeds a critical value which is proportional to the Fermi velocity. In this work, we investigate the electronic properties of twisted bilayer graphene (tBLG) with charged defects using tight-binding calculations. Like monolayer graphene, tBLG exhibits linear bands near the Fermi level but with a dramatically reduced Fermi velocity near the magic angle (approximately 1.1°). This suggests that the critical value of the defect charge in magic-angle tBLG should al…
Gate-tunable Josephson diodes in magic-angle twisted bilayer graphene
RWTH Aachen University（亚琛工业大学）；Forschungszentrum Jülich（于利希研究中心）；University of Hamburg（汉堡大学）；University of Würzburg（维尔茨堡大学）；National Institute for Materials Science（国立材料研究所）；University of Vienna（维也纳大学）
The importance of phonons in the strong correlation phenomena observed in twisted bilayer graphene (TBG) at the so-called magic-angle is under debate. Here we apply gate-dependent micro-Raman spectroscopy to monitor the G band linewidth in TBG devices of twist angles $θ=0^{\circ}$, $\sim 1.1^{\circ}$ (magic-angle) and $\sim 7^{\circ}$ (large angle). The results show a broad and p/n-asymmetric doping behavior at the magic-angle, in clear contrast to the behavior observed in twist angles above and below. Atomistic modeling reproduces the experimental observations, revealing how the unique electr…
Graphene, a one-layer honeycomb lattice of carbon atoms, exhibits unconventional phenomena and attracts much interest since its discovery. Recently, an unexpected Mott-like insulator state induced by moiré pattern and a superconducting state are observed in magic-angle-twisted bilayer graphene, especially, without correlations between electrons, which gives more hints for the understanding and investigation of strongly correlated phenomena. The photon as boson, behaving differently with fermion, can also retrieve the unconventional phenomena of graphene, such as the bearded edge state which is…
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…
Twisting two layers into a magic angle (MA) of ~1.1° is found essential to create low energy flat bands and the resulting correlated insulating, superconducting, and magnetic phases in twisted bilayer graphene (TBG). While most of previous works focus on revealing these emergent states in MA-TBG, a study of the twist angle dependence, which helps to map an evolution of these phases, is yet less explored. Here, we report a magneto-transport study on one non-magic angle TBG device, whose twist angle θ changes from 1.25° at one end to 1.43° at the other. For θ=1.25°, we observe an emergence of to…
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.
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…
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…
Twisted bilayered graphenes at magic angles are systems housing long ranged periodicity of Moiré pattern together with short ranged periodicity associated with the individual graphenes. Such materials are a fertile ground for novel states largely driven by electronic correlations. Here we find that the ubiquitous Casimir force can serve as a platform for macroscopic manifestations of the quantum effects stemming from the magic angle bilayered graphenes properties and their phases determined by electronic correlations. By utilizing comprehensive calculations for the electronic and optical respo…
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 study the stability and electronic structure of magic-angle twisted bilayer graphene on the hexagonal boron nitride (TBG/BN). Full relaxation has been performed for commensurate supercells of the heterostructures with different twist angles ($θ'$) and stackings between TBG and BN. We find that the slightly misaligned configuration with $θ' = 0.54^\circ$ and the AA/AA stacking has the globally lowest total energy due to the constructive interference of the moiré interlayer potentials and thus the greatly enhanced relaxation in its $1 \times 1$ commensurate supercell. Gaps are opened at the F…
Magic-angle twisted bilayer graphene (MATBG) is notable as a highly tunable platform for investigating strongly correlated phenomena such as high-$T_c$ superconductivity and quantum spin liquids, due to easy control of doping level through gating and sensitive dependence of the magic angle on hydrostatic pressure. Experimental observations of correlated insulating states, unconventional superconductivity and ferromagnetism in MATBG indicate that this system exhibits rich exotic phases. In this work, using density functional theory calculations in conjunction with the effective screening medium…
Recent research on twisted bilayer graphene (TBG) uncovered that its twist-angle-dependent electronic structure leads to a host of unique properties, such as superconductivity, correlated insulating states, and magnetism. The flat bands that emerge at low twist angles in TBG result in sharp features in the electronic density of states (DOS), affecting transport. Here we show that they lead to superior and tuneable thermoelectric (TE) performance. Combining an iterative Boltzmann transport equation solver and electronic structure from an exact continuum model, we calculate thermoelectric transp…
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…
The long wavelength moiré superlattices in twisted 2D structures have emerged as a highly tunable platform for strongly correlated electron physics. We study the moiré bands in twisted transition metal dichalcogenide homobilayers, focusing on WSe$_2$, at small twist angles using a combination of first principles density functional theory, continuum modeling, and Hartree-Fock approximation. We reveal the rich physics at small twist angles $θ<4^\circ$, and identify a particular magic angle at which the top valence moiré band achieves almost perfect flatness. In the vicinity of this magic angle, …
In the magic-angle twisted bilayer graphene (MA-TBG), strong electron-electron (e-e) correlations caused by the band-flattening lead to many exotic quantum phases such as superconductivity, correlated insulator, ferromagnetism, and quantum anomalous Hall effects, when its low-energy van Hove singularities (VHSs) are partially filled. Here our high-resolution scanning tunneling microscope and spectroscopy measurements demonstrate that the e-e correlation in a non-magic-angle TBG with a twist angle θ = 1.49 still plays an important role in determining its electronic properties. Our most interest…
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…
Flat band electronic modes are responsible for superconductivity in twisted bilayer graphene (TBG) rotated at magic angles. From there other magic angles can be found for any multilayered twisted graphene systems. Eventually, this lead to the discovery of the highest ever known electron-electron correlated material. Moreover, the quantum phase diagram of TBG is akin to those observed among high-$T_{c}$ superconductors and thus there is a huge research effort to understand TBG in the hope of clarifying the physics behind such strong correlations. A particularity of the TBG is the coexistence of…
In the vicinity of the magic angle in twisted bilayer graphene (TBG), the two low-energy van Hove singularities (VHSs) become exceedingly narrow1-10 and many exotic correlated states, such as superconductivity, ferromagnetism, and topological phases, are observed11-16. Heterostrain, which is almost unavoidable in the TBG, can modify its single-particle band structure and lead to novel properties of the TBG that have never been considered so far. Here, we show that heterostrain in a TBG near the magic angle generates a new zero-energy flat band between the two VHSs. Doping the TBG to partially …
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…
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…
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…
Emergent quantum phases driven by electronic interactions can manifest in materials with narrowly dispersing, i.e. "flat", energy bands. Recently, flat bands have been realized in a variety of graphene-based heterostructures using the tuning parameters of twist angle, layer stacking and pressure, and resulting in correlated insulator and superconducting states. Here we report the experimental observation of similar correlated phenomena in twisted bilayer tungsten diselenide (tWSe2), a semiconducting transition metal dichalcogenide (TMD). Unlike twisted bilayer graphene where the flat band appe…
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 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 …
