Session B51: Graphene: Electronic Structure and Interactions Interactions: Moire, Correlations, and Topology

Ground State of Magic Angle Twisted Bilayer Graphene at Charge Neutrality II

In magic angle twisted bilayer graphene (MATBG), interactions dominate over the kinetic energy, resulting in correlated insulating states and superconductivity whose origin remains a mystery. Here, using a combination of analytical arguments and numerical calculations we identify a family of candidate insulating ground states at charge neutrality and discuss how external perturbations such as the influence of the substrate or strain can alter the phase diagram.   

Marginal Fermi liquid and dynamical symmetry breaking from Coulomb interaction in twisted bilayer graphene

We investigate the effects of the strong Coulomb interaction near the magic angle of twisted bilayer graphene, focusing on the charge neutrality point and near half-filling of the highest valence band. In this latter instance, we predict the emergence of a marginal Fermi liquid, which can be traced back to the proximity to an extended van Hove singularity and the development of straight segments in the Fermi line. This leads to the linear scaling with energy of particle-hole excitations across the Fermi line, implying in turn the linear temperature dependence of the resistivity, logarithmic corrections to the heat capacity, and the consequent modification of the Wiedemann-Franz law. At the charge neutrality point, we show that the Coulomb interaction may be responsible for the opening of a gap through the condensation of particle-hole excitations about the Dirac nodes. We find in this case a direct competition between the dynamical breakdown of chiral symmetry (which prevails in the strong coupling regime) and the breakdown of time-reversal invariance (which has instead a stronger onset and leads to a Chern insulator phase at intermediate coupling).   

Electrostatic gate-controlled fermi level dependent electronic band structure of graphene

The observation of electronic band structure in 2D material devices as they operate opens limitless opportunities to explore fundamental physics. The most robust technique to probe electronic structure is through angle-resolved photoemission spectroscopy (ARPES) and can now be used to investigate mesoscopic sized 2D materials and their heterostructures. Only being sensitive to filled states, ARPES measurements are restricted to states below the Fermi energy of the sample. Historically, chemical doping has been the preferred technique to manipulate the Fermi energy, but is difficult to control, introduces electronic states that are not intrinsic to the sample of interest, and can only be reversed through high-temperature annealing. Electrostatic doping, having none of these drawbacks, allows us to reversibly investigate the electron energy and momentum states of graphene far above the Dirac point. We will present our results on the electrostatic gate controlled electronic band structure of graphene using nanoARPES.   

Correlated states in magic angle twisted bilayer graphene under the optical conductivity scrutiny

Moiré systems displaying flat bands have emerged as novel platforms to study correlated electron physics. There is evidence of correlation induced effects at the charge neutrality point (CNP) of twisted bilayer graphene which could originate from spontaneous symmetry breaking. We will show how optical conductivity measurements allow to distinguish different symmetry breaking states and to follow the evolution of the band distortions with doping. In the specific case of a nematic order, which breaks the discrete rotational symmetry of the lattice, we find that the Dirac cones tend to be displaced, not only in momentum space but also in energy, inducing a finite density of states and Drude weight at the CNP. The nematic order is revealed in a dc conductivity anisotropy with its sign depending on the degree of relaxation, the doping and the nature of the symmetry breaking   

Correlated states and tunable topological bands in twisted monolayer-bilayer graphene heterostructures

We experimentally investigate twisted van der Waals heterostructures of monolayer graphene rotated with respect to a bernal stacked graphene bilayer. We report transport measurements for devices with twist angles between 0.9 and 1.4°. The electric field allows efficient tuning of the width, isolation and the topology of the moiré bands in this system. By comparing magnetoresistance measurements to numerical simulations, we develop an understanding of the band structure. Finally, we observe correlated states at half- and quarter-fillings, which arise when narrow moire sublattice band is isolated by energy gaps from dispersive bands. We investigate the effects of in-plane and out-of-plane magnetic field on these states and discuss the implication for their spin- and valley- polarization.   

Hartree Fock study of insulating states in twisted bilayer graphene using hybrid Wannier basis

In this work, the insulating behavior of twisted bilayer graphene and in particular the quantum anomalous Hall state has been studied; the effects of electron-electron interaction are taken into account by performing a Hartree-Fock analysis which is the standard approach for finding symmetry broken states. The model is truncated to the active relevant bands and the study is done using the basis of maximally localized Hybrid Wannier functions; this basis on the one hand respects important symmetries of the system, and on the other hand makes the interaction local at least in one direction. It also implies that the geometry of the system is that of a cylinder. Furthermore, by tuning the form/strength of the interaction, we are able to predict some other interesting phases which might potentially be found in the future.   

Local electronic compressibility of magic angle twisted bilayer graphene

Twisted bilayer graphene near the magic angle (MATBG) exhibits remarkably rich electron correlation physics, displaying insulating, magnetic, and superconducting phases. In this talk, we probe the local electronic compressibility of MATBG using a scanning single electron transistor. We find that when carriers are added into this system, they repeatedly refill the same bands, leading to a Dirac-like compressibility cascade near integer moiré fillings. Additionally, we present a clear compressibility asymmetry around the center of the conduction and valence bands, reflecting the evolution from low DOS at charge neutrality to high DOS at the band edges. A mean-field theory that includes this asymmetry reproduces the experimental results, and explains previous observations that were not yet fully understood. This cascade of Dirac revivals should thus serve as the starting point for understanding the unusual behavior in this system.   

Towards correlated electron states in trilayer-graphene Moiré band

The recent discovery of Moiré superconductivity in twisted-bilayer graphene (tBLG) and twisted-double bilayer-graphene (tDBG) systems [1][2][3] has generated a great amount of interest in the condensed matter community. Beyond this model system, this work focuses on studying a new Moiré platform based on the twisted trilayer-graphene. Preliminary magneto-transport measurements will be presented. Characterization of interlayer screening, band evolution with displacement field and Moiré periodicity will also be discussed.

[1] Yuan Cao et al, Nature 556, 43-50 (2018).
[2] Xiaomeng Liu et al, arXiv 1903.08130 (2019).
[3] Xiaobo Lu et al, arXiv 1903.06513 (2019).   

Band flattening in slightly twisted bilayers of Bravais networks

Discovery of superconductivity in twisted bilayer graphene ignited the current intensive studies on stacked 2D materials with moire patterns, especially focusing on flat bands and associated correlated physics. Here, we demonstrate band flattening in twisted bilayers of generic but high symmetric 2D lattices, i.e., 2D Bravais networks [1]. We first show how symmetry of each network gives constraints on the effective potential governing low-energy physics in twisted bilayers. We further numerically demonstrate the band flattening due to the constrained potential using tight-binding models. From the generic theory, we can find an interesting possibility of anisotropic band flattening, in which quasi 1D band dispersion is generated from relatively isotropic original band dispersion. Rich physics is expected with the anisotropic band flattening, ranging from the valley dependent transport to the spin-orbital intertwined model in the strongly correlated limit.

[1] T. Kariyado and A. Vishwanath, arXiv:1905.02206, to appear in Phys. Rev. Research.   

Twist disorder in twisted bilayer graphene

Recent experiments in twisted bilayer graphene have set off a flurry of work due to the observation of purportedly correlated phases at the so-called ``magic-angle.'' The nearly pristine samples of graphene used in the experiment mainly have one significant source of disorder: the twist angle is not uniform throughout the sample. Current models in the literature are inadequate to fully capture this effect, so we introduce and study a new microscopic model in which the twist angle enters as a free parameter in real space. After benchmarking the results of the model with the continuum model, we simulate the effects of twist-angle disorder by constructing “patches” of uniform twist angle. We find that while the minibandwidth and gap are renormalized substantially, the Fermi velocity is not significantly altered. We discuss the implications of this for existing and ongoing experiments on twisted bilayer graphene.   

Higher-Order Topological Insulator in Twisted Bilayer Graphene

Higher-order topological insulators are newly proposed topological phases of matter, whose bulk topology manifests as localized modes at two-or higher-dimensional lower boundaries. In this work, we propose the twisted bilayer graphenes with large angles as higher-order topological insulators, hosting topological corner charges. At large commensurate angles, the intervalley scattering opens up the bulk gap and the corner states occur at half filling. Based on both first-principles calculations and analytic analysis, we show the striking results that the emergence of the corner states do not depend on the choice of the specific angles as long as the underlying symmetries are intact. Our results show that the twisted bilayer graphene can serve as a robust candidate material of two-dimensional higher-order topological insulator.

Ref: arXiv:1907.02868 (2019)   

Topological flat bands without magic angles in massive twisted bilayer graphenes

We show that in massive twisted bilayer graphenes, 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. The phase diagram of finite valley Chern numbers of the isolated moire bands expands with increasing difference between the sublattice selective interlayer tunneling parameters. The valley contrasting circular dichroism for interband optical transitions is constructive near 0° and destructive near 60° alignments and can be tuned through electric field and gate driven polarization of the mini-valleys. Combining massive Dirac materials with various intrinsic gaps, Fermi velocities, interlayer tunneling strengths suggest optimistic prospects of increasing θ_c and achieving correlated states with large U/W effective interaction versus bandwidth ratios.   

Attractive electron-electron interactions from internal screening in magic angle twisted bilayer graphene

Twisted bilayer graphene (tBLG) has emerged as a new platform for studying electron correlations. tBLG exhibits correlated insulating and superconducting states at twist angles close to the largest magic angle, with the phase diagram resembling that of cuprates, which suggests an unconventional mechanism for superconductivity. We have studied the effect of internal screening on electron-electron interactions and Hubbard parameters in undoped tBLG, within the random phase approximation (RPA) and constrained RPA (cRPA). Near the magic angle, the flattening of bands drastically increases the RPA dielectric constant of tBLG and the abrupt change in the band velocity as function of the band energy gives rise to attractive regions in the RPA screened interaction in real space, which could be intimately connected to the reported correlated-insulator and superconducting phases. The cRPA polarizability was used to parametrize a twist-angle-dependent Keldysh model which exhibits a dramatic enhancement with decreasing twist angle, and to calculate the extended Hubbard parameters of a downfolded Hamiltonian. We find that the extended Hubbard parameters depend sensitively on the twist angle and the on-site Hubbard U is a not simply a linear function of twist angle.   

Twistronics in bilayer graphene and other systems

The discovery of twisted bilayer graphene initiated the idea that a novel platform with unprecedented tunability can be garnered with a simple relative twist between two layers. For graphene systems, this technology has generated a versatile system where flat band, superconductivity and magnetism are intertwined. We present our work on the theory of Wannier pair in twisted bilayer graphene. For comparisons, we also study graphene on boron-nitride (GBN) possessing a different Moire pattern, and single-layer graphene (SLG) without a Moire pattern. We will also present novel properties emanating from similar bi-layer systems.

[1] S. Ray, J. Jung, and T. Das, Wannier pairs in the superconducting twisted bilayer graphene and related systems, Phys. Rev. B, 99, 134515 (2019).   

Symmetry breaking states at commensurate fillings of the Moire bands of the twisted bilayer graphene

We study the twisted bilayer graphene system with the continuous model together with the long-range Coulomb interaction. Within the Hartree Fock approximation, we are able to find some symmetry breaking ground states at commensurate fillings of the Moire bands, which will gap out the Dirac points at the reduced Brillouin Zone that are otherwise protected by the symmetry.