Bulletin of the American Physical Society
APS March Meeting 2021
Volume 66, Number 1
Monday–Friday, March 15–19, 2021; Virtual; Time Zone: Central Daylight Time, USA
Session J42: Theory of Twisted BilayerLive

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Sponsoring Units: DCMP Chair: Michael Zaletel 
Tuesday, March 16, 2021 3:00PM  3:12PM Live 
J42.00001: Ab initio fourband Wannier tightbinding model for generic twisted graphene systems Jin Cao, Maoyuan Wang, ChengCheng Liu, Yugui Yao The newly realized twisted graphene systems such as twisted bilayer graphene (TBG), twisted double bilayer graphene (TDBG), and twisted trilayer graphene (TTG) have attracted widespread theoretical attention. Therefore, a simple and accurate model of the systems is of vital importance for the further study. Here, we construct the symmetryadapted localized Wannier orbitals and the corresponding ab initio minimal twovalley fourband effective tightbinding models for generic twisted graphene systems with small twist angle. Such twovalley model evades the Wannier obstruction caused by the fragile topology in onevalley model. The real space valley operator is introduced to explicitly describe the valley U_{v}(1) symmetry. Each symmetryadapted Wannier orbital shows a peculiar threepeak form with its maximum at AA spots and its center at AB or BA spots. An extended Hubbard model is also obtained and the related parameters are presented explicitly. We provide an approach to systematically build the Wannier tightbinding model for generic twisted graphene systems. Our model provides a firm basis for further study of the manybody effects in these systems. 
Tuesday, March 16, 2021 3:12PM  3:24PM Live 
J42.00002: Flat band carrier confinement in magic angle twisted bilayer Graphene Nikhil Tilak, Xinyuan Lai, Shuang Wu, zhenyuan zhang, Mingyu Xu, RAQUEL DE ALMEIDA RIBEIRO, Paul C Canfield, Eva Andrei Magic angle twisted bilayer graphene has emerged as a powerful platform for studying strongly correlated electron physics, owing to its almost dispersionless lowenergy, flat, 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 correlation physics from disorder effects. However, owing to the 2D nature of the system and the relatively low carrier density, the samples are highly susceptible to doping inhomogeneity which can drastically modify the local potential landscape. This potential disorder is distinct from the twistangle variation which has been studied elsewhere. Using low temperature scanning tunneling spectroscopy we demonstrated that the flat bands in magic angle twisted bilayer graphene can substantially amplify even negligibly small doping inhomogeneity. As a result the charge carriers become confined, obscuring the correlation effects associated with the intrinsic physics of magicangle twisted bilayer graphene 
Tuesday, March 16, 2021 3:24PM  3:36PM Live 
J42.00003: Flat bands and gaps in twisted double bilayer graphene Francisco Culchac, Rafael Del Grande, Rodrigo Capaz, Leonor Chico, Eric Suarez Morell We present electronic structure calculations of twisted double bilayer graphene (TDBG): a tetralayer graphene structure composed of two ABstacked graphene bilayers with a relative rotation angle between them. Using firstprinciples calculations, we find that TDBG is semiconducting with a band gap that depends on the twist angle, that can be tuned by an external electric field. The gap is consistent with TDBG symmetry and its magnitude is related to surface effects, driving electron transfer from outer to inner layers. The surface effect competes with an energy upshift of localized states at inner layers, giving rise to the peculiar angle dependence of the band gap, which reduces at low angles. For these low twist angles, the TDBG develops flat bands, in which electrons in the inner layers are localized at the AA regions, as in twisted bilayer graphene. 
Tuesday, March 16, 2021 3:36PM  3:48PM Live 
J42.00004: General Theory of Flat Bands and Magic Angles in Twisted Dirac Materials Aaron Dunbrack, Jennifer Cano Twisted bilayer graphene has been a center of recent theoretical and experimental interest due to the emergence of magic angles and the interactiondriven insulating and superconducting phases that result from nearlyflat bands. The BistritzerMacDonald model provides a framework to understand the origin of the flat bands. Using perturbation theory, we generalize this analysis to any interface between two twisted 2D Dirac materials, one with N Dirac cones and one with M Dirac cones (where N and M may be odd, as surface states of topological insulators), under assumptions of timereversal and rotational symmetry. We then use this framework to consider two special cases: a TIonTI interface and a grapheneonTI interface. We find that spinflipping interactions serve a vital role in forming magic angles in both systems. 
Tuesday, March 16, 2021 3:48PM  4:00PM Live 
J42.00005: Higher Order Magic in Twisted Four Layer Graphene Adam Eaton, Herb Fertig, Yantao Li, Babak Seradjeh

Tuesday, March 16, 2021 4:00PM  4:12PM Live 
J42.00006: Onedimensional flat bands in twisted bilayer germanium selenide Dante Kennes, Lede Xian, Martin Claassen, Angel Rubio Experimental advances in the fabrication and characterization of fewlayer materials stacked at a relative twist of small angle have recently shown the emergence of flat energy bands. As a consequence electron interactions become relevant, providing inroads into the physics of strongly correlated twodimensional systems. Here, we demonstrate by combining large scale ab initio simulations with numerically exact strong correlation approaches that an effective onedimensional system emerges upon stacking two twisted sheets of GeSe, in marked contrast to all moiré systems studied so far. This not only allows to study the necessarily collective nature of excitations in one dimension, but can also serve as a promising platform to scrutinize the crossover from two to one dimension in a controlled setup by varying the twist angle, which provides an intriguing benchmark with respect to theory. We thus establish twisted bilayer GeSe as an intriguing inroad into the strongly correlated physics of lowdimensional systems. 
Tuesday, March 16, 2021 4:12PM  4:24PM Live 
J42.00007: Relaxation Effects in Twisted Bilayer Graphene: a MultiScale Approach Nicolas Leconte, Srivani Javvaji, Jiaqi An, Appalakondaiah Samudrala, Jeil Jung We present a multiscale approach to capture the interdependent atomic and electronic structures of suspended and hexagonal boron nitride (hBN) supported twisted bilayer graphene (tBG) by using rescaled two center interlayer hopping terms to calibrate the flat band magic angle to ∼ 1.08^{ο}, as a way to resolve the indeterminacy of atomic/electronic structure models whose magic angles are bracketed between 0.9^{ο} −1.3^{ο}. We use electronic structrure hopping parameters extracted from density functional local density approximation except for an enhanced Fermi velocity of υ_{F} ≈ 10^{6} m/s and atomic force fields informed by stacking and interlayer distancedependent density functional theory total energies, including systematically improved exact exchange and random phase approximation (EXX+RPA), to calculate the highresolution spectral functions that can be compared with experimental angleresolved photoemission spectra (ARPES). 
Tuesday, March 16, 2021 4:24PM  4:36PM Live 
J42.00008: Theory of moiré nematic state in twisted doublebilayer graphene Mathias Scheurer, Rhine Samajdar, Simon Turkel, Carmen Rubio Verdú, Larry Song, Lennart Klebl, Kenji Watanabe, Takashi Taniguchi, Hector Ochoa, Lede Xian, Dante Kennes, Angel Rubio, Jörn W Venderbos, Abhay Narayan, Rafael Fernandes Graphenebased moiré superlattice systems, such as twisted bilayer graphene, have attracted considerable interest in the last few years, as they display a remarkable variety of correlated phenomena. In particular, besides correlated insulating phases in the vicinity of integer fillings, separated by superconducting domes, there is evidence of other ordering tendencies at noninteger fillings; these, however, remain less explored. A notable example is provided by scanning tunneling microscopy measurements on twisted doublebilayer graphene, which reveal the presence of spontaneous threefold symmetry breaking for partially filled flat bands, i.e. nematic order. Here we discuss how these experimental results allow us to determine the underlying microscopic form of the nematic order parameter. Through a detailed comparison of theory and experiment, we show that the dominant contribution to the observed nematic pattern arises from states at the moiré scale rather than at the microscopic scale of the individual graphene lattices. We will also discuss theoretically that twisted doublebilayer graphene allows for an unprecedented tunability of the orientation of the nematic director via the displacement field. 
Tuesday, March 16, 2021 4:36PM  4:48PM Live 
J42.00009: Atomicscale structure and electronic properties of twisted double bilayer graphene: topological edge states and broken symmetries Carmen Rubio Verdú, Alexander Kerelsky, Simon Turkel, Larry Song, Lennart Klebl, Rhine Samajdar, Mathias Scheurer, Jorn W. F. Venderbos, Lei Wang, Dorri Halbertal, Nathan R Finney, Kenji Watanabe, Takashi Taniguchi, Hector Ochoa, Lede Xian, Dante Kennes, James Hone, Cory Dean, Dmitri Basov, Rafael Fernandes, Angel Rubio, Abhay Narayan Van der Waals materials stacked with an interlayer twist are an excellent platform towards achieving gatetunable correlated phenomena linked to the formation of flat bands. We demonstrate the formation of correlated phases in twisted double bilayer graphene (tDBG) in two regimes of twist angle: minimally twisted (<0.1°) and 1.1°. Tinyangle tDBG host large regions of uniform rhombohedral graphene where scanning tunneling spectroscopy reveals a sharp flat band of 35 meV halfwidth. We demonstrate that, when this flat band straddles the Fermi level, a correlated manybody gap emerges. Moreover, we show that ABCA graphene hosts surface topological edge states at natural interfaces with ABAB graphene. Scanning tunneling microscopy on tDBG at higher twist (~1.1°) reveals the presence of van Hove singularities on all inequivalent moiré sites. Tuning carrier density and displacement field reveals longrange broken C_{3} symmetry that emerge when the Fermi level is at the electronic flat bands. We demonstrate that the C_{3} symmetry breaking is a manifestation of an interactiondriven electronic nematic phase, which emerges even away from integer fillings. The nematic instability is an emergent phenomenon at the scale of the moiré lattice, pointing to its universal character. 
Tuesday, March 16, 2021 4:48PM  5:00PM Live 
J42.00010: Electronic nematicity in a transition metal dichalcogenide heterobilayer Moire system Michael Matty, Steven Allan Kivelson, EunAh Kim Moiré systems have recently garnered tremendous attention due to their highly tunable electronic properties, which allow them to realize a rich set of electronic states. Recent experiments on a WS2/WSe2 heterobilayer system reveal a series of chargeordered states at various commensurate Moiré lattice fillings. These experiments also find evidence for rotational symmetry breaking in the entire filling region between 1/3 and 2/3. Specifically, we use Monte Carlo simulations to explore the phase diagram for charge density wave and nematic phases at nonzero temperatures in the vicinity of and away from various commensurate densities. We also study the properties of topological defects involved in the melting of the charge density waves. 
Tuesday, March 16, 2021 5:00PM  5:12PM Live 
J42.00011: Nematic order in twisted bilayer graphene by valley + spin fluctuation interference mechanism Seiichiro Onari, Hiroshi Kontani In the magic angle twisted bilayer graphene (TBG), the nearly flat band emerges as a good platform of the strongly correlated electron systems. Especially, the C_{3}symmetrybreaking nematic state observed in the TBG near the van Hove singularity (VHS) filling attracts increasing attention [1]. Here, we analyze the nematic state by focusing on the quantum interference mechanism, which was developed in the field of Febased superconductors [2]. We identify the nematic state in the TBG as the bond order [3], which is consistent with experiments. This nematic state originates from the interferences among the valley + spin fluctuations, due to the presence of the valley degrees of freedom and absence of the onsite Hund's coupling in the TBG. 
Tuesday, March 16, 2021 5:12PM  5:24PM Live 
J42.00012: Flat bands in twisted transition metal dichalcogenide bilayers C Stephen Hellberg, Madeleine Phillips The electronic properties of transition metal dichalcogenide (TMD) bilayers vary according to the local atomic structure [1]. In minimally twisted bilayers, there is significant atomic reconstruction away from the rigid moiré pattern [2]. We present the results of density functional theory (DFT) calculations that model the electronic properties of MoSe_{2}/WSe_{2} bilayers with a small twist away from commensurate 180degree stacking. We present band structures and local densities of states that exhibit flat bands in the gap near the band edges. 
Tuesday, March 16, 2021 5:24PM  5:36PM Live 
J42.00013: Twisted bilayer WSe_{2} (II): Quantum phase diagram of a MoiréHubbard model Fengcheng Wu, Haining Pan We theoretically study a generalized Hubbard model on moiré superlattices of twisted bilayers, and find very rich fillingfactordependent quantum phase diagrams tuned by interaction strength and twist angle. Strong longrange Coulomb interaction in the moiréHubbard model induces Wigner crystals at a series of fractional filling factors. The effective lattice of the Wigner crystal is controlled by the filling factor, and can be triangle, rectangle, honeycomb, kagome, etc., providing a single platform to realize many different spin models on various lattices by simply tuning carrier density. In addition to Wigner crystals that are topologically trivial, interactioninduced Chern insulators emerge in the phase diagram. This finding paves a way for engineering interactioninduced quantum anomalous Hall effect in moiréHubbard systems where the corresponding singleparticle moiré band is topologically trivial. 
Tuesday, March 16, 2021 5:36PM  5:48PM Live 
J42.00014: Twisted bilayer physics in the square lattice Fan Cui, Qiang Zhang, Congcong Le, ChingKai Chiu, Jiangping Hu Twisted bilayer graphene brings the flatness of the Moire energy bands serving a new playground for strong correlations and topological phases. Beyond the hexagonal lattice, a similar twisted platform might emerge in other crystal structures. We explore twisted bilayer physics in different types of lattices. In particular, we focus on the twisted physics in the square lattice and propose material realizations. 
Tuesday, March 16, 2021 5:48PM  6:00PM Live 
J42.00015: Accurate abinitio tightbinding model for twisted transition metal dichalcogenide bilayers Kemal Atalar, Valerio Vitale, Johannes Lischner, Arash A Mostofi The discovery of correlated and superconducting states in magicangle twisted bilayer graphene has generated interest in twisted heterostructures composed of other 2D materials. For example, signatures of superconductivity [12] and exotic optical behaviour [3] have been observed recently in twisted bilayers of transition metal dichalcogenides (TMDs). 
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