Bulletin of the American Physical Society
APS March Meeting 2021
Monday–Friday, March 15–19, 2021; Virtual; Time Zone: Central Daylight Time, USA
Session A42: Bandstructures of Twisted BilayersLive

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Sponsoring Units: DCMP Chair: Jianhao Chen, Peking Univ 
Monday, March 15, 2021 8:00AM  8:12AM Live 
A42.00001: Controlling a quadratic band touching with an incommensurate potential Junhyun Lee, Jed Pixley We theoretically investigate semimetals with quadratic band touching points in the presence of incomensurate potentials. Several different models with different symmetries, each realizing the quadratic band touching dispersions are considered. We combine analytical and numerical methods to examine the properties of the reconstructed quadratic touching bands such as the effective mass and whether the system remains as a semimetal. It is determined under what general conditions can this problem have a "magicangle" where the curvature of the quadratic band touching vanishes. The experimental implications of these results are discussed. 
Monday, March 15, 2021 8:12AM  8:24AM Live 
A42.00002: Flat Bands on Honeycomb Superlattices Zihao Qi, Eric Bobrow, Yi Li Flat bands on a honeycomb lattice have provided useful platforms to study strong correlation and topological physics. Honeycomb superlattices of sorbitals have been discovered to host flat bands. We study the origin of the robustness of flat bands in the presence of local perturbations respecting lattice symmetry. Analytically, we derive the flat band energies when various additional hoppings are introduced. Moreover, we argue that we can obtain flat bands at arbitrary energies by tuning the perturbation strengths. We also construct localized states due to destructive interference in real space that give rise to the flat bands. We show that symmetryprotected degeneracy is key to the stability of these states and of the flat bands. Finally, we point out the noncontractible loop states in the flat bands of the system. 
Monday, March 15, 2021 8:24AM  8:36AM 
A42.00003: Inducing flat bands in twodimensional materials by zone folding and hybridization Niels Ehlen, Martin Hell, Giovanni Marini, Gianni Profeta, Alexander Grüneis A twodimensional material hosting a flat electronic dispersion at the Fermi level is an appealing system^{1} since the associated singularity in the density of states promotes a variety of electronic and structural instabilities and can drive phase transitions into a superconductor, a chargedensity wave state or magnetic order. In graphene the presence of the Van Hove singularity is a possible way to induce a flat band, though its realization is hindered by the extreme doping needed. We present a method to induce a flat band at the Fermi level of graphene by sandwiching it in between two ordered metal layers. We realize this system by depositing cesium on graphene grown on Ir(111) substrate. By ARPES, we observe a flat dispersion in a large portion of the Brillouin zone. We propose a microscopic structural model, demonstrating that zonefolding due to cesium reconstruction and the consequent cesium/graphene hybridization are at the origin of the flat band formation^{2} and predicting the experimental results with excellent accuracy. 
Monday, March 15, 2021 8:36AM  8:48AM Live 
A42.00004: Multiorbital Flat Band Ferromagnetism with a Provable Percolation Representation Eric Bobrow, Junjia Zhang, Yi Li We consider a twolayer multiorbital system consisting of a p_{x} and p_{y}orbital honeycomb lattice layer and an f_{y(3x2y2)}orbital triangular lattice layer centered on the honeycomb plaquettes. With an appropriately tuned chemical potential difference between these two layers, the system exhibits a flat band with provably ferromagnetic ground states at half filling in the presence of intraorbital Hubbard interactions and Hund’s coupling. Away from half filling, the interacting system admits a percolation representation, where the ground state space is spanned by maximumspin clusters of localized singleparticle states. A paramagneticferromagnetic transition occurs as the band approaches half filling and the space of degenerate ground states becomes dominated by clusters with macroscopic spin. The critical filling of the flat band where this transition occurs can be found through Monte Carlo simulation for spinweighted percolation. 
Monday, March 15, 2021 8:48AM  9:00AM Live 
A42.00005: Supermoire lattices and flat bands in hBN encapsulated graphene Lucian Covaci, Misa Andelkovic, Slavisa Milovanovic, Francois Peeters Although the encapsulation of graphene between hBN layers has been routinely used to improve the electric properties of graphene, it is only recently that an almost perfect alignment with both top and bottom hBN layers has been realized [13]. This has paved the way to combining the effect of the moire patterns induced by each hBN layer and thus generating a longerrange composite supermoire structure. With experimental precision of ~0.1 degrees, this allows for the modification of the low energy electronic properties in the graphene layer by generating new minibands and Dirac points. Furthermore, we have shown that relaxation effects provide a further enhancement of the these effects, generating bandgaps at the principal and secondary Dirac points [4]. We show that under certain conditions flat minibands can develop, making this system amenable to the appearance of strong correlations. Finally, we explore additional effects and degrees of freedom by considering instead an encapsulated bilayer graphene. 
Monday, March 15, 2021 9:00AM  9:12AM Live 
A42.00006: ΓValley TransitionMetalDichalcogenide Moirè Bands Mattia Angeli, Allan MacDonald The valence band maxima of most groupVI transition metal dichalcogenide thin films remain at the Γpoint all the way from bulk to bilayer. In this talk, I will describe a recently developed continuum theory of the moirè minibands that are formed in the valence bands of Γvalley homobilayers by a small relative twist. Our effective theory is benchmarked against largescale ab initio electronic structure calculations that account for lattice relaxation. As a consequence of an emergent D_6 symmetry we find that lowenergy Γvalley moirè holes differ qualitatively from their Kvalley counterparts addressed previously; in energetic order the first three bands realize i) a singleorbital model on a honeycomb lattice, ii) a twoorbital model on a honeycomb lattice, and iii) a singleorbital model on a kagome lattice 
Monday, March 15, 2021 9:12AM  9:24AM Live 
A42.00007: An Exact Diagonalization Study of Twisted Bilayer Graphene at Integer Fillings: Phase Diagram Fang Xie, Aditya Cowsik, Zhida Song, Biao Lian, Andrei B Bernevig, Nicolas Regnault We study the projected Hamiltonian with Coulomb interaction in the 8 flat bands of first magic angle twisted bilayer graphene using exact diagonalization. Employing the U(4) (U(4)xU(4)) symmetries in the nonchiral (chiral) flat band limit, we reduced the Hilbert space to an extent which allows for study around ν=±3, ±2, ±1 fillings. In the first chiral limit, we find that the ground states at these fillings are extremely welldescribed by Chern insulator Slater determinants. We also find that the Flat Metric Condition (FMC) for obtaining a series of exact ground states holds in a large parameter space. For ν=3, the ground state is the spin and valley polarized Chern insulator with ν_{C}=±1 at w_0/w_1≤0.3 (0.9) with (without) FMC. At ν=2, we can only numerically access the valley polarized sector, and we find a spin ferromagneticsinglet phase transition, confirming the perturbative calculation. 
Monday, March 15, 2021 9:24AM  9:36AM Live 
A42.00008: An Exact Diagonalization Study of Twisted Bilayer Graphene at Integer Fillings: Charge Excitation Aditya Cowsik, Fang Xie, Zhida Song, Biao Lian, Andrei B Bernevig, Nicolas Regnault Using exact diagonalization, we study the projected Hamiltonian with Coulomb interaction in the 8 flat bands of first magic angle twisted bilayer graphene. Employing the U(4)xU(4) symmetries in the chiral flat band limit, we reduce Hilbert space which allows for study near integer fillings. In the first chiral limit, we find that the ground states at these fillings are extremely welldescribed by Slater determinants in the Chern basis, and the exactly solvable charge excitations are the lowest charge excitations up to system sizes of 8x8 (for restricted Hilbert space). Physically, the excitations can be understood as adding electrons (holes) to empty bands (filled bands) with either the same or opposite chern number. Higher excitations constitute further U(4)xU(4) excitations on top of the additional particle and justify focusing on excitations close to the analytic and ED ground states. This agreement is apparent at smaller system sizes with the flat metric condition than without, justifying its validity. 
Monday, March 15, 2021 9:36AM  9:48AM Live 
A42.00009: The Plasmon Spectrum of Twisted Bilayer Graphene Nicholas Werner, Andreas Bill Low energy electron collective modes (acoustic plasmons) are an expected feature of layered systems. The unique band structure of Twisted Bilayer Graphene (TBLG) supports longlived acoustic plasmons in the meV energy range. We summarize the relevant features of the continuum band structure with a focus on the flat moiré bands. We then discuss how they shape the plasmon spectrum for several twist angles at varying doping levels. 
Monday, March 15, 2021 9:48AM  10:00AM Live 
A42.00010: Incommensurabilityinduced subballistic narrowbandstates in twisted bilayer graphene Eduardo Castro, Miguel Gonçalves, Hadi Z. Olyaei, Bruno Amorim, Rubem Mondaini, Pedro Ribeiro The localization properties of electrons in incommensurate twisted bilayer graphene 
Monday, March 15, 2021 10:00AM  10:12AM Live 
A42.00011: Twisted van der Waals Metamaterials Syeda Minhal Gardezi, Harris S Pirie, Stephen Carr, William Dorrell, Jenny E. Hoffman Twisted van der Waals (vdW) heterostructures have recently emerged as a tunable platform for studying correlated electrons. However, these materials require significant effort for theoretical and experimental exploration. Here we present a simple platform to reproduce twistronic behavior using acoustic metamaterials made of interconnected air cavities in stacked steel plates [1]. Our classical analog of twisted bilayer graphene (TBG) perfectly replicates the band structures of its quantum counterpart, including mode localization at a magic angle of 1.12°. We then tune the interlayer membrane thickness to achieve an acoustic magic angle as high as 6.01°, equivalent to applying 130 GPa to TBG. In this regime, the localized modes are over five times closer together than at 1.12°, increasing the strength of any emergent nonlinear acoustic couplings. Our results enable greater interconnectivity between quantum materials and acoustic research: twisted vdW metamaterials provide simplified models for exploring twisted electronic systems and may allow the enhancement of nonlinear effects to be translated into acoustics. 
Monday, March 15, 2021 10:12AM  10:24AM Live 
A42.00012: Soft modes in magic angle twisted bilayer graphene Eslam Khalaf, Nick Bultinck, Ashvin Vishwanath, Michael Zaletel We present a systematic study of the lowenergy collective modes for different insulating states at integer fillings in twisted bilayer graphene. In particular, we provide a simple counting rule for the total number of soft modes, and analyze their energies and symmetry quantum numbers in detail. We find two different types of lowenergy modes  (i) approximate Goldstone modes associated with breaking an enlarged U(4)xU(4) symmetry and, surprisingly, a second branch (ii) of nematic modes with nonzero angular momentum under threefold rotation. While the modes of type (ii) are always gapped, we show that their gap depends sensitively on the distribution of Berry curvature, decreasing as the Berry curvature grows more concentrated. For realistic parameter values, the gapped soft modes of both types are found to have comparable gaps of only a few meV, and lie completely inside the meanfield bandgap. Finally, we present a general analysis of the symmetry representations of the soft modes for all possible insulating Slater determinant states, independent of the energetic details. The resulting soft mode degeneracies and symmetry quantum numbers provide a fingerprint of the different insulting states enabling their experimental identification from a measurement of their soft modes. 
Monday, March 15, 2021 10:24AM  10:36AM Live 
A42.00013: Correlations in moiré heterostructures from atomistic modeling Lennart Klebl, Zachary Goodwin, Arash A Mostofi, Johannes Lischner, Carsten Honerkamp, Dante Kennes VanderWaals moiré heterostructures have proven to be highly tunable materials that display a wide variety of anomalous and correlated states of matter (correlated insulators, superconductivity, nematicity). We present how several of these phenomenæ found in different graphenebased multilayer structures can be explained from tightbinding models on the Ångström scale using realistic interactions. We employ the random phase approximation in twisted bilayer graphene with and without Hartree interactions to describe correlated insulating states at integer fillings [1] and further use this method to propose ABC graphene twisted relative to another sheet of graphene as a highly tunable platform for correlated insulating and superconducting states. Functional renormalization group methods are used to characterize the magnetic phases in twisted bilayer graphene for realistic interaction profiles [2] and nematic orderings in twisted double bilayer graphene [3]. 
Monday, March 15, 2021 10:36AM  10:48AM On Demand 
A42.00014: Infrared absorption of gatetuned twisted bilayer graphene Eunjip Choi We report an infrared transmission measurement performed on electrically gated twisted bilayer graphene. The optical 
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