Bulletin of the American Physical Society
APS March Meeting 2023
Volume 68, Number 3
Las Vegas, Nevada (March 5-10)
Virtual (March 20-22); Time Zone: Pacific Time
Session A21: Flatbands without Moire |
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Sponsoring Units: DCMP Chair: Sayed Ali Akbar Ghorashi, Stonybrook University Room: Room 213 |
Monday, March 6, 2023 8:00AM - 8:12AM |
A21.00001: Gate tunable topological phase transitions in superlattice potential modulated bilayer graphene Yongxin Zeng, Tobias M Wolf, Chunli Huang, Nemin Wei, Sayed Ali Akbar Ghorashi, Allan H MacDonald, Jennifer Cano Superlattice potential modulation combined with a displacement field produces flat bands in bilayer graphene [1], some of which have nonzero valley-projected Chern numbers. In this talk I will show that at integer fillings of the topological flat bands, phase transitions between quantum anomalous Hall, valley Hall, and trivial insulator states can be driven by tuning displacement field and the shape and strength of the superlattice potential. The topologically trivial flat bands are localized in space and display Hubbard model physics. I will present mean-field phase diagrams in the parameter space of displacement field and superlattice potential strength at various filling factors. Finally, I will discuss the similarities and differences between the correlated insulating states in superlattice potential modulated bilayer graphene and those in magic-angle twisted bilayer graphene and transition metal dichalcogenide heterobilayers. |
Monday, March 6, 2023 8:12AM - 8:24AM |
A21.00002: Topological and stacked flat bands in bilayer graphene with a superlattice potential Sayed Ali Akbar Ghorashi, Aaron P Dunbrack, Jiacheng Sun, Xu Du, Jennifer Cano We show that bilayer graphene in the presence of a 2D superlattice potential provides a highly tunable setup that can realize a variety of flat band phenomena. We focus on two regimes: (i) topological flat bands with non-zero Chern numbers, C, including bands with higher Chern numbers |C| > 1; and (ii) an unprecedented phase consisting of a stack of nearly flat bands with C = 0. For realistic values of the potential and superlattice periodicity, this stack can span nearly 100 meV, encompassing nearly all of the low-energy spectrum. Our results provide a realistic guide for future experiments to realize a new platform for flat band phenomena. |
Monday, March 6, 2023 8:24AM - 8:36AM |
A21.00003: Flat band construction scheme characterized by quantum distance Kim Hyeongseop, Jun-Won Rhim Flat bands, usually considered topologically trivial, can be nontrivial in the perspective of another geometric quantity called the quantum distance. We present a general construction scheme for a tight-binding model hosting a flat band with a quadratic band crossing characterized by the maximum quantum distance. First, we introduce how to build a compact localized state(CLS) leading to the quadratic band touching and the specific value of the maximum quantum distance, where the CLS is the characteristic eigenstate of a flat band. Second, we develop a systematic strategy to obtain a tight-binding Hamiltonian with the desired hopping range and symmetry starting from the given CLS. The scheme can be applied to any dimensions and lattice structure. Using the scheme, we propose several simple flat band models on the square and kagome lattices, where the maximum quantum distance is controllable by tuning the next nearest neighbor hopping parameters. Finally, we discuss how to realize our flat band models in artificial systems. |
Monday, March 6, 2023 8:36AM - 8:48AM |
A21.00004: Perpendicular space accounting of localized states in quasicrystals Mehmet O Oktel, mehmet keskiner Quasicrystals can be described as projections of sections of higher dimensional periodic lattices into real space. The image of the lattice points in the projected-out dimensions, called the perpendicular space, carries valuable information about the local structure of the real space lattice. We use perpendicular space projections to analyze the strictly localized states in four quasicrystal tight-binding models. These zero energy states form a massively degenerate manifold akin to flat bands in periodic systems. For the Penrose lattice, we reproduce the six types of localized states and investigate their overlaps and linear independence. For the Ammann-Beenker and Socolar dodecagonal lattices, an infinite number of localized state types are needed to explain the numerically observed degeneracy. We also consider all pentagonal quasicrystals which have the same projection window as the Penrose lattice and show that the behavior of the zero energy manifold on the two sublattices of the quasicrystal show marked differences. |
Monday, March 6, 2023 8:48AM - 9:00AM |
A21.00005: Phase transitions between competing correlated states in a low-twist semiconductor moiré lattice Carlos R Kometter, Jiachen Yu, Trithep Devakul, Aidan P Reddy, Yang Zhang, Kenji Watanabe, Takashi Taniguchi, Liang Fu, Ben Feldman Transition metal dichalcogenide (TMD) moiré superlattices are an ideal platform to study strongly correlated quantum phases because they host flat electronic bands which are highly tunable. In this talk, I will present scanning single-electron transistor measurements of a twisted TMD bilayer with a long moiré wavelength. The large moiré unit cell area enables experimental access over a broad range of charge density and magnetic flux per moiré unit cell. Our local electronic compressibility measurements reveal an intricate phase diagram with regions of competing and coexisting correlated phases with distinct physical character separated by phase transitions. I will discuss how the phase diagram reflects the ability to experimentally control the occupation of multiple moiré bands and the effective interactions within them. |
Monday, March 6, 2023 9:00AM - 9:12AM |
A21.00006: Coulomb Interactions and Renormalization of Anisotropic Flat 2D Bands Valeri N Kotov We discuss electron-electron Coulomb interaction effects in a system of highly anisotropic 2D higher-order “Dirac” fermions with electronic dispersion characterized by arbitrary (even) power in one direction, and linear in the other direction. This model contains the simple semi-Dirac case (power two) and describes flat unidirectional bands for higher powers. |
Monday, March 6, 2023 9:12AM - 9:24AM |
A21.00007: RKKY interaction in one-dimensional flat band lattices Katharina Laubscher, Clara S Weber, Maximilian Hünenberger, Herbert Schoeller, Dante M Kennes, Daniel Loss, Jelena Klinovaja We study the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between two classical magnetic impurities in one-dimensional lattice models with flat bands. As two representative examples, we pick the stub lattice and the diamond lattice at half filling. We first calculate the exact RKKY interaction numerically and then compare our data to results obtained via different analytical techniques. In both our examples, we find that the RKKY interaction exhibits peculiar features that can directly be traced back to the presence of a flat band. Importantly, these features are not captured by the conventional RKKY approximation based on non-degenerate perturbation theory. Instead, we find that degenerate perturbation theory correctly reproduces our exact results if there is an energy gap between the flat and the dispersive bands, while a non-perturbative approach becomes necessary in the absence of a gap. |
Monday, March 6, 2023 9:24AM - 9:36AM |
A21.00008: Flat-band correlated phases on kagome lattice Yu-Ping Lin, Joel E Moore The discovery of moire correlated phases has boosted similar search in the other flat-band systems. In this talk, I show that the flat band on the kagome lattice offers a fertile ground for the birth of correlated phases. Using the Hartree-Fock approximation, I present the rich phase diagrams under electronic repulsion at the 2/3 and 5/6 fillings, where the flat band is empty and half-filled, respectively. The possible ground states include Chern insulator, (semimetallic or Chern-insulating) ferromagnetism, spin and/or charge density waves, as well as nematicity. I further demonstrate the realization of unconventional phases by doping these commensurate ground states. |
Monday, March 6, 2023 9:36AM - 9:48AM |
A21.00009: Electrical detection of the flat-band position in field-effect van der Waals structures Edoardo Lopriore, Gabriele Pasquale, ZHE SUN, Kristians Cernevics, Fedele Tagarelli, Kenji Watanabe, Takashi Taniguchi, Oleg V Yazyev, Andras Kis Flat-band systems of two-dimensional materials have enabled the investigation of emergent quantum phenomena and correlated states in van der Waals heterostructures. However, the electrical detection of the energetic position of van Hove singularities in field-effect structures has been hindered by the critically high effective masses of carriers at flat dispersions. Here, we exploit tunneling mechanisms in heterostructures based on different thicknesses of indium selenide in order to demonstrate the electrical detection of the van Hove singularity position in layer-dependent field-effect structures from cryogenic to room temperature. Our work indicates the study of tunneling currents as a viable approach to investigate the properties of van der Waals flat-band systems. |
Monday, March 6, 2023 9:48AM - 10:00AM |
A21.00010: Nontrivial quantum geometry of nondegenerate and degenerate bands and its implications for flat-band systems Johannes Mitscherling The importance of quantum geometry and, in particular, of the quantum metric has been identified throughout various fields in the recent years. Especially flat-band systems are promising candidates for new relevant quantum metric effects, since well-known contributions to observables that depend on the slope or curvature of the dispersion vanish. For instance, the superfluid stiffness and the dc electrical conductivity yield dominant contributions proportional to the integrated quantum metric for flat bands. In this talk, I will address the role of band degeneracy for these quantum metric effects. I will discuss how the quantum metric of both degenerate and nondegenerate bands can be naturally described via the geometry of different Grassmannian manifolds, specific to the band degeneracies. An interesting property is the non-additivity of the quantum metric under the collapse of a collection of bands. In contrast, the Berry curvature is additive. We will discuss this effect for a non-trivial three-band model, where the quantum metric gets enhanced, reduced, or remains unaffected depending on which bands collapse. I will use the developed framework for dc electrical conductivity [1,2] to discuss differences and similarities when bands are nondegenerate or degenerate, which can be directly applied and extended to other observables. |
Monday, March 6, 2023 10:00AM - 10:12AM |
A21.00011: Doping a Wigner-Mott insulator: Electron slush in transition-metal dichalcogenide moiré heterobilayers Louk Rademaker, Yuting Tan, Henry Tsang, Vladimir Dobrosavljevic The moiré pattern induced by lattice mismatch in transition-metal dichalcogenide heterobilayers causes the formation of flat bands, where interactions dominate the kinetic energy. At fractional fillings of the flat valence band, the long-range electron interactions then induce Wigner-Mott crystals. In this Letter we investigate the nontrivial electronic phases appearing away from commensurate fillings. Here, competing phases arise that are either characterized as doped Wigner-Mott charge transfer insulators or alternatively, a novel state with frozen charge order yet is conducting: the 'electron slush'. We propose that an extremely spatially inhomogeneous local density of states can serve as a key signature of the electron slush. |
Monday, March 6, 2023 10:12AM - 10:24AM |
A21.00012: Bulk-interface correspondence from quantum distance in flat band systems Jun-Won Rhim, Chang-geun Oh, Dohee Cho, Se Young Park The key notion of topological analysis is the bulk-boundary correspondence, which provides us with direct access to the topological structure of a Bloch wave function via the existence of boundary or interface modes. While only the topology of the wave function has been considered relevant to boundary modes, we demonstrate that another geometric quantity, the so-called quantum distance, can also host a bulk-interface correspondence. We consider a generic class of two-dimensional flat band systems, where the flat band has a parabolic band-crossing with another dispersive band. While such flat bands are known to be topologically trivial, we show that the nonzero maximum quantum distance between the eigenstates of the flat band around the touching point guarantees the existence of boundary modes at the interfaces between two domains with different chemical potentials or different maximum quantum distances. Moreover, the maximum quantum distance can predict even the explicit form of the dispersion relation and decay length of the interface modes. |
Monday, March 6, 2023 10:24AM - 10:36AM |
A21.00013: Torsional strain engineering of nanotubes with flat bands Shivam Sharma, Amartya S Banerjee In recent years, dispersionless electronic states (or flat bands) in various 2D nanomaterials and layered structures have been intensely investigated due to their connections with strong electronic correlation and exotic phases of matter. In this work, we employ symmetry adapted first principles calculations and tight-binding models to explore the possibility of realizing and modulating flat bands in quasi-one-dimensional materials. Specifically, two prototypical nanotube systems, based on Kagome lattices of carbon and phosphorus-carbon are explored. Both these materials systems host flat bands with quadratic band crossing (QBC) and their electronic structures can be classified based on the type of singularities in the Bloch wavefunctions. We observe that the phosphorus-carbon nanotubes may have singular or non-singular QBC, based on chirality, whereas the carbon tubes are exclusively associated with singular QBC. We show that such differences can be brought out by subjecting these materials to torsional strains, with different classes of electronic phase transitions being affected in these materials, as a result to such deformations. |
Monday, March 6, 2023 10:36AM - 10:48AM |
A21.00014: Harmonic Oscillator States in Acoustic Twisted Bilayer Graphene Jeffrey B Shi, Benjamin H November, Harris S Pirie, Stephen T Carr, Jenny E Hoffman The discovery of twisted van der Waals heterostructures hosting moiré lattices has opened a parameter space of materials and twist angles too vast for direct exploration. Acoustic metamaterials can be used to mimic the behaviors of quantum materials, serving as cheap and rapid prototypes for their expensive and laborious quantum counterparts. For example, twisted bilayer graphene (TBG) has already been successfully translated into the field of acoustics [1]. While TBG is known to feature isolated flat bands due to the hybridization of dispersive Dirac states, it is also possible to manifest a ladder of flat band harmonic oscillator states originating at the parabolic band edges farther from the Fermi level [2]. Using COMSOL Multiphysics, we discover emergent harmonic oscillator modes in acoustic twisted bilayer graphene, and we simulate their real space distribution. The twist angle and interlayer coupling strength of our metamaterial can be easily tuned to control the energy spacing of the flat bands and their localization across the moiré lattice supercell. Our metamaterial may serve as a tunable platform for emergent phenomena such as second harmonic generation. |
Monday, March 6, 2023 10:48AM - 11:00AM |
A21.00015: Emergence of flat bands in mean field limit of Tight Binding Models George P Tsironis, Efthimios Kaxiras We investigate the emergence of flat bands in simple Tight Binding Models (TBM) with variable connectivity between the sites and periodic boundary conditions. As a first step, we consider a one-dimensional TBM with sites and nearest neighbor (nn) interaction , to which we then add random bonds with the same strength linking different pairs of sites of the chain. When the number of additional bonds is (that is, for large ), every site is pairwise linked with every other site. The TBM model has two limits which yield an analytical solution, namely, the simple one-band solution in the limit , and the mean field (MF) limit for . In the former case, the density of states (DOS) takes the familiar square root singularity form of the one dimensional TMB, while in the MF limit it has a singular state, in addition to a highly degenerate flat band which contains the remaining eigenstates. For close to the MF limit, the flat band obtains a Wigner-like distribution. The transition from the one-band regime to the MF regime occurs at only a few percent of additional bonds , compared to the single-band limit. This demonstrates that only a small degree of long range interactions can in fact induce a flat band-like behavior in this simple TBM. In addition to the DOS, we study how the eigen-functions as well as the inverse participation ratio changes as a function of . Finally, we comment of the extension of the model to the two-dimensional case, which may share some features with more realistic systems where flat bands emerge, such as twisted bilayers of 2D materials like graphene. |
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