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 V45: Topological Insulators: Theory ILive
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Sponsoring Units: DCMP Chair: Benjamin J. Wieder |
Thursday, March 18, 2021 3:00PM - 3:12PM Live |
V45.00001: Hofstadter Topology: Complete Classification and Non-crystalline Projective Symmetries Jonah Herzog-Arbeitman, Zhida Song, Nicolas Regnault, Andrei Bernevig The Hofstadter problem is the lattice analog of the quantum Hall effect and is the paradigmatic example of topology induced by an applied magnetic field. Conventionally, the Hofstadter problem involves adding approximately 104 T magnetic fields to a trivial band structure. In this work, we show that when a magnetic field is added to an initially topological band structure, a wealth of possible phases emerges. First, we prove that at fixed filling, a nonzero Chern number creates a discontinuous many-body gap closing at zero flux, and that a nonzero mirror or valley Chern number enforces a bulk gap closing at finite flux. We then study Hofstadter Hamiltonians with nontrivial space group symmetries. Remarkably, we find that at critical values of the flux, the symmetries realize projective representations of the space group which cannot be obtained in any crystalline insulator. We completely classify these novel space groups and their topological invariants, and show that they are be determined by the zero-flux Wannier functions. Our classification reveals topologically protected edge and corner mode pumping, which we expect to be observable in Moiré materials where laboratory-strength fields can reach one flux per unit cell. |
Thursday, March 18, 2021 3:12PM - 3:24PM Live |
V45.00002: Quantum criticality in Hofstadter-Chern bands of graphene superlattices Jian Wang, Luiz Santos In the conventional quantum Hall effect, the magnetic flux per unit cell is orders of magnitude smaller than the magnetic flux quantum h/e, giving rise to degenerate Landau levels characterizing topological states of electrons in the continuum. Recent progress in the fabrication of superlattices with nanometer scale unit cells has led to the experimental realization of Hofstadter-Chern insulators with large magnetic fluxes per unit cell, where the interplay between lattice effects and electron topology extends beyond the Landau level regime. In this setting, we present an analytical framework to classify the hopping-tuned topological critical points in graphene superlattices subject to a background external magnetic field, which are characterized by multi-component Dirac fermions and large changes in Chern number, as opposed to conventional quantum Hall transitions. We then describe an intimate relationship between the energy scale of such quantum phase transitions and van Hove singularities in Chern bands. Our work provides a route to critical phenomena beyond conventional quantum Hall plateau transitions, and uncover integer and fractional states characterized by strong coupling of electron topology with the lattice. |
Thursday, March 18, 2021 3:24PM - 3:36PM Live |
V45.00003: Multicellularity of delicate topological insulators Aleksandra Nelson, Titus Neupert, Tomas Bzdusek, Aris Alexandradinata We enrich the notions of stable and fragile topology by introducing delicate topological insulators: band structures possessing topological invariants that can be trivialized through an addition of a trivial conduction band. We find that although delicate topological insulators are Wannier representable with exponentially-localized symmetry-preserving Wannier functions, they can possess a different type of obstruction to an atomic limit. Namely, the impossibility to localize all Wannier functions to one unit cell, i.e. multicellularity. |
Thursday, March 18, 2021 3:36PM - 3:48PM Live |
V45.00004: 2N-rule: Searching topological phases and robust edge modes in carbon nanotubes Chen Hu, Hong Guo Carbon nanotubes (CNTs) can be generally classified to two phases, metal or insulator, depending on their tube indexes. So far, the insulating CNTs are considered identical apart for some quantitative gap difference. However, here we show that the insulating phases may be topologically nonequivalent. We theoretically report an explicit and robust scheme, 2N-rule, for systematically searching topological phases in CNTs of all diameters. By investigating the topological Zak phase based on both analytical model and first-principles approaches, such a 2N-rule of insulating CNT(n,0) is generally established: when n = 2N where N is an integer, it is a topological insulator; otherwise, it is a normal insulator. For finite-length topological CNTs, topologically protected quantum modes naturally occur at the tube ends, which hold significant robustness against external environment perturbations, taking advantage over fragile edge states in conventional systems. |
Thursday, March 18, 2021 3:48PM - 4:00PM Live |
V45.00005: Topological magnetoelectric effect (TME) and quantum anomalous Hall effect (QAHE) of topological-insulator (TI) thin films Nezhat Pournaghavi, Anna Pertsova, Carlo Canali, Allan MacDonald We present a theoretical study of the two-dimensional (2D) surface states and orbital magnetoelectric response of TI thin films in which time-reversal symmetry is broken by magnetism at the surface. In the limit of large thickness d and small exchange coupling, the magnetization can be decomposed into independent contributions from top (t) and bottom (b) surfaces, with the single-surface magnetization Ms=t,b(Js, EDs) being a function of its exchange coupling Js and the Dirac point energy EDs relative to chemical potential. In the QAHE phase, appearing for Jt Jb > 0, |∂Ms/∂EDs| equals e/2h in the small-J large-d limit when the chemical potential lies in the surface state gap. Since Ms(Js, EDs) = - Ms(-Js, EDs) by time-reversal symmetry, it follows that when Jt Jb < 0 (the axion insulator phase) the 3D magnetization M3D = (Mt + Mb)/d response to a vertical electric field E is ∂M3D/∂E = e2/2h, a relationship referred to as the TME. By combining an effective model of the Dirac-cone surface states with tight-binding model calculations, we conclude that the TME is in fact robust against Js and remains quantized even at exchange strengths for which a half-quantized surface anomalous Hall conductance cannot be properly defined. We comment on how the TME can be realized experimentally. |
Thursday, March 18, 2021 4:00PM - 4:12PM Live |
V45.00006: Aperiodic and quasi-periodic dynamical quantum phase transitions in multi-band topological insulators Nicholas Sedlmayr Dynamical quantum phase transitions are non-equilibrium phenomena where non-analyticities occur in dynamically evolving correlation functions, in analogy with the non-analyticities in the derivatives of the free energy for a standard phase transition. Topological phase transitions sperate phases of equivalent symmetry but different topology. The ways in which these two phenomena can be connected has recently become a topic of great interest. Here we will report on dynamical phase transitons in many-band one dimensional topological insulators which demonstrate curious quaisi-periodic, rather than periodic, dynamical phase transitions. Furthermore we will consider the role of the topologically protected edge states in the dynamics and connections with fidelity susceptibility and dynamical entanglement entropy. |
Thursday, March 18, 2021 4:12PM - 4:24PM Live |
V45.00007: 2D to 3D crossover in topological insulators Corentin Morice, Thilo Kopp, Arno P Kampf At the heart of the study of topological insulators lies a fundamental dichotomy: topological invariants are defined in infinite systems, but their main footprint, surface states, only exists in finite systems. In systems in the slab geometry, namely infinite in two dimensions and finite in one, the 2D topological invariant was shown to display three different types of behaviours. In the limit of zero Dirac velocity along z, these behaviours extrapolate to the three 3D topological phases: trivial, weak and strong topological insulators. We show analytically that the boundaries of these regions are topological phase transitions of particular significance, and allow one to fully predict the 3D topological invariants from finite-thickness information. Away from this limit, we show that a new phase arises, which displays surface states but no band inversion at any finite thickness, disentangling these two concepts closely linked in 3D. |
Thursday, March 18, 2021 4:24PM - 4:36PM Live |
V45.00008: Fragile topology in line-graph lattices Christie Chiu, Da-Shuai Ma, Zhida Song, Andrei B Bernevig, Andrew Houck The geometric properties of a lattice can have profound consequences on its band spectrum. For example, symmetry constraints and geometric frustration can give rise to topologicially nontrivial and dispersionless bands, respectively. Line-graph lattices are a perfect example of both of these features: their lowest energy bands are perfectly flat, and we have found and proved connections between their geometric properties and the presence or absence of fragile topology in their flat bands [1]. In this talk, I present these connections. This theoretical work will enable experimental studies of fragile topology in several types of line-graph lattices, most naturally suited to superconducting circuits. |
Thursday, March 18, 2021 4:36PM - 4:48PM Live |
V45.00009: Spin-triplet excitonic states and electron-electron correlations on the Topological Insulator surface Sparsh Mishra, Keiji Yada, Akito Kobayashi, Yukio Tanaka Topological insulators are novel states of matter that host Dirac-dispersion on its surface. The spectrum also supports helical spin texture and unscreened Coulomb potential as a result of the 2D geometry. We investigate the electron-electron correlations on the surface of a topological Insulators that produce a gap in the spectrum and discuss the enhancement of spin-triplet excitonic states as a result of this spin texture. Using Green’s function technique and numerical diagonalization of the equation we find the possible order parameters that describe the systems that retain their topological structure. We discuss realistic mechanisms that enhance this state taking into account spin and charge fluctuations. |
Thursday, March 18, 2021 4:48PM - 5:00PM Live |
V45.00010: General Construction and Topological Classification of Perfectly Flat Bands Dumitru Calugaru, Aaron Chew, Luis Elcoro, Da-Shuai Ma, Zhida Song, Andrei B Bernevig Systems harboring flat bands are excellent testbeds for strongly interacting physics, having generated much excitement in the condensed matter community. We present a generic technique to construct perfectly flat bands (FBs) from bipartite crystalline lattices (BCLs). Our prescription generalizes the line- and split-graph constructions encapsulating many of the various other models from literature. Using Topological Quantum Chemistry, we create a full topological classification in terms of symmetry eigenvalues of all (gapped and gapless) BCL FBs, in all Magnetic Space Groups (MSGs). We argue that the BCL FBs can be understood as formal differences of band representations. This allows us to find criteria for the existence of (and fully classify) unitary symmetry-protected touching points between the flat and dispersive bands, and identify the gapped FBs as prime candidates for fragile topological bands. Finally, we show that the set of BCL FBs is finitely generated and construct the corresponding bases in all MSGs, providing a comprehensive list of BCLs realizable in real materials. |
Thursday, March 18, 2021 5:00PM - 5:12PM Live |
V45.00011: Finite-temperature spectroscopy of dirty helical Luttinger liquids Tzu-Chi Hsieh, Yang-Zhi Chou, Leo R Radzihovsky I will discuss a theory of finite-temperature momentum-resolved tunneling spectroscopy (MRTS) for disordered two-dimensional interacting topological-insulator edges. The MRTS setup measures the spectral properties and thus complements conventional electrical transport measurement in characterizing helical Luttinger liquid edges of topological insulators. The (exact within bosonization) finite-temperature spectral function and the tunneling current of MRTS are derived in the presence of disorder and interaction. The theory provides a detailed analytical characterization of MRTS between helical edges, that should be of interest for corresponding experimental studies. |
Thursday, March 18, 2021 5:12PM - 5:24PM Live |
V45.00012: A Bulk-Boundary Correspondence for 2D Fermionic Symmetry Protected Topological Phases Kyle Kawagoe, Michael Levin A universal property of symmetry protected topological (SPT) phases is that they have low energy boundary modes that are protected under the symmetry. This fact inspires an important problem in the theory of SPT phases: How does one identify a bulk SPT phase given a low energy theory of its boundary? This question is particularly challenging in the case of interacting SPT phases where band theory approaches are inapplicable. In this talk, we present a general method for solving this problem in the case of (2+1)D interacting Fermionic systems with internal (non-spatial) symmetries. |
Thursday, March 18, 2021 5:24PM - 5:36PM Live |
V45.00013: Transport signature of helical hinge states of quasi-one-dimensional topological insulators Yanfeng Zhou, Fan Zhang Higher-order topological insulators exhibit protected corner or hinge states generalizing the bulk-boundary correspondence. The quasi-one-dimensional materials Bi4Br4 and Bi4I4 have been predicted to be prototypical examples of such topological matter with helical hinge states along the atomic chain direction. We examine the electronic behavior of their helical hinge states and predict unique signatures in transport experiment. We further show how these signatures depend on the applied electric and magnetic fields. |
Thursday, March 18, 2021 5:36PM - 5:48PM Live |
V45.00014: Engineering Topological Phases Guided by Statistical and Machine Learning Methods Thomas Mertz, Roser Valenti The search for materials with topological properties is an ongoing effort. In this talk we will discuss our recent proposal [1] on a systematic statistical method supported by machine learning techniques that is capable of constructing topological models for a generic lattice without prior knowledge of the phase diagram. |
Thursday, March 18, 2021 5:48PM - 6:00PM On Demand |
V45.00015: Transport in high D-dimensional topological insulators models Leonardo LIMA We study the longitudinal conductivity $\sigma^{reg}_{xx}(\omega)$ in the neighboring of the phase transition of the topological charge in topological insulators models in (4+1)-D dimensions [1-4] employing the Kubo formalism of the linear response theory [5-6]. Thus we analyze the effect of topological phase transition of the sudden variation of the second Chern number $Q_2$ in higher dimensions on AC conductivity. In addition, we investigate the effect of the sudden variation of the second Chern number in von Neumann entropy [7-8]. |
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