Bulletin of the American Physical Society
APS March Meeting 2022
Volume 67, Number 3
Monday–Friday, March 14–18, 2022; Chicago
Session G59: Correlated Topology II: Theoretical ProgressRecordings Available
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Sponsoring Units: DCMP Chair: Bitan Roy, Lehigh University Room: Hyatt Regency Hotel -DuSable AB |
Tuesday, March 15, 2022 11:30AM - 11:42AM |
G59.00001: Anomaly cascade in (2+1)D fermionic topological phases Danny S Bulmash, Maissam Barkeshli We develop a theory of anomalies of fermionic topological phases of matter in (2+1)D with a general fermionic symmetry group Gf. In general, Gf can be a non-trivial central extension of the bosonic symmetry group Gb by fermion parity. We encounter four layers of obstructions to lifting a Gf symmetry action on a super-modular category C to a minimal modular extension Č, which we dub the anomaly cascade: (i) An H1(Gb,ZT) obstruction to extending autoequivalences of C to Č, (ii) An H2(Gb, ker r) obstruction to extending the Gb group structure of the symmetry action to Č, where r is a map that restricts autoequivalences of Č to C, (iii) An H3(Gb, Z2) obstruction to extending the symmetry fractionalization class to Č, and (iv) the well-known H4(Gb,U(1)) obstruction to developing a consistent Gb-crossed theory of symmetry defects for Č. A number of conjectures regarding symmetry actions on super-modular categories, guided by general expectations of anomalies in physics, are also presented. |
Tuesday, March 15, 2022 11:42AM - 11:54AM |
G59.00002: (3+1)D topological order with gravitational anomaly and exactly solvable lattice models for beyond group cohomology SPT phases Yu-An Chen, po-shen hsin We construct infinitely many new exactly solvable local commuting projector lattice Hamiltonian models for general bosonic beyond group cohomology invertible topological phases of order 2 and 4 in any spacetime dimensions, whose boundaries are characterized by gravitational anomalies. Examples include the beyond group cohomology invertible phase without symmetry in (4+1)D that has anomalous boundary Z2 topological order with fermion particle and fermionic loop excitation that have mutual π statistics. We argue the construction gives a new non-trivial quantum cellular automaton (QCA) in (4+1)D of order 2. We also present an explicit construction of gapped symmetric boundary state for the bosonic beyond group cohomology invertible phase with unitary Z2 symmetry in (4+1)D. |
Tuesday, March 15, 2022 11:54AM - 12:06PM |
G59.00003: Translation symmetry-enriched toric code insulator Pok Man Tam, Jörn W Venderbos, Charles L Kane Weak topological phases with strong electronic correlation could lead to exotic interplay between topology and translation symmetry. Here we introduce a 2D electronic insulator that possesses a toric code topological order, enriched by translation symmetry. This state can be realized from disordering a weak topological superconductor by double-vortex condensation. We term this toric code insulator, whose anyonic excitations consist of a charge-e chargon, a neutral fermion and two types of visons. In this talk, we first explain the distinction of two types of visons through the fractional Josephson effect of 1D topological superconductor. We show that these two types of visons are related by a discrete translation symmetry and have mutual semionic braiding statistics, leading to a symmetry-enrichment akin to the type in Wen's plaquette model and Kitaev's honeycomb model. We provide a microscopic construction of this state using a three-fluid coupled-wire model, from which we explore the consequences of symmetry-enrichment, as well as potential experimental realizations. |
Tuesday, March 15, 2022 12:06PM - 12:18PM |
G59.00004: Symmetry-Protected Topological Order in Open Systems Alex Turzillo, Caroline de Groot, Norbert Schuch This talk will discuss the robustness of symmetry protected topological (SPT) order to evolution by noisy channels. By studying the evolution of non-local string order parameters, we find that one-dimensional SPT order is destabilized by generic couplings to the environment as well as by couplings satisfying a weak symmetry condition that directly generalizes from closed systems. We introduce a stronger symmetry condition on channels that ensures SPT order is preserved. |
Tuesday, March 15, 2022 12:18PM - 12:30PM |
G59.00005: Absence of Friedel oscillations in the entanglement entropy profile of one-dimensional intrinsically gapless topological phases Shun-Chiao Chang, Pavan R Hosur Topological quantum matter is typically associated with gapped phases. For instance, the bulk energy gap of symmetry-protected topological phases localizes edge modes near the boundary. Here, we study the proposed intrinsically gapless topological phase (Phys. Rev. B 104, 075132) in one dimension -- or topological Luttinger liquid -- via DMRG. For such phases, the string order forbidden in gapped phases defines the bulk-edge correspondence and protects the edge modes. In this work, we examine the entanglement entropy profile of the phase and find that it lacks Friedel oscillations that ordinary Luttinger liquids invariably contain. We find that the lack of Friedel oscillations stems from the mere existence of a string order regardless of the precise form of the order parameter. Thus, it gives us a more unbiased way to diagnose the above topological phase. It would be interesting to study other gapless topological phases using this method. |
Tuesday, March 15, 2022 12:30PM - 12:42PM |
G59.00006: Multitude of Topological Phase Transitions in Bipartite Lattices with Interacting Electrons and Rashba Coupling Rahul Soni, Amit B Sanyal, Nitin Kaushal, Satoshi Okamoto, Adriana Moreo, Elbio R Dagotto
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Tuesday, March 15, 2022 12:42PM - 12:54PM |
G59.00007: Stability against contact interactions of a topological superconductor in two-dimensional space protected by time-reversal and reflection symmetries Ömer Mert Aksoy, Jyong-Hao Chen, Shinsei Ryu, Akira Furusaki, Christopher M Mudry We study the stability of topological crystalline superconductors in the symmetry class DIIIR and in two-dimensional space when perturbed by quartic contact interactions. It is known that no less than eight copies of helical pairs of Majorana edge modes can be gapped out by an appropriate interaction without spontaneously breaking any protecting symmetries. Hence, the noninteracting classification Z reduces to Z8 when these interactions are present. It is also known that the stability when there are less than eight modes can be understood in terms of the presence of topological obstructions in the low-energy bosonic effective theories, which prevent opening of a gap. Here, we investigate the stability of the edge theories with four, two, and one edge modes, respectively. We give an analytical derivation of the topological term for the first case, because of which the edge theory remains gapless. For two edge modes, we employ bosonization methods to derive an effective bosonic action. When gapped, this bosonic theory is necessarily associated to the spontaneous breaking of either time-reversal or reflection symmetry whenever translation symmetry remains on the boundary. For one edge mode, stability is explicitly established in the Majorana representation of the edge theory. |
Tuesday, March 15, 2022 12:54PM - 1:06PM |
G59.00008: Edge states of 2D time-reversal-invariant topological superconductors with strong interactions and disorder: A view from the lattice Jun Ho Son, Jason F Alicea, Olexei I Motrunich Two-dimensional time-reversal-invariant topological superconductors host helical Majorana fermions at their boundary. We study the fate of these edge states under the combined influence of strong interactions and disorder, using the effective 1D lattice model for the edge introduced by Jones and Metlitski. We specifically develop a strong-disorder renormalization group analysis of the lattice model and identify a regime in which time-reversal is broken spontaneously, creating random magnetic domains; Majorana fermions living on domain walls form an infinite-randomness fixed point, identical to that appearing in the random transverse field Ising model. While this infinite-randomness fixed point describes a critical point in a purely 1D system, in our edge context there is no obvious time-reversal-preserving perturbation that destabilizes the fixed point. Our analysis thus suggests that the infinite-randomness fixed point emerges as a stable phase on the edge of 2D topological superconductors when strong disorder and interactions are present. |
Tuesday, March 15, 2022 1:06PM - 1:18PM |
G59.00009: A proposal to extract and enhance four-Majorana interactions in hybrid nanowires. Tasnum Reza, Sergey M Frolov, David Pekker The Sachdev-Ye-Kitaev (SYK) model is an N-Majorana model with 4-body random all to all interactions. It is exactly solvable in large N-limit and mimics black holes physics, thus providing insights to the theory of quantum gravity. In this work, we simulate smallest unit of the SYK model, i.e., a 4-MZM (quartic) interaction model in a 1D nanowire system. We model a 3-segment Kitaev chain hosting 4 MZMs and add a non-local interaction term to introduce quartic interaction in the MZMs. We tune this system to the SYK criteria by minimizing other (2-body/bilinear) interactions and enhancing the quartic interaction. Extracting and tuning these interacting strengths is done by analyzing energy level spacings between even and odd parity states of a 2-complex-fermion model that resembles low-energy level physics of the interacting Kitaev chain model. We propose that this study can be performed in an experimental setup since eigenspectral characterization of 1D nanowire devices can be done in quantum transport measurements. We further propose that this model could be extended to an N>4 MZM SYK model and present an N=6 model as an example. |
Tuesday, March 15, 2022 1:18PM - 1:30PM |
G59.00010: Orbital magnetization and susceptibility in Moire flat Chern bands: a case study in twisted homobilayer MoS2 Shannon Egan In a recent pre-print, we proposed that the conduction bands (CB) in a twisted homobilayer of the transition metal dichalcogenide (TMD) MoS2 form Moire flat Chern bands, whose nontrivial topology is generated by both Moire potential and spin-orbit couplings. At 1/2 filling we predict that electron correlations drive the system into a valley polarized (VP) state with spontaneously broken time-reversal symmetry, making it a possible platform for realizing a correlated quantum anomalous Hall (QAH) state. |
Tuesday, March 15, 2022 1:30PM - 1:42PM |
G59.00011: Twisted Bilayer Graphene at 2π Flux: Magnetic Bloch Theorem and Reentrant Correlated Insulators Jonah Herzog-Arbeitman, Andrei B Bernevig, Aaron Chew, Dmitri K Efetov In 1964, Zak's discovery of the magnetic translation group demonstrated the possibility of reentrant electronic phases when the flux through a single unit cell is 2π. For the first time, the large unit cell of twisted bilayer graphene (TBG) has made it possible to test Zak's prediction in a real material. We use a newly developed gauge-invariant formalism to determine the exact single-particle band structure, topology, and correlated insulator states of magic angle TBG at 25T. We find that the characteristic flat bands reemerge at 2π flux, but, due to the magnetic field breaking C2T, they split and acquire nonzero Chern number. We then show that reentrant correlated insulators reappear at 2π flux driven by the Coulomb interaction, and we predict the characteristic Landau fans from their excitation spectrum. Initial experiments are consistent with these predictions. Finally, we conjecture that superconductivity can also be re-entrant at 2π flux due to an emergent Hofstadter symmetry. |
Tuesday, March 15, 2022 1:42PM - 1:54PM |
G59.00012: Gapping fragile topological bands by interactions Ady L Stern, Erez Berg, Ari Turner We consider the stability of fragile topological bands protected by space-time inversion symmetry in the presence of strong electron-electron interactions. At the single-particle level, the topological nature of the bands prevents the opening of a gap between them. In contrast, we show that when the fragile bands are half filled, interactions can open a gap in the many-body spectrum without breaking any symmetry or mixing degrees of freedom from remote bands. Furthermore, the resulting ground state is not topologically ordered. Thus, a fragile topological band structure does not present an obstruction to forming a "featureless insulator" ground state. Our construction relies on the formation of fermionic bound states of two electrons and one hole, known as "trions". The trions form a band whose coupling to the electronic band enables the gap opening. This result may be relevant to the gapped state indicated by recent experiments in magic angle twisted bilayer graphene at charge neutrality. |
Tuesday, March 15, 2022 1:54PM - 2:06PM |
G59.00013: Mechanism of skyrmion condensation and pairing for twisted bilayer graphene Dian Jing When quantum flavor Hall insulator phases of itinerant fermions are disordered by strong quantum fluctuations, the condensation of skyrmion textures of order parameter fields can lead to superconductivity. In this work, we address the mechanism of skyrmion condensation by considering the scattering between (2+1)-dimensional, Weyl fermions and hedgehog type tunneling configurations of order parameters that violate the skyrmion-number conservation law. We show the quantized, flavor Hall conductivity (σfxy) controls the degeneracy of topologically protected, fermion zero-modes, localized on hedgehogs, and the overlap between zero-mode eigenfunctions or 't Hooft vertex determines the nature of pairing. We demonstrate the quantum-disordered, flavor Hall insulators with σfxy=2N lead to different types of charge 2Ne− superconductivity. Implications for the competition among flavor Hall insulators, the charge 2e− paired states in BCS and pair-density-wave channels, and the composite, charge 4e− superconductors for twisted bilayer graphene are outlined. |
Tuesday, March 15, 2022 2:06PM - 2:18PM |
G59.00014: Superconductivity and disorder in topological flat bands Valerio Peri, Andrei B Bernevig, Sebastian Huber, Zhida Song, Frank Schindler, Jonah Herzog-Arbeitman, Sam Bird The geometry of the single-particle wave function can have a profound impact on the phases emerging upon the inclusion of interactions and disorder, especially in dispersionless bands. Here, we show via auxiliary-field Monte Carlo simulations how the non-trivial geometry enhances the superfluid weight and hence the superconducting critical temperature in flat-band systems. We further show how fragile and obstructed flat bands possess different properties upon the inclusion of weak disorder. Therefore, we establish the superfluid weight and the eigenstate localization as nontrivial bulk properties that distinguish among fragile topological, obstructed, and trivial flat bands in the presence of interactions and disorder. |
Tuesday, March 15, 2022 2:18PM - 2:30PM |
G59.00015: Single-Electron Spectra and Plasmonic Excitations in Chern Insulators Zhihao Jiang, Stephan W Haas Collective excitations in topological insulators have drawn increasing attention in recent years. On the fundamental science level, these systems incorporate an interplay between topology and interactions. Technologically, it is promising to make functional plasmonic and magnonic devices by exploiting the topological feature of the underlying structures. We have investigated plasmons in one-dimensional (1D) and two-dimensional (2D) Su-Schrieffer-Heeger (SSH) models in previous studies [1-3] where some topological features are reflected and observed in collective excitations. In this work, we focus on plasmonic excitations in Chern insulators. The model being considered is the Qi-Wu-Zhang (QWZ) model, which is a 2D square lattice with two internal degrees of freedom on each site. By fixing the nearest-neighbor hopping and varying the on-site energy, we can tune the model into different topological sectors with Chern numbers C=-1, 0 or 1. We study the QWZ model in various forms: 2D periodic case (torus), ribbon (cylinder) and 2D open case (finite-sized). In the 2D periodic model, the plasmon dispersion in momentum space has different characteristic shapes in the different topological sectors. Generally, plasmons in topologically nontrivial phases (C=1,-1) show enhanced dispersion spectra compared to the trivial phase (C=0). On the open edges of the ribbon structure and on the open boundaries of finite-sized samples, plasmonic edge states are observed in the topologically non-trivial phases. These results assume that the Coulomb interaction does not specifically depend on the internal degrees of freedom. We discuss how to extend this method to cases when the Coulomb interaction takes different forms in the internal subspace. |
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