Bulletin of the American Physical Society
APS March Meeting 2022
Volume 67, Number 3
Monday–Friday, March 14–18, 2022; Chicago
Session T59: Floquet Topological Systems: TheoryRecordings Available

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Sponsoring Units: DCMP Chair: Mahmoud Asmar, Kennesaw State University Room: Hyatt Regency Hotel DuSable AB 
Thursday, March 17, 2022 11:30AM  11:42AM 
T59.00001: Topological classification of Local Unitary Operators Rahul Roy, Xu Liu, Fenner Harper, Adrian B Culver Local unitary operators arise naturally as time evolution operators generated by Hamiltonians and also in the context of quantum walks. In one dimension, the flow index is a topological invariant which distinguishes classes of local unitary operators up to equivalence by smooth deformation. We propose a higherdimensional generalization of this index and obtain a topological classification of noninteracting local unitary operators. We extend this classification to local unitary operators with symmetry and show that the result can be represented in a periodic table with a period of eight, similar to the periodic table of topological insulators. Our classification naturally distinguishes unitary operators that are locally generated from those that cannot be locally generated. 
Thursday, March 17, 2022 11:42AM  11:54AM 
T59.00002: Dynamical symmetry indicators for Floquet crystals Jiabin Yu, RuiXing Zhang, Zhida Song In this talk, I will discuss our recent work on a general theory for (effectively) noninteracting topological Floquet crystals, which is applicable to all crystalline symmetry groups with spatial dimensions no larger than three. In our work, we first introduce quotient winding data to classify the dynamics of the Floquet crystals with equivalent symmetry data, and then construct dynamical symmetry indicators (DSIs) to sufficiently indicate the inherently dynamical Floquet crystals. The DSI and quotient winding data, as well as the symmetry data, are all computationally efficient since they only involve a small number of Bloch momenta. We demonstrate the high efficiency by computing all elementary DSI sets for all spinless and spinful plane groups using the mathematical theory of monoid, and find a large number of different nontrivial classifications, which contain both firstorder and higherorder 2+1D anomalous Floquet topological phases. Using the framework, we further find a new 3+1D anomalous Floquet secondorder topological insulator (AFSOTI) phase with anomalous chiral hinge modes. 
Thursday, March 17, 2022 11:54AM  12:06PM 
T59.00003: Dynamic bulkboundary correspondence for anomalous Floquet topology from dimensional hierarchy DinhDuy Vu Periodically driven systems with internal and spatial symmetries can exhibit a variety of anomalous boundary behaviors at both the zero and π quasienergies despite the trivial bulk Floquet bands. These phenomena are called anomalous Floquet topology (AFT) as they are unconnected from their static counterpart, arising from the winding of the time evolution unitary rather than the bulk Floquet bands at the end of the driving period. In this paper, we systematically derive the first and inversionsymmetric secondorder AFT bulkboundary correspondence for AltlandZirnbauer (AZ) classes BDI, D, DIII, AII. For each AZ class, we start the dimensional hierarchy with the parent dimension having Zclassification, then use it as a interpolating map to classify the lowerdimensional descendants. From the AtiyahHierzebruch spectral sequence (AHSS), we identify the subspace that contains the topological information and faithfully derive the AFT bulkboundary correspondence for both the parent and descendants. Our theory provides analytic tools for Floquet topological phenomena. 
Thursday, March 17, 2022 12:06PM  12:18PM 
T59.00004: Universal delocalization transition in chiralsymmetric Floquet drives Adrian B Culver, Pratik Sathe, Albert Brown, Fenner Harper, Rahul Roy Periodically driven (Floquet) systems often exhibit behavior distinct from undriven systems. Any amount of disorder in onedimensional undriven systems generically localizes all eigenstates. In contrast, we show that in topologically nontrivial, noninteracting Floquet loop drives with chiral symmetry, a delocalization transition occurs at as the time t is varied within the driving period (0 < t < T_{drive}). We find that the localization length L_{loc} at all quasienergies diverges with a universal exponent of 2 as t approaches the midpoint of the drive: L_{loc} ~ (t  T_{drive}/2)^{2}. We provide numerical evidence for the universality of this exponent by studying a variety of such drives using exact diagonalization, and we also present an analytical argument based on scattering theory. 
Thursday, March 17, 2022 12:18PM  12:30PM 
T59.00005: Lightinduced quantum anomalous Hall effecton the 2D surfaces of 3D topological insulators Haowei Xu Quantum anomalous Hall (QAH) effect generates quantized electric charge Hall conductance without external magnetic field. It requires both nontrivial band topology and timereversal symmetry (TRS) breaking. In most cases, one could break the TRS of timereversal invariant topological materials to yield QAH effect, which is essentially a topological phase transition. Conventional topological phase transition induced by external field/stimulus needs a route along which the bandgap closes and reopens. Hence, the phase transition occurs only when the magnitude of field/stimulus is larger than a critical value. In this work we propose that using gapless surface states, the transition can happen at arbitrarily weak (but finite) external field strength. This can be regarded as an unconventional topological phase transition, where the bandgap closing is guaranteed by bulkedge correspondence and symmetries, while the bandgap reopening is induced by external fields. We demonstrate this concept on the 2D surface states of 3D topological insulators like Bi_{2}Se_{3}, which become 2D QAH insulators once a circularly polarized light is turned on, according to van Vleck’s effective Hamiltonian in Floquet time crystal theory. The sign of quantized Chern number can be controlled via the chirality of the light. This provides a convenient and dynamical approach to trigger topological phase transitions and create QAH insulators. 
Thursday, March 17, 2022 12:30PM  12:42PM 
T59.00006: Lightinduced Topological Phase transitions in 1T' Transition Metal Dichalcogenides Xiangru Kong, Wei Luo, Linyang Li, Mina Yoon, Tom Berlijn, Liangbo Liang Using ab initio tightbinding approaches, we investigate Floquet band engineering of the 1T' phase of transition metal dichalcogenides (MX2, M = W, Mo and X = Te, Se, S) monolayers under the irradiation with circularly polarized light. Our first principles calculations demonstrate that light can induce important transitions in the topological phases of this emerging materials family. For example, upon irradiation, Tebased MX2 undergoes a phase transition from quantum spin Hall (QSH) semimetal to timereversal symmetry broken QSH insulator with a nontrivial band gap of up to 92.5 meV. On the other hand, Se and Sbased MX2 undergoes the topological phase transition from the QSH effect to the quantum anomalous Hall (QAH) effect and into trivial phases with increasing light intensity. From a general perspective, our work brings further insight into nonequilibrium topological systems. 
Thursday, March 17, 2022 12:42PM  12:54PM 
T59.00007: Topological Phases of the SuSchriefferHeeger Model Driven by Two CommensurateFrequency Drives Samuel W Olin, WeiCheng Lee Topological materials in Floquet (periodically driven) systems have attracted a great deal interest recently due to the ability to engineer topological phases by tuning the driving parameters. We study the physical and topological properties of the SuSchriefferHeeger model driven by two timedependent periodic sources with commensurate frequencies. The ability to introduce more than one driving frequency allows us to realize even more exotic topological phases resulting from new coupling appearing in the Fourier space representation. In order to compute the system topology in this space, we employ the local Chern marker, a real space representation of the wellknown Chern number. Using this, we obtain topological phase diagrams and explore the phase boundaries resulting from new commensurate drives and demonstrate how this reallife experimental control can realize unique topological phases. We also calculate the current for a variety of cases in the time domain and we will discuss the implication of the current as it is related to topological phase transitions. 
Thursday, March 17, 2022 12:54PM  1:06PM 
T59.00008: Topological two frequency conversion in doubly driven Weyl semimetal Gil Refael, Ivar Martin, Frederik S Nathan A doubly driven spin could give rise to topological energy pumping between the two drives. We investigate a Weyl semimetal irradiated by two electromagnetic modes with distinct frequencies. Under suitable driving, each electron near the Weyl node transfers energy from one mode to the other at a universal rate of Planck's constant multiplied by the product of the frequencies of the modes. Due to the macroscopic number of electrons involved,the power of conversion can be very large (of order MW/cm^3). This effect may be used for optical amplification, and terahertz (THz) generation. I will discuss the calculation and the (yet to be fulfilled) requirements for such a topological amplifier. 
Thursday, March 17, 2022 1:06PM  1:18PM 
T59.00009: Stirring by Staring: Measurement Induced Chirality Matthew Wampler, Brian Jia Jiunn Khor, Gil Refael, Israel Klich Controlling the dynamics of quantum systems is a current frontier of quantum manybody physics. Recent advancements in experimental techniques suggest exciting new directions in driveinduced quantum states. Here, we present a simple scheme that relies solely on occupation measurements to induce a chiral quantum phase. Namely, we show that by utilizing a pattern of repeated quantum measurements we can produce chiral edge transport of fermions hopping on a Lieb lattice. We study in detail the dependence on measurement frequency, showing that in the Zeno limit the system can be described by a classical stochastic dynamics, yielding protected transport. As the frequency of measurements is reduced, the charge flow is reduced and vanishes when no measurements are done. 
Thursday, March 17, 2022 1:18PM  1:30PM 
T59.00010: Optical Ninsulators: topological obstructions in the atomistic susceptibility tensor Todd F Van Mechelen, RobertJan Slager, Sathwik Bharadwaj, Zubin Jacob A powerful result of topological band theory is that nontrivial phases manifest obstructions to constructing localized Wannier functions. In Chern insulators, it is impossible to construct Wannier functions that respect translational symmetry in both directions. Similarly, Wannier functions that respect timereversal symmetry cannot be formed in quantum spin Hall insulators. This molecular orbital interpretation of topology has been enlightening and was recently extended to topological crystalline insulators which include obstructions tied to space group symmetries. In this article, we introduce a new class of twodimensional topological materials known as optical Ninsulators that possess obstructions to constructing localized molecular polarizabilities. The optical Ninvariant is the winding number of the atomistic susceptibility tensor and counts the number of singularities in the electromagnetic linear response theory. We decipher these singularities by analyzing the optical band structure of the material. The localized basis of these eigenvectors are optical Wannier functions which represent the molecular polarizabilities at different lattice sites. We prove that in a nontrivial optical phase, such a localized polarization basis is impossible to construct. 
Thursday, March 17, 2022 1:30PM  1:42PM 
T59.00011: Symmetries and exceptional points of discrete Floquet mechanical systems Abhijeet Melkani Classical mechanical springmass systems with timeperiodic modulation of spring stiffnesses are Floquet systems with the added feature that the solutions are realvalued and lie in a symplectic manifold. This constrains the Floquet exponents  complexvalued generalizations of the oscillation frequencies  to obey certain relations enabling new kinds of topologically protected phenomena and topological classifications. 
Thursday, March 17, 2022 1:42PM  1:54PM 
T59.00012: Observing Floquet topological order by symmetry resolution Daniel Azses, Emanuele G Dalla Torre, Eran Sela Symmetry protected topological order in one dimension leads to protected degeneracies between symmetry blocks of the reduced density matrix. In the presence of periodic driving, topological Floquet phases can be identified in terms of a cycling of these symmetry blocks between different charge quantum numbers. We discuss an example of this phenomenon with an Ising Z_{2} symmetry, using both analytic methods and real quantum computers. By adiabatically moving along the phase diagram, we demonstrate that the cycling periodicity is broken in Floquet topological phase transitions. An equivalent signature of the topological Floquet phase is identified as a computational power allowing to teleport quantum information. 
Thursday, March 17, 2022 1:54PM  2:06PM 
T59.00013: Fate of topological edge states in periodically driven nonlinear systems Ken Mochizuki, Kaoru Mizuta, Norio Kawakami Topological edge states unique to periodically driven systems (Floquet systems) have been observed in optical systems [1], in which nonlinear effects can be relevant when the light intensity is high. In this study, we explore edge states in the nonlinear regime and obtain stationary states associated with topological phases unique to Floquet systems [2]. In addition, we study the stability of these edge states and reveal a sort of transition between two regions I and II, in which lifetimes of these edge states are extremely long and short, respectively. We characterize the transitions in lifetimes by Krein signatures or equivalently the pseudoHermiticity breaking, which highlights the intimate relationship between transitions in nonlinear systems and nonHermitian open systems. We also clarify that lifetimes of various stationary edge states are equalized due to random potentials, resulting in prolongation of lifetimes in region II and vice versa in region I. 
Thursday, March 17, 2022 2:06PM  2:18PM 
T59.00014: HighTemperature Fractional Quantum Hall State in FloquetKagome Flat Band Hang Liu, Gurjyot S Sethi, Donna Sheng, Yinong Zhou, JiaTao Sun, Sheng Meng, Feng Liu Fractional quantum Hall effect (FQHE) has been predicted in topological flat band (FB) by singleparticle band structure combined with phenomenological theory or solution of manybody lattice Hamiltonian with fuzzy parameters. A longstanding roadblock towards realization of FBFQHE is lacking the manybody solution of specific materials under realistic conditions. Here, we demonstrate a combined study of singleparticle Floquet band theory with exact diagonalization (ED) of manybody Hamiltonian. We show that a timeperiodic circularly polarized laser inverts the sign of secondnearestneighbor hopping in a Kagome lattice and enhances spinorbit coupling in one spin channel, to produce a Floquet FB with a high flatness ratio of bandwidth over band gap, as exemplified in monolayer Pt_{3}C_{36}S_{12}H_{12}. The ED of the resultant FloquetKagome lattice Hamiltonian gives a onethirdfilling ground state with a laserdependent excitation gap of FQH state, up to an estimated temperature above 70 K. Our findings pave the way to explore the alluding hightemperature FBFQHE. 
Thursday, March 17, 2022 2:18PM  2:30PM 
T59.00015: Floquet engineering of electric polarization with twofrequency drive Yuya Ikeda, Sota Kitamura, Takahiro Morimoto Electric polarization is a geometric phenomenon in solids and has a close relationship to the symmetry of the system. Here we propose a mechanism to dynamically induce and manipulate electric polarization by using an external light field. Specifically, we show that application of bicircular lights (BCLs) control the rotational symmetry of the system and can generate electric polarization. To this end, we use Floquet theory to study a system subjected to a twofrequency drive. We derive an effective Hamiltonian with high frequency expansions, for which the electric polarization is computed with the Berry phase formula. We demonstrate the dynamical control of polarization for a onedimensional SSH chain, a square lattice model, and a honeycomb lattice model. 
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