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 X46: Floquet Topological InsulatorsLive

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Sponsoring Units: DCMP Chair: Zhicheng Yang, University of Maryland, College Park 
Friday, March 19, 2021 8:00AM  8:12AM Live 
X46.00001: Theory of Anomalous Floquet HigherOrder Topology: Classification, Characterization, and BulkBoundary Correspondence Ruixing Zhang, Zhicheng Yang Periodicallydriven or Floquet systems can realize anomalous topological phenomena that do not exist in any equilibrium states of matter, whose classification and characterization require new theoretical ideas that are beyond the wellestablished paradigm of static topological phases. In this work, we provide a general framework to understand anomalous Floquet higherorder topological insulators (AFHOTIs), the classification of which has remained a challenging open question. In two dimensions (2D), such AFHOTIs are defined by their robust, symmetryprotected corner modes pinned at special quasienergies, even though all their Floquet bands feature trivial band topology. The cornermode physics of an AFHOTI is found to be generically indicated by 3D Dirac/Weyllike topological singularities living in the phase spectrum of the bulk timeevolution operator. Physically, such a phaseband singularity is essentially a "footprint" of the topological quantum criticality, which separates an AFHOTI from a trivial phase adiabatically connected to a static limit. We establish the above higherorder bulkboundary correspondence through a dimensional reduction technique, which also allows for a systematic classification of 2D AFHOTIs protected by point group symmetries. 
Friday, March 19, 2021 8:12AM  8:24AM Live 
X46.00002: Topological Floquet Engineering of Twisted Bilayer Graphene Gabriel Topp, Gregor Jotzu, James McIver, Lede Xian, Angel Rubio, Michael Sentef In twisted bilayer graphene (TBG), the choice of the twist angle allows for tailored engineering of the low energy absorption spectrum. This tunability makes TBG a perfect playground for Floquet engineering. Motivated by the measurement of ultrafast lightinduced Hall currents in monolayer graphene [1], we investigate the topological properties of twisted bilayer graphene for an intermediate twisting angle in and out of equilibrium on the basis a full Moiréunitcell tightbinding model [2]. By breaking timereversal symmetry with a circularly polarized light field, we induce a transition to a topologically nontrivial Floquet band structure with a Berry curvature analogous to a Chern insulator, which can be controlled via inversionsymmetrybreaking backgate potentials. Additionally, I will discuss preliminary results of my ongoing work on lightmatter couplings in magicangle twisted bilayer graphene (MATBG). 
Friday, March 19, 2021 8:24AM  8:36AM Live 
X46.00003: Floquet engineering of twisted double bilayer graphene Martin Rodriguezvega, Michael R Vogl, Gregory Fiete We study the effects of circularly polarized light propagating in free space and confined in a waveguide on the band structure and topological properties of twisted double bilayer graphene (TDBG) samples. These two Floquet protocols allow us to selectively tune different parameters of the system by varying the intensity and light frequency. For the drive protocol in free space, we find that in TDBG with AB/BA stacking, we can selectively close the zonecenter quasienergy gaps around one valley while increasing the gaps near the opposite valley by tuning the parameters of the drive. In TDBG with AB/AB stacking, a similar effect can be obtained upon the application of a perpendicular static electric field. We study the topological properties of the driven system in different settings, provide accurate effective Floquet Hamiltonians, and show that relatively strong drives can generate flat bands. Longitudinal light confined in a waveguide couples to the components of the interlayer hopping that are perpendicular to the TDBG sheet, allowing for selective engineering of the bandwidth of Floquet zonecenter quasienergy bands. 
Friday, March 19, 2021 8:36AM  8:48AM Live 
X46.00004: Anomalous levitation and annihilation in Floquet topological insulators Hui Liu, Ion Cosma Fulga, Janos Asboth Anderson localization in twodimensional topological insulators takes place via the socalled levitation and pair annihilation process. As disorder is increased, extended bulk states carrying opposite topological invariants move towards each other in energy, reducing the size of the topological gap, eventually meeting and localizing. This results in a topologically trivial Anderson insulator. Here, we introduce the anomalous levitation and pair annihilation, a process unique to periodically driven, or Floquet, systems. Due to the periodicity of the quasienergy spectrum, we find it is possible for the topological gap to increase as a function of disorder strength. Thus, after all bulk states have localized, the system remains topologically nontrivial, forming an anomalous FloquetAnderson insulator (AFAI) phase. 
Friday, March 19, 2021 8:48AM  9:00AM Live 
X46.00005: Bulk Invariants for 2D Floquet Topological Systems Carolyn Zhang, Michael Levin In many examples of topological phases, there exists a bulkboundary correspondence that relates topological properties of the edge to topological properties of the bulk. In this talk, we present a bulkboundary correspondence for noninteracting and interacting Floquet MBL systems in two spatial dimensions. Using this correspondence, we derive bulk invariants for several classes of Floquet systems, including interacting systems without symmetry and with U(1) symmetry, and noninteracting systems. The bulk invariants do not require translation symmetry or flux threading. In systems with $U(1)$ symmetry, the bulk invariant can be related to both a magnetization density and a conserved edge current. 
Friday, March 19, 2021 9:00AM  9:12AM Live 
X46.00006: Stability of topological edge states in nonlinear quantum walks: Bifurcations unique to Floquet systems Ken Mochizuki, Norio Kawakami, Hideaki Obuse Quantum walk, which is a kind of Floquet systems where time evolves in a discrete manner, can possess nontrivial topological phases. Recently, quantum walks with nonlinear effects have been proposed theoretically. Taking these features into account, we study the stability of topologically protected edge states in nonlinear quantum walks. In contrast to the previous work [1] which ignores the discretetime nature, we analyze the stability taking the discreteness of time into account [2]. As a result, we find a new bifurcation where edge states change from stable attractors to unstable repellers. The bifurcation is unique to Floquet systems since it originates from the discreteness of time. Furthermore, because of the simpleness of the quantum walk, we analytically derive the bifurcation thresholds, which are generally difficult to obtain in a wide range of nonlinear systems. 
Friday, March 19, 2021 9:12AM  9:24AM Live 
X46.00007: Floquet topological flat bands and Landau Levels in twodimensional systems Muhammad Tahir, Aidan Winblad, Hua Chen Flat electronic bands and Landau levels in equilibrium condensed matter systems have been common avenues to nontrivial correlation effects, with the twisted bilayer graphene being a most recent prominent example. It is expected that flat quasienergy bands can also enhance interaction effects in timeperiodic Floquet systems and may lead to novel interaction driven metastable phases. Here, we propose a general approach to realizing Floquet flat bands and Landau levels with nontrivial topology in 2D or quasi2D systems subject to circularlypolarized light. The Floquet flat bands and Landau levels in this work can be realized without the need of fine tuning in contrast to twisted bilayer graphene. Our proposal may pave the way to novel interactiondriven phases in nonequilibrium systems. 
Friday, March 19, 2021 9:24AM  9:36AM Live 
X46.00008: Kagome lattice network model as a chiral Floquet topological insulator Matteo Wilczak, Dmitry K Efimkin, Itamar Kimchi, Victor Gurarie

Friday, March 19, 2021 9:36AM  9:48AM Live 
X46.00009: Adding Doublons to Floquet Topological Insulators Helena Drueeke, Dieter Bauer We investigate Floquet topology in a tightbinding model on a finitesized, twodimensional, square lattice. Hoppings between neighboring sites vary in time according to a periodic protocol. An appropriate driving protocol makes the bulk of the system insulating while topologically protected edge currents flow around its borders. 
Friday, March 19, 2021 9:48AM  10:00AM Live 
X46.00010: Realization of Unidirectional Solitonlike Edge States in Nonlinear Floquet Topological Insulators Sebabrata Mukherjee, Mikael C Rechtsman Over the past decades, intriguing topological states have been extensively studied in electronic, photonic, ultracold atomic, and other systems. How topological edge states behave in the presence of interparticle interactions and nonlinearity is an important and open question in this field. Here we demonstrate unidirectional solitonlike nonlinear states on the edge of photonic Floquet topological insulators formed by modulated optical waveguides. A wellcontrolled modulation of waveguide paths gives rise to a topologically nontrivial photonic band, characterized by an integervalued topological invariant (winding number). Optical Kerr nonlinear interaction is introduced by using intense laser pulses. The observed nondiffracting, solitonlike wavepackets slowly radiate power because of the intrinsic gaplessness of the system. The rich and distinct localization characteristics measured as a function of nonlinearity confirms the existence of these solitonlike edge states. Our results are universal to other interacting bosonic systems, described by the focusing nonlinear Schrödinger equation or the attractive Gross Pitaevskii equation. 
Friday, March 19, 2021 10:00AM  10:12AM Live 
X46.00011: Quantum Hall Network Models as Floquet Topological Insulators Andrew C Potter, John Chalker, Victor Gurarie Network models for equilibrium integer quantum Hall (IQH) transitions are described by unitary scattering matrices that can also be viewed as representing nonequilibrium Floquet systems. The resulting Floquet bands have zero Chern number, and are instead characterized by a chiral Floquet winding number. This begs the question, how can a model without Chern number describe IQH systems? We resolve this puzzle by showing that nonzero Chern number is recovered from the network model via the energy dependence of network model scattering parameters. This relationship shows that, despite their topologically distinct origins, IQH and chiral Floquet topologychanging transitions share identical universal scaling properties. 
Friday, March 19, 2021 10:12AM  10:24AM Not Participating 
X46.00012: Homotopy classification of Floquet band singularities XiaoQi Sun, RobertJan Slager, Tomas Bzdusek The spectrum of periodically driven (i.e. “Floquet”) crystalline systems is characterized by energy bands in momentum space. Due to the discrete nature of their timetranslation symmetry, Floquet systems conserve energy only modulo the angular frequency of the drive, resulting in the wellknown compactification of the real energy axis into a looping “quasienergy”. The resulting quasienergy bands can exhibit topologically nontrivial gaps, robust band singularities, and anomalous boundary modes  including ones that are impossible in static systems. 
Friday, March 19, 2021 10:24AM  10:36AM Live 
X46.00013: Spacetime symmetry indicator for Floquet topological states Shuangyuan Lu, YuanMing Lu Symmetry plays an important role in topological states. In a band insulator, usually the band topology is a global property of Bloch wavfunctions over the whole Brillouin zone. In the presence of crystalline symmetries, however, the band topology can sometimes be inferred just from knowledge of Bloch wavefunctions at high symmetry momenta in k space, known as symmetry indicators. In this work, we generalize the concept of symmetry indicators from spatial crystalline symmetries to spacetime symmetry in periodically driven Floquet systems. In the presence of spacetime screw symmetry, a combination of time translation and spatial rotation, we derive the symmetry indicators for Floquet topological insulators in 2+1D. This provides a convenient tool to identify and engineer nontrivial Floquet topological phases in periodically driven materials. 
Friday, March 19, 2021 10:36AM  10:48AM Live 
X46.00014: Floquet Gauge Pump Abhishek Kumar, Gerardo Ortiz, Philip Richerme, Babak Seradjeh Gauge pumps are spatiallyresolved probes that can reveal discrete symmetries due to nontrivial topology. We introduce the Floquet gauge pump whereby a dynamically engineered Floquet Hamiltonian is employed to reveal the inherent topology of the ground state in interacting systems. We demonstrate this concept in a 1D XY model with periodically driven couplings and a transverse field. In the highfrequency limit, we obtain a Floquet Hamiltonian consisting of the static XY and dynamically generated DzyaloshinskyMoriya interactions (DMI) terms. We show that anisotropy in the couplings facilitates a magnetization current across a dynamically imprinted junction. In fermionic language, this corresponds to an unconventional Josephson junction with both hopping and pairing tunneling terms. The magnetization current depends on the phases of complex coupling terms, with the XY interaction as the real and DMI as the imaginary part. It shows 4π periodicity revealing the topological nature of the ground state manifold in the ordered phase, in contrast to the trivial topology in the disordered phase. We discuss the requirements to realize the Floquet gauge pump with interacting trapped ions. 
Friday, March 19, 2021 10:48AM  11:00AM Live 
X46.00015: Driving QuantumConfined Massless Dirac Fermions: Floquet Graphene Antidot Lattices Andrew Cupo, Vincent Flynn, Emilio Cobanera, James Brown, James D Whitfield, Chandrasekhar Ramanathan, Lorenza Viola Graphene antidot lattices are a convenient platform for exploring the properties of quantumconfined Dirac fermions in 2D. Changing the confinement strength by varying the geometric parameters (hole diameter and spacing) results in a widely tunable band gap. In similarity to pristine graphene [1], periodic driving with timereversal symmetry breaking circularly polarized light has the potential to induce nontrivial topology in the quasienergy spectra. Based on the FloquetKubo formalism, the conductivity is calculated as the photon energy and electric field amplitude are varied across the topological transition, and constitutes a starting point for bridging between theory and future experiments. Furthermore, timedependent density functional theory calculations are used to validate the simple Dirac Hamiltonian and Peierls substitution approaches. Floquet graphene antidot lattices may find application in solar cells, solid state spin qubit arrays, and parallel DNA sequencers. 
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