Bulletin of the American Physical Society
APS March Meeting 2019
Volume 64, Number 2
Monday–Friday, March 4–8, 2019; Boston, Massachusetts
Session K01: Floquet SystemsFocus

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Sponsoring Units: DCMP Chair: Lukasz Fidkowski, University of Washington Room: BCEC 106 
Wednesday, March 6, 2019 8:00AM  8:12AM 
K01.00001: Central Charge of Periodically Driven Critical Kitaev Chains Daniel Yates, Yonah S Lemonik, Aditi Mitra Periodically driven Kitaev chains show a rich phase diagram as the amplitude and frequency of the drive is varied, with topological phase transitions separating regions with different number of Majorana zero and π modes. We explore whether the critical point separating different phases of the periodically driven chain may be characterized by a universal central charge. We affirmatively answer this question by studying the entanglement entropy (EE) numerically, and analytically for the lowest entangled many particle eigenstate at arbitrary nonstroboscopic and stroboscopic times. We find that the EE at the critical point scales logarithmically with a timeindependent central charge, and that the Floquet micromotion gives only subleading corrections to the EE. This result also generalizes to multicritical points where the EE is found to have a central charge which is the sum of the central charges of the intersecting critical lines. 
Wednesday, March 6, 2019 8:12AM  8:24AM 
K01.00002: Signatures of Floquet Majorana Fermions in Planar Josephson Junctions Dillon Liu, Javad Shabani, Aditi Mitra We show how Floquet Majorana fermions may be experimentally realized in a periodically driven solid state platform. We consider a planar Josephson junction formed via a superconductingproximitized 2D electron gas (2DEG) with Rashba spinorbit coupling and inplane Zeeman field. Using bulk Floquet topological invariants we analyze the number of zero and pi Majorana modes for experimentally realistic parameters. Then we describe several experimental signatures of these exotic modes in finite wires, including differential conductance and local density of states. Notably, features in these quantities exhibit subharmonic responses to the drive. 
Wednesday, March 6, 2019 8:24AM  8:36AM 
K01.00003: TimeCrystalline Topological Superconductors Aaron Chew, David Mross, Jason Alicea Time crystals form when arbitrary physical states of a periodically driven system spontaneously break discrete timetranslation symmetry. We introduce the notion of 1D timecrystalline topological superconductors, for which timetranslation symmetry breaking and Majorana physics nontrivially intertwine. In the simplest realization, such a phase exhibits a bulk magnetization that returns to its original form after two drive periods, together with unconventional Floquet Majorana end modes that recover their initial form only after four drive periods. We also propose experimental implementations and detection schemes for this new phase. 
Wednesday, March 6, 2019 8:36AM  8:48AM 
K01.00004: Threedimensional Chiral Lattice Fermion in Floquet Systems XiaoQi Sun, Meng Xiao, Tomas Bzdusek, Shoucheng Zhang, Shanhui Fan We show that the NielsenNinomiya nogo theorem still holds on Floquet lattice: there is an equal number of righthanded and lefthanded Weyl points in threedimensional Floquet lattice. However, in the adiabatic limit, where the time evolution of lowenergy subspace is decoupled from the highenergy subspace, we show that the bulk dynamics in the lowenergy subspace can be described by Floquet bands with extra left/righthanded Weyl points, despite the nogo theorem. Assuming adiabatic evolution of two bands, we show that the difference of the number of righthanded and lefthanded Weyl points equals twice the winding number of the adiabatic Floquet operator over the Brillouin zone. Based on these findings, we propose a realization of purely left or righthanded Weyl particles on a 3D lattice using a Hamiltonian obtained through dimensional reduction of a fourdimensional quantum Hall system. We argue that the breakdown of the adiabatic approximation on the surface facilitates unusual closed orbits of wave packets in applied magnetic field, which traverse alternatively through the lowenergy and highenergy sector of the spectrum. 
Wednesday, March 6, 2019 8:48AM  9:00AM 
K01.00005: Disentangling beyondcohomology symmetry protected topological phases Jeongwan Haah, Lukasz Fidkowski, Matthew Hastings We construct a threedimensional locality preserving unitary operator which disentangles the ground state of the WalkerWang three fermion model. We show that this locality preserving unitary operator cannot be a quantum circuit, or otherwise one could construct a commuting projector model which realizes a phase with nonzero chiral central charge, which is widely believed to be impossible. We comment on the relation to Manybody localized Floquet topological phases. 
Wednesday, March 6, 2019 9:00AM  9:12AM 
K01.00006: Transport signatures of symmetry protection in onedimensional topological insulators Oleksandr Balabanov, Henrik Johannesson The unique feature of any topological insulator is presence of gapless states on its boundaries. In one dimension these states live on the edges and are protected against symmetrypreserving local perturbations. Here we describe a scheme for probing the robustness of the edge states by calculating the transport characteristics of an array of dimers attached to external leads. Numerical results obtained from nonequilibrium Green's function theory will be presented. It will be shown that there is a drop in the differential conductance as the dimer array is perturbed by a local symmetrybreaking perturbation, while the drop is strongly suppressed if the symmetries are maintained. A brief analytic description will be provided in support of the numerics. Both types of 1D topological insulators, conventional timeindependent and periodicallydriven (Floquet), are considered. 
Wednesday, March 6, 2019 9:12AM  9:24AM 
K01.00007: Topologically protected braiding in a single wire using Floquet Majorana modes Torsten Karzig, Bela Bauer, Tami PeregBarnea, MariaTheresa Rieder, Gil Refael, Erez Berg, Yuval Oreg The nonAbelian nature of Majorana zero modes is most prominently exhibited through braiding. While originally formulated for 2D systems, it has been shown that braiding can also be realized using 1D wires by forming an essentially 2D network. Here, we show that in driven systems far from equilibrium, one can do away with the second spatial dimension altogether by instead using quasienergy as the second dimension. To realize this, we use a Floquet topological superconductor which can exhibit Majorana modes at two special eigenvalues of the evolution operator, 0 and Pi, and thus can realize four Majorana modes in a single, driven quantum wire. We describe and numerically evaluate a protocol that realizes nonlocal braiding of two Majorana zero modes in a single wire by adiabatically modulating the Floquet drive and using the Pi modes as auxiliary degrees of freedom. 
Wednesday, March 6, 2019 9:24AM  9:36AM 
K01.00008: Metal to insulator phase transitions in FloquetBloch systems Iliya Esin, Mark Rudner, Netanel Lindner Timeperiodic drives provide a versatile tool for inducing topological phenomena in quantum many body systems. In this work, we study steadystates of lowdimensional semiconductors subjected to strong resonant periodic drives. Stable steadystates in these systems arise from the balance between phononassisted relaxation processes, electronhole recombination via photoemission and electronelectron scattering. We show that tuning the parameters of the phonon bath drives the system through a critical point, which separates an electronhole metal phase from a Floquet insulator phase. Our results may help guide future studies towards inducing novel nonequilibrium phases of matter by periodic driving. 
Wednesday, March 6, 2019 9:36AM  9:48AM 
K01.00009: Dissipative nonadiabatic topological pumping in an open Floquet system Tanay Nag, Kush Saha, Babak Seradjeh, Takashi Oka

Wednesday, March 6, 2019 9:48AM  10:00AM 
K01.00010: HigherOrder Floquet Topological Phases and Defects Martin RodriguerzVega, Abhishek Kumar, Babak Seradjeh We report the existence of higherorder Floquet topological phases. As a prototypical model, we study, both analytically and numerically, the twodimensional πflux square lattice with timedependent nearestneighbor hopping modulation. We show that with open boundary conditions, the quasienergy spectrum supports fourfold degenerate steady states at the center and/or edge of the Floquet zone localized at corners. The number of these Floquet corner states can be tuned by the amplitude and frequency of the drive. Under periodic boundary conditions and when the hopping modulation preserves diagonal mirror symmetry, the higherorder Floquet topology is revealed through a mirrorgraded Floquet winding number. Moreover, we show that in a strip geometry, the eigenvalues of the Floquet Wannier operator reveal edge polarization. Finally, we show that inhomogeneous driving protocols can be used to “stir” domain walls defects to generate lowerdimensional Floquet topological vortex defects. 
Wednesday, March 6, 2019 10:00AM  10:12AM 
K01.00011: Optical response of Floquet topological insulators Abhishek Kumar, Martin RodriguerzVega, Tami PeregBarnea, Babak Seradjeh Optical probes provide detailed information about electronic excitations in equilibrium, but a new formulation is needed to understand their utility in nonequilibrium Floquet system. Motivated to find useful signatures of Floquet topological phases, we formulate a linear response theory for a Floquet system subjected to an external field and derive the generalized optical conductivity. We recover Kubo or Floquet optical Hall conductivity previously discussed in the literature in appropriate limits. In a Floquet system, optical conductivity acquires a Fourier decomposition, describing the response to a probe frequency displaced by the harmonics of the drive frequency. We obtain analytical results and perform numerical calculations for different scenarios of the occupation of the bands, in particular, the diagonal Floquet distribution and the distribution obtained after a quench. We discuss the structure of optical Hall and longitudinal conductivity in different topological phases. 
Wednesday, March 6, 2019 10:12AM  10:24AM 
K01.00012: Solutions to the Chiral Fermion Problem from Topological Orders and Floquet NonHermition Field Integrals Michael DeMarco, XiaoGang Wen Defining a chiral gauge theory nonperturbatively on a lattice has posed a longstanding issue for a nonperturbative definition of the standard model. However, recent insights connecting quantum anomalies with topologically ordered states have led to a breakthrough in lattice formulations of chiral gauge theories: any anomalyfree chiral gauge theory may be formulated as the edge theory of a 2+1d slab with topogical order that is reduced to trivial order by interactions. We keep the `width' of the slab finite so that the system is truly 1+1d. We can then develop a recipe for defining chiral gauge theories that can be extended to higher dimensions. In a parallel development, our recent formulations of discretetime field integrals allow us to formulate several chiral Floquet phases as local field integrals in discretized spacetime. Intriguingly, these field integrals have unitary correlation functions, even though their Lagrangians are nonHermitian operators. This provides a second nonperturbative definition of a chiral field theory in 1+1d, and we will discuss future generalizations to higher dimensions. 
Wednesday, March 6, 2019 10:24AM  10:36AM 
K01.00013: Floquet Topological Semimetal with Nodal Helix Kwon Park, Kun Woo Kim, HyunWoong Kwon Topological semimetal with nodal line is a novel class of topological matter extending the concept of topological matter beyond topological insulators and Weyl/Dirac semimetals. Here, we show that a Floquet topological semimetal with nodal helix can be generated by irradiating graphene or the surface of a topological insulator with circularly polarized light. Nodal helix is a form of nodal line running across the Brillouin zone with helical winding. Specifically, it is shown that the dynamics of irradiated graphene is described by the time Stark Hamiltonian, which can host a Floquet topological insulator and a weakly driven Floquet topological semimetal with nodal helix in the high and low frequency limits, respectively. One of the most striking features of the Floquet topological semimetal at low frequency is that the Berry phase accumulated along the time direction, also known as the Zak phase, has a topological discontinuity of π across the projected nodal helix. It is predicted that such a topological discontinuity of the Berry phase manifests itself as the topological discontinuity of the Floquet states. At intermediate frequency, this topological discontinuity can create an interesting change of patterns in the quasienergy dispersion of the Floquet states. 
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