Topological Origin of π Interface Modes Induced by Floquet Gauge Transition

Abstract

Abstract: Topological insulator is a kind of phase of matter that is internally insulated and can conduct electricity on the surface. The energy band of a topological insulator has non-trivial topological characteristics, which supports a boundary state that can propagate in one direction. The appearance of topological states usually depends on the topological phase transition at the interface or boundary. Recently, a new topological π mode induced by gauge transitions has been successfully observed experimentally in Floquet systems, despite the same topological order across the whole lattices. In this paper, the origin of the topological π mode induced by the gauge field transition are discussed. The Hamiltonian of two Floquet systems with different gauges has opposite π gap mass terms due to gauge transition, thus leads to the emergence of interface states, which is similar to the Jackiw-Rebbi model. The research of this paper provides a theoretical basis for the generation of topological states from gauge transitions, and deepen the understanding of the Floquet gauge.

Key words: Floquet system, topological π mode, artificial gauge field, Su-Schriffer-Heeger model, Jackiw-Rebbi model, topological insulator

CLC Number:

O469

SONG Wange, ZHU Shining, LI Tao. Topological Origin of π Interface Modes Induced by Floquet Gauge Transition[J]. Journal of Synthetic Crystals, 2021, 50(7): 1340-1347.

References

[1] VON KLITZING K. The quantized Hall effect[J]. Reviews of Modern Physics, 1986, 58(3): 519-531.
[2] KANE C L, MELE E J. Quantum spin Hall effect in graphene[J]. Physical Review Letters, 2005, 95(22): 226801.
[3] BERNEVIG B A, ZHANG S C. Quantum spin Hall effect[J]. Physical Review Letters, 2006, 96(10): 106802.
[4] HASAN M Z, KANE C L. Colloquium: topological insulators[J]. Reviews of Modern Physics, 2010, 82(4): 3045-3067.
[5] QI X L, ZHANG S C. Topological insulators and superconductors[J]. Reviews of Modern Physics, 2011, 83(4): 1057-1110.
[6] CHIU C K, TEO J C Y, SCHNYDER A P, et al. Classification of topological quantum matter with symmetries[J]. Reviews of Modern Physics, 2016, 88(3): 035005.
[7] HATSUGAI Y. Chern number and edge states in the integer quantum Hall effect[J]. Physical Review Letters, 1993, 71(22): 3697-3700.
[8] QI X L, WU Y S, ZHANG S C. General theorem relating the bulk topological number to edge states in two-dimensional insulators[J]. Physical Review B, 2006, 74(4): 045125.
[9] KRAUS Y E, LAHINI Y, RINGEL Z, et al. Topological states and adiabatic pumping in quasicrystals[J]. Physical Review Letters, 2012, 109(10): 106402.
[10] BENALCAZAR W A, BERNEVIG B A, HUGHES T L. Quantized electric multipole insulators[J]. Science, 2017, 357(6346): 61-66.
[11] SONG W, SUN W, CHEN C, et al. Breakup and recovery of topological zero modes in finite non-Hermitian optical lattices[J]. Physical Review Letters, 2019, 123(16): 165701.
[12] LINDNER N H, REFAEL G, GALITSKI V. Floquet topological insulator in semiconductor quantum wells[J]. Nature Physics, 2011, 7(6): 490-495.
[13] SU W P, SCHRIEFFER J R, HEEGER A J. Solitons in polyacetylene[J]. Physical Review Letters, 1979, 42(25): 1698-1701.
[14] HEEGER A J, KIVELSON S, SCHRIEFFER J R, et al. Solitons in conducting polymers[J]. Reviews of Modern Physics, 1988, 60(3): 781-850.
[15] RYU S, HATSUGAI Y. Topological origin of zero-energy edge states in particle-hole symmetric systems[J]. Physical Review Letters, 2002, 89(7): 077002.
[16] BLANCO-REDONDO A, ANDONEGUI I, COLLINS M J, et al. Topological optical waveguiding in silicon and the transition between topological and trivial defect states[J]. Physical Review Letters, 2016, 116(16): 163901.
[17] ST-JEAN P, GOBLOT V, GALOPIN E, et al. Lasing in topological edge states of a one-dimensional lattice[J]. Nature Photonics, 2017, 11(10): 651-656.
[18] WANG Y H, LIU W J, JI Z R, et al. Coherent interactions in one-dimensional topological photonic systems and their applications in all-optical logic operation[J]. Nano Letters, 2020, 20(12): 8796-8802.
[19] MUKHERJEE S, SPRACKLEN A, VALIENTE M, et al. Experimental observation of anomalous topological edge modes in a slowly driven photonic lattice[J]. Nature Communications, 2017, 8: 13918.
[20] LIU D T, SHABANI J, MITRA A. Floquet Majorana zero and π modes in planar Josephson junctions[J]. Physical Review B, 2019, 99(9): 094303.
[21] POTTER A C, MORIMOTO T, VISHWANATH A. Classification of interacting topological floquet phases in one dimension[J]. Physical Review X, 2016, 6(4): 041001.
[22] CHENG Q Q, PAN Y M, WANG H Q, et al. Observation of anomalous π modes in photonic floquet engineering[J]. Physical Review Letters, 2019, 122(17): 173901.
[23] ASBÓTH J K, TARASINSKI B, DELPLACE P. Chiral symmetry and bulk-boundary correspondence in periodically driven one-dimensional systems[J]. Physical Review B, 2014, 90(12): 125143.
[24] DAL LAGO V, ATALA M, FOA TORRES L E F. Floquet topological transitions in a driven one-dimensional topological insulator[J]. Physical Review A, 2015, 92(2): 023624.
[25] FRUCHART M. Complex classes of periodically driven topological lattice systems[J]. Physical Review B, 2016, 93(11): 115429.[26] BUKOV M, D′ALESSIO L, POLKOVNIKOV A. Universal high-frequency behavior of periodically driven systems: from dynamical stabilization to Floquet engineering[J]. Advances in Physics, 2015, 64(2): 139-226.
[27] ECKARDT A, ANISIMOVAS E. High-frequency approximation for periodically driven quantum systems from a Floquet-space perspective[J]. New Journal of Physics, 2015, 17(9): 093039.
[28] SONG W G, CHEN Y X, LI H M, et al. Gauge-induced Floquet topological states in photonic waveguides[J]. Laser & Photonics Reviews, 2021, 15: 2000584.
[29] JACKIW R, REBBI C. Solitons with fermion number 1/2[J]. Physical Review D, 1976, 13(12): 3398-3409.
[30] CHERPAKOVA Z F, JÖRG C, DAUER C, et al. Limits of topological protection under local periodic driving[J]. Light: Science & Applications, 2019, 8: 63.
[31] PAN Y M, WANG B. Time-crystalline phases and period-doubling oscillations in one-dimensional Floquet topological insulators[J]. Physical Review Research, 2020, 2(4): 043239.