zbMATH — the first resource for mathematics

Bulk-edge correspondence for two-dimensional Floquet topological insulators. (English) Zbl 1392.82008
Summary: Floquet topological insulators describe independent electrons on a lattice driven out of equilibrium by a time-periodic Hamiltonian, beyond the usual adiabatic approximation. In dimension two, such systems are characterized by integer-valued topological indices associated with the unitary propagator, alternatively in the bulk or at the edge of a sample. In this paper, we give new definitions of the two indices, relying neither on translation invariance nor on averaging, and show that they are equal. In particular, weak disorder and defects are intrinsically taken into account. Finally, indices can be defined when two driven samples are placed next to one another either in space or in time and then shown to be equal. The edge index is interpreted as a quantized pumping occurring at the interface with an effective vacuum.

82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics
82D20 Statistical mechanical studies of solids
82B44 Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics
82B27 Critical phenomena in equilibrium statistical mechanics
Full Text: DOI
[1] Asbóth, JK; Tarasinski, B; Delplace, P, Chiral symmetry and bulk-boundary correspondence in periodically driven one-dimensional systems, Phys. Rev. B, 90, 125143, (2014)
[2] Avron, J; Seiler, R; Simon, B, The index of a pair of projections, J. Funct. Anal., 120, 220-237, (1994) · Zbl 0822.47033
[3] Carpentier, D; Delplace, P; Fruchart, M; Gawędzki, K, Topological index for periodically driven time-reversal invariant 2D systems, Phys. Rev. Lett., 114, 106806, (2015) · Zbl 1331.82065
[4] Carpentier, D; Delplace, P; Fruchart, M; Gawędzki, K; Tauber, C, Construction and properties of a topological index for periodically driven time-reversal invariant 2D crystals, Nucl. Phys. B, 896, 779-834, (2015) · Zbl 1331.82065
[5] Elgart, A; Graf, GM; Schenker, JH, Equality of the bulk and edge Hall conductances in a mobility gap, Commun. Math. Phys., 259, 185-221, (2005) · Zbl 1086.81081
[6] Fruchart, M, Complex classes of periodically driven topological lattice systems, Phys. Rev. B, 93, 115429, (2016)
[7] Fulga, IC; Maksymenko, M, Scattering matrix invariants of Floquet topological insulators, Phys. Rev. B, 93, 075405, (2016)
[8] Graf, GM; Porta, M, Bulk-edge correspondence for two-dimensional topological insulators, Commun. Math. Phys., 324, 851-895, (2013) · Zbl 1291.82120
[9] Hatsugai, Y, Chern number and edge states in the integer quantum Hall effect, Phys. Rev. Lett., 71, 3697, (1993) · Zbl 0972.81712
[10] Inoue, JI; Tanaka, A, Photoinduced transition between conventional and topological insulators in two-dimensional electronic systems, Phys. Rev. Lett., 105, 017401, (2010)
[11] Kitagawa, T; Berg, E; Rudner, M; Demler, E, Topological characterization of periodically driven quantum systems, Phys. Rev. B, 82, 235114, (2010)
[12] Klinovaja, J; Stano, P; Loss, D, Topological Floquet phases in driven coupled Rashba nanowires, Phys. Rev. Lett., 116, 176401, (2016)
[13] Lindner, NH; Refael, G; Galitski, V, Floquet topological insulator in semiconductor quantum wells, Nat. Phys., 7, 490-495, (2011)
[14] Nathan, F; Rudner, MS; Lindner, NH; Berg, E; Refael, G, Quantized magnetization density in periodically driven systems, Phys. Rev. Lett., 119, 186801, (2016)
[15] Oka, T; Aoki, H, Photovoltaic Hall effect in graphene, Phys. Rev. B, 79, 081406, (2009)
[16] Prodan, E., Schulz-Baldes, H.: Bulk and Boundary Invariants for Complex Topological Insulators. Mathematical Physics Studies. Springer, Berlin (2016) · Zbl 1342.82002
[17] Prodan, E; Schulz-Baldes, H, Non-commutative odd Chern numbers and topological phases of disordered chiral systems, J. Funct. Anal., 271, 1150-1176, (2016) · Zbl 1344.82055
[18] Reed, M., Simon, B.: Method of Modern Mathematical Physics, vol. II. Academic Press, Cambridge (1980) · Zbl 0459.46001
[19] Rudner, MS; Lindner, NH; Berg, E; Levin, M, Anomalous edge states and the bulk-edge correspondence for periodically driven two-dimensional systems, Phys. Rev. X, 3, 031005, (2013)
[20] Sadel, C; Schulz-Baldes, H, Topological boundary invariants for Floquet systems and quantum walks, Math. Phys. Anal. Geom., 20, 22, (2017) · Zbl 1413.46061
[21] Titum, P; Berg, E; Rudner, MS; Refael, G; Lindner, NH, Anomalous Floquet-Anderson insulator as a nonadiabatic quantized charge pump, Phys. Rev. X, 6, 021013, (2016)
[22] Thouless, DJ, Quantization of particle transport, Phys. Rev. B, 27, 6083, (1983)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.