Bulk-Edge correspondence for two-dimensional Floquet topological insulators

TL;DR

This paper introduces new, robust definitions of topological indices for two-dimensional Floquet topological insulators that account for disorder and defects, establishing their equivalence and linking edge phenomena to quantized pumping.

Contribution

It provides disorder- and defect-inclusive definitions of bulk and edge topological indices, proving their equality and extending the bulk-edge correspondence in Floquet systems.

Findings

New definitions of topological indices that do not rely on translation invariance.

Proof that bulk and edge indices are equal in disordered Floquet insulators.

Edge index corresponds to quantized pumping at the interface.

Abstract

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 to 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 sample 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.