Multiscale Invariants of Floquet Topological Insulators

TL;DR

This paper investigates the topological properties of Floquet topological insulators under electromagnetic irradiation, focusing on bulk and edge invariants, interface states, and the effects of high-frequency modulations.

Contribution

It introduces a detailed analysis of bulk and interface topologies in Floquet insulators, including invariants and a bulk-interface correspondence, under various modulation regimes.

Findings

Topologically protected interface states can be created by spatial modulation of drive polarization.

A sequence of topologies emerges at different high-frequency regimes.

Large-gap effective topologies are achievable with high-frequency, high-amplitude modulation, but only for moderate times.

Abstract

This paper analyzes Floquet topological insulators resulting from the time-harmonic irradiation of electromagnetic waves on two dimensional materials such as graphene. We analyze the bulk and edge topologies of approximations to the evolution of the light-matter interaction. Topologically protected interface states are created by spatial modulations of the drive polarization across an interface. In the high-frequency modulation regime, we obtain a sequence of topologies that apply to different time scales. Bulk-difference invariants are computed in detail and a bulk-interface correspondence is shown to apply. We also analyze a high-frequency high-amplitude modulation resulting in a large-gap effective topology topologically that remains valid only for moderately long times.