Scattering matrix invariants of Floquet topological insulators

TL;DR

This paper introduces a scattering matrix approach to identify and analyze topological phases in Floquet insulators, revealing new phases and invariants that are robust to disorder and distinct from static systems.

Contribution

It develops a unified scattering theory framework for Floquet topological phases, including the discovery of new weak topological phases with unique properties.

Findings

Scattering matrix invariants accurately characterize topological phases in driven systems.

Identification of new weak Floquet topological insulators with previously unknown invariants.

Weak phases can be destroyed by breaking translational symmetry in time.

Abstract

Similar to static systems, periodically driven systems can host a variety of topologically non-trivial phases. Unlike the case of static Hamiltonians, the topological indices of bulk Floquet bands may fail to describe the presence and robustness of edge states, prompting the search for new invariants. We develop a unified description of topological phases and their invariants in driven systems, by using scattering theory. We show that scattering matrix invariants correctly describe the topological phase, even when all bulk Floquet bands are trivial. Additionally, we use scattering theory to introduce and analyze new periodically driven phases, such as weak topological Floquet insulators, for which invariants were previously unknown. We highlight some of their similarities with static systems, including robustness to disorder, as well as some of the features unique to driven systems, showing that the weak phase may be destroyed by breaking translational symmetry not in space, but in time.