Periodic Table for Floquet Topological Insulators

TL;DR

This paper develops a comprehensive classification scheme, called a 'periodic table', for Floquet topological insulators, extending static classifications to time-dependent systems using K-theory and revealing new edge mode phenomena.

Contribution

It introduces a systematic K-theory-based classification for Floquet topological insulators across all symmetry classes and dimensions, generalizing static topological classifications.

Findings

Classification scheme extends static group G to G×G for Floquet systems

Topologically protected edge modes are characterized by bulk invariants

Mapping between edge modes and bulk topological invariants established

Abstract

Dynamical phases with novel topological properties are known to arise in driven systems of free fermions. In this paper, we obtain a `periodic table' to describe the phases of such time-dependent systems, generalizing the periodic table for static topological insulators. Using K-theory, we systematically classify Floquet topological insulators from the ten Altland-Zirnbauer symmetry classes across all dimensions. We find that the static classification scheme described by a group $G$ becomes $G\times G$ in the time-dependent case, and interpret the two factors as arising from the bipartite decomposition of the unitary time-evolution operator. Topologically protected edge modes may arise at the boundary between two Floquet systems, and we provide a mapping between the number of such edge modes and the topological invariant of the bulk.