Floquet higher-order topological insulators and superconductors with space-time symmetries

TL;DR

This paper classifies Floquet higher-order topological insulators and superconductors with space-time symmetries, providing a systematic framework and model construction methods for understanding their topological phases.

Contribution

It introduces a classification scheme for Floquet HOTI/SCs with order-two space-time symmetries using unitary loops and maps them to static Hamiltonians, advancing the theoretical understanding.

Findings

Complete classification of Floquet HOTI/SCs with space-time symmetries.

Identification of a correspondence between space-time and static crystalline symmetries.

Provision of a model construction recipe for Floquet HOTI/SCs.

Abstract

Floquet higher-order topological insulators and superconductors (HOTI/SCs) with an order-two space-time symmetry or antisymmetry are classified. This is achieved by considering unitary loops, whose nontrivial topology leads to the anomalous Floquet topological phases, subject to a space-time symmetry/antisymmetry. By mapping these unitary loops to static Hamiltonians with an order-two crystalline symmetry/antisymmetry, one is able to obtain the $K$ groups for the unitary loops and thus complete the classification of Floquet HOTI/SCs. Interestingly, we found that for every order-two nontrivial space-time symmetry/antisymmetry involving a half-period time translation, there exists a unique order-two static crystalline symmetry/antisymmetry, such that the two symmetries/antisymmetries give rise to the same topological classification. Moreover, by exploiting the frequency-domain formulation of the Floquet problem, a general recipe that constructs model Hamiltonians for Floquet HOTI/SCs is provided, which can be used to understand the classification of Floquet HOTI/SCs from an intuitive and complimentary perspective.