Topological invariants of Floquet systems: General formulation, special properties, and Floquet topological defects

TL;DR

This paper provides a comprehensive framework for defining and analyzing topological invariants in Floquet systems, including their application to defects and Majorana modes, advancing the understanding of driven topological phases.

Contribution

It introduces a systematic formulation of topological invariants for all symmetry classes in Floquet systems and develops a theory of Floquet topological defects.

Findings

Constructed topological invariants for all symmetry classes and dimensions.

Established the equivalence between different types of Floquet topological invariants.

Proposed models and identified defect modes like Floquet Majorana zero modes.

Abstract

Periodically driven (Floquet) systems have been under active theoretical and experimental investigations. This paper aims at a systematic study in the following aspects of Floquet systems: (i) A systematic formulation of topological invariants of Floquet systems based on the cooperation of topology and symmetries. Topological invariants are constructed for the ten symmetry classes in all spatial dimensions, for both homogeneous Floquet systems (Floquet topological insulators and superconductors) and Floquet topological defects. Meanwhile, useful representative Dirac Hamiltonians for all the symmetry classes are obtained and studied. (ii) A general theory of Floquet topological defects, based on the proposed topological invariants. (iii) Models and proposals of Floquet topological defects in low dimensions. Among other defect modes, we investigate Floquet Majorana zero modes and Majorana Pi modes in vortices of topologically trivial superconductors under a periodic drive. In addition, we clarified several notable issues about Floquet topological invariants. Among other issues, we prove the equivalence between the effective-Hamiltonian-based band topological invariants and the frequency-domain band topological invariants.