Topological invariants of Floquet topological phases under periodical driving

Abstract

Owing to the replication of Floquet bands and the presence of additional gaps in the quasienergy dimension, the topological phases in a periodically driven system cannot be fully characterized by the conventional topological invariants used in static systems. In particular, an anomalous strong topological phase can be a host in driven systems, featured by nontrivial counterpropagating edge modes which cannot be characterized by the bulk band structure. In this paper, we propose a scheme to obtain a complete characterization of Floquet topological phases using only information about bulk dispersions under the condition that both the location and chirality of Floquet band-touching points are not changed by the periodical driving. A set of topological invariants associated with the band-touching points are formulated to establish a one-to-one correspondence to the number of edge modes. Finally, we discuss the experimental realization and detection scheme using cold atomic gases.