RSS icon
Twitter icon
Facebook icon
Vimeo icon
YouTube icon

Dynamical symmetry indicators for Floquet crystals

TitleDynamical symmetry indicators for Floquet crystals
Publication TypeJournal Article
Year of Publication2021
AuthorsJ. Yu, R-X. Zhang, and Z-. Da Song
JournalNat. Commun.
Volume12
Date PublishedOCT 13
Type of ArticleArticle
Abstract

Various exotic topological phases of Floquet systems have been shown to arise from crystalline symmetries. Yet, a general theory for Floquet topology that is applicable to all crystalline symmetry groups is still in need. In this work, we propose such a theory for (effectively) non-interacting Floquet crystals. We first introduce quotient winding data to classify the dynamics of the Floquet crystals with equivalent symmetry data, and then construct dynamical symmetry indicators (DSIs) to sufficiently indicate the inherently dynamical Floquet crystals. The DSI and quotient winding data, as well as the symmetry data, are all computationally efficient since they only involve a small number of Bloch momenta. We demonstrate the high efficiency by computing all elementary DSI sets for all spinless and spinful plane groups using the mathematical theory of monoid, and find a large number of different nontrivial classifications, which contain both first-order and higher-order 2+1D anomalous Floquet topological phases. Using the framework, we further find a new 3+1D anomalous Floquet second-order topological insulator (AFSOTI) phase with anomalous chiral hinge modes. A general theory for Floquet topology applicable to all crystalline symmetry groups is lacking. Here, the authors propose such a theory for noninteracting Floquet crystals and predict an inversion-protected Floquet higher-order topological phase with anomalous chiral hinge modes.

DOI10.1038/s41467-021-26092-3