Topological singularities and the general classification of Floquet-Bloch systems

TL;DR

This paper introduces a new topological classification framework for Floquet-Bloch systems based on the time-dependent spectrum of the evolution operator, revealing protected degeneracies that influence the system's topological properties.

Contribution

It develops a novel paradigm for classifying Floquet-Bloch bands by analyzing the evolution operator spectrum over one period, incorporating symmetries for a comprehensive understanding.

Findings

Topologically-protected degeneracies occur at intermediate times during the driving cycle.

The classification framework unifies driven and non-driven topological phases.

Symmetries play a crucial role in determining the topological features.

Abstract

Recent works have demonstrated that the Floquet-Bloch bands of periodically-driven systems feature a richer topological structure than their non-driven counterparts. The additional structure in the driven case arises from the periodicity of quasienergy, the energy-like quantity that defines the spectrum of a periodically-driven system. Here we develop a new paradigm for the topological classification of Floquet-Bloch bands, based on the time-dependent spectrum of the driven system's evolution operator throughout one driving period. Specifically, we show that this spectrum may host topologically-protected degeneracies at intermediate times, which control the topology of the Floquet bands of the full driving cycle. This approach provides a natural framework for incorporating the role of symmetries, enabling a unified and complete classification of Floquet-Bloch bands and yielding new insight into the topological features that distinguish driven and non-driven systems.