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arXiv · 1506.07647

Topological singularities and the general classification of Floquet-Bloch systems

Frederik Nathan·Mark S. Rudner
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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.

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Frederik Nathan, Mark S. Rudner. 2015-06-25. Topological singularities and the general classification of Floquet-Bloch systems. https://doi.org/10.1088/1367-2630/17/12/125014

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