Topological singularities and the general classification of Floquet–Bloch systems

By Frederik Nathan, Mark Rudner. 2015

280 citations recorded by the source corpus.

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.

Subfields: Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/fe0347299364cf0163b26e85b5d60e8e1bb001fd

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In Atomic and Molecular Physics, and Optics

1. Nathan Goldman
2. A. Amo
3. M. Aidelsburger
4. T. Ozawa
5. H. Price
6. M. Rechtsman
7. I. Carusotto
8. David I. Schuster

Citations in the corpus

• Realization of an anomalous Floquet topological system with ultracold atoms (2020, background): “[27] F.”
• Artificial gauge fields in materials and engineered systems (2017, unknown): “Similar photonic crystals were recently produced to engineer “anomalous Floquet topological bands” for light [251,252], whose topological classification goes beyond that of static systems [54,253,254].”
• Topological bands for ultracold atoms (2018, unknown): “Recent works have constructed a general theory of the topological classification of time-varying single-particle Hamiltonians (Fruchart, 2016; Nathan and Rudner, 2015; Roy and Harper, 2016).”
• Periodic table for Floquet topological insulators (2016, background): “We note that our definition of chiral symmetry for periodic systems is slightly different from that used in some previous works [34, 36].”
• Topological photonics (2018, background): “…invariants (winding numbers) were identified by Kitagawa, Berg et al. (2010), Asbóth (2012), Rudner et al. (2013), Carpentier et al. (2015), Nathan and Rudner (2015), Bi et al. (2017b), and Yao, Yan, and Wang (2017) and were indeed shown to depend on the complete time-evolution operator…”