Topological invariants of Floquet systems: General formulation, special properties, and Floquet topological defects
By Shunyu Yao, Zhongbo Yan, Zhong Wang. 2017
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Periodically driven (Floquet) systems have been under active theoretical and experimental investigations. This paper aims at a systematic study in the following aspects of Floquet systems: (i) a systematic formulation of topological invariants of Floquet systems based on the cooperation of topology and symmetries. Topological invariants are constructed for the ten symmetry classes in all spatial dimensions, for both homogeneous Floquet systems (Floquet topological insulators and superconductors) and Floquet topological defects. Meanwhile, useful representative Dirac Hamiltonians for all the symmetry classes are obtained and studied. (ii) A general theory of Floquet topological defects, based on the proposed topological invariants. (iii) Models and proposals of Floquet topological defects in low dimensions. Among other defect modes, we investigate Floquet Majorana zero modes and Majorana Pi modes in vortices of topologically trivial superconductors under a periodic drive. In addition, we clarified several notable issues about Floquet topological invariants. Among other issues, we prove the equivalence between the effective-Hamiltonian-based band topological invariants and the frequency-domain band topological invariants.
Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics
View Paper: https://www.semanticscholar.org/paper/be7ab7ab201b5c2af62683387548b8af6130748e
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In Atomic and Molecular Physics, and Optics
In Condensed Matter Physics
Citations in the corpus
- Topological photonics (2018, background): “(Asbóth, 2012; Bi et al., 2017b; Carpentier et al., 2015; Kitagawa et al., 2010a; Nathan and Rudner, 2015; Rudner et al., 2013; Yao et al., 2017), and were indeed shown to depend on the complete time-evolution operator Û(t, t0); the crucial role played by the micro-motion in this topological charact”