Topological invariants of Floquet systems: General formulation, special properties, and Floquet topological defects

Abstract

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.

54 pages, 13 figures. For higher resolution figures please see the published version

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• Symmetry and topological classification of Floquet non-Hermitian systems
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• Floquet engineering of low-energy dispersions and dynamical localization in a periodically kicked three-band system
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• Floquet engineering and simulating exceptional rings with a quantum spin system
• Topological characterization and stability of Floquet Majorana modes in Rashba nanowire
• Generalized bulk-boundary correspondence in periodically driven non-Hermitian systems
• Dissipative Floquet Majorana modes in proximity-induced topological superconductors
• Floquet-Bloch Oscillations and Intraband Zener Tunneling in an Oblique Spacetime Crystal
• Fermionic quantum cellular automata and generalized matrix product unitaries
• Mixed higher-order topology: boundary non-Hermitian skin effect induced by a Floquet bulk
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• Topological phase transitions at finite temperature
• Two-dimensional quantum walk with non-Hermitian skin effects
• Engineering of topological phases in driven thin topological insulator: Structure inversion asymmetry effect
• Floquet Mode Resonance: Trapping light in the bulk mode of a Floquet topological insulator by quantum self-interference
• Universal driving protocol for symmetry-protected Floquet topological phases
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• Unconventional Floquet topological phases from quantum engineering of band inversion surfaces
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• Unsupervised identification of Floquet topological phase boundaries
• Disconnected entanglement entropy as a marker of edge modes in a periodically driven Kitaev chain
• Theory of Anomalous Floquet Higher-Order Topology: Classification, Characterization, and Bulk-Boundary Correspondence
• Local and energy-resolved topological invariants for Floquet systems
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• Distinct Floquet topological classifications from color-decorated frequency lattices with space-time symmetries
• Floquet chiral hinge modes and their interplay with Weyl physics in a three-dimensional lattice
• Josephson current signature of Floquet Majorana and topological accidental zero modes in altermagnet heterostructures
• Quantum phase transitions and a disorder-based filter in a Floquet system
• Topological excitations at time vortices in periodically driven systems
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• Majorana modes in trapped-ion system and their Floquet engineering
• Floquet Amorphous Topological Orders in a One-dimensional Rydberg Glass
• Dynamical Chiral Symmetry and Symmetry-Class Conversion in Floquet Topological Insulators
• Designing nontrivial one-dimensional Floquet topological phases using a spin-1/2 double-kicked rotor
• Characterizing Floquet topological phases by quench dynamics: A multiple-subsystem approach
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• Topological hybrid semimetal phases and anomalous Hall effects in a three dimensional magnetic topological insulator
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• Steering edge currents through a Floquet topological insulator
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