Topological index for periodically driven time-reversal invariant 2D systems

Abstract

We define a new $Z_2$-valued index to characterize the topological properties of periodically driven two dimensional crystals when the time-reversal symmetry is enforced. This index is associated with a spectral gap of the evolution operator over one period of time. When two such gaps are present, the Kane-Mele index of the eigenstates with eigenvalues between the gaps is recovered as the difference of the gap indices. This leads to an expression for the Kane-Mele invariant in terms of the Wess-Zumino amplitude. We illustrate the relation of the new index to the edge states in finite geometries by numerically solving an explicit model on the square lattice that is periodically driven in a time-reversal invariant way.

5 pages, 3 figures

References in corpus (11)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Topological Insulators with Inversion Symmetry
• Photonic Analogue of Two-dimensional Topological Insulators and Helical One-Way Edge Transport in Bi-Anisotropic Metamaterials
• Topological characterization of periodically-driven quantum systems
• Quantum Spin Hall Effect and Topologically Invariant Chern Numbers
• Non-Abelian gauge fields and topological insulators in shaken optical lattices
• Photoinduced transition between conventional and topological insulators in two-dimensional electronic systems
• Symmetries, Topological Phases and Bound States in the One-Dimensional Quantum Walk
• Floquet Edge States with Ultracold Atoms
• Dynamics of tunneling into nonequilibrium edge states

Cited by in corpus (24)

• Topological Photonics
• Out of equilibrium electrons and the Hall conductance of a Floquet topological insulator
• Topological invariants of Floquet systems: General formulation, special properties, and Floquet topological defects
• Floquet Topological Order in Interacting Systems of Bosons and Fermions
• Bimorphic Floquet Topological Insulators
• Floquet Semimetal with Floquet-band Holonomy
• Floquet Engineering of Haldane Chern Insulators and Chiral bosonic phase transitions
• Measurement of spin Chern numbers in quantum simulated topological insulators
• Construction and properties of a topological index for periodically driven time-reversal invariant 2D crystals
• Topology and localization of a periodically driven Kitaev model
• Topological invariants for Floquet-Bloch systems with chiral, time-reversal, or particle-hole symmetry
• Universal driving protocol for symmetry-protected Floquet topological phases
• Floquet exceptional contours in Lindblad dynamics with time-periodic drive and dissipation
• Dynamical control of electron-phonon interactions with high-frequency light
• Topological Floquet states on a Möbius band irradiated by circularly polarised light
• Three dimensional two-band Floquet topological insulator with $Z_2$ index
• Extrinsic topology of Floquet anomalous boundary states in quantum walks
• Dynamical decoupling for realization of topological frequency conversion
• Floquet engineering of edge states in the presence of staggered potential and interactions
• Cosine Edge Mode in a Periodically Driven Quantum System
• Interband coherence induced correction to Thouless pumping: possible observation in cold-atom systems
• Immutable quantized transport in Floquet chains
• Digital Quantum Simulation of Floquet Topological Phases with a Solid-State Quantum Simulator
• Orbital magnetization of Floquet topological systems