Symmetry Analysis of Anomalous Floquet Topological Phases

Abstract

The topological characterization of nonequilibrium topological matter is highly nontrivial because familiar approaches designed for equilibrium topological phases may not apply. In the presence of crystal symmetry, Floquet topological insulator states cannot be easily distinguished from normal insulators by a set of symmetry eigenvalues at high symmetry points in the Brillouin zone. This work advocates a physically motivated, easy-to-implement approach to enhance the symmetry analysis to distinguish between a variety of Floquet topological phases. Using a two-dimensional inversion-symmetric periodically-driven system as an example, we show that the symmetry eigenvalues for anomalous Floquet topological states, of both first-order and second-order, are the same as for normal atomic insulators. However, the topological states can be distinguished from one another and from normal insulators by inspecting the occurrence of stable symmetry inversion points in their microscopic dynamics. The analysis points to a simple picture for understanding how topological boundary states can coexist with localized bulk states in anomalous Floquet topological phases.

4+ pages of main text, plus 3 pages of supplementary material, 7 figures in total, comments welcome

References in corpus (11)

• Topological Insulators with Inversion Symmetry
• Topological characterization of periodically-driven quantum systems
• The space group classification of topological band insulators
• Bulk Topological Invariants in Noninteracting Point Group Symmetric Insulators
• Wannier representation of Z_2 topological insulators
• Building Blocks of Topological Quantum Chemistry: Elementary Band Representations
• Multiterminal Conductance of a Floquet Topological Insulator
• Measurement of a topological edge invariant in a microwave network
• Quantized Adiabatic Transport in Momentum Space
• Compactly-supported Wannier functions and algebraic $K$-theory
• Theory of Anomalous Floquet Higher-Order Topology: Classification, Characterization, and Bulk-Boundary Correspondence

Cited by in corpus (17)

• Hybrid skin-topological modes without asymmetric couplings
• Weyl nodes with higher-order topology in an optically driven nodal-line semimetal
• Floquet Weyl semimetal phases in light-irradiated higher-order topological Dirac semimetals
• Floquet higher-order Weyl and nexus semimetals
• Dynamic bulk-boundary correspondence for anomalous Floquet topology
• Floquet band engineering with Bloch oscillations
• Tailoring Quadrupole Topological Insulators with Periodic Driving and Disorder
• Generating many Majorana corner modes and multiple phase transitions in Floquet second-order topological superconductors
• Characteristic, dynamic, and near saturation regions of Out-of-time-order correlation in Floquet Ising models
• Dynamical Fragile Topology in Floquet Crystals
• Unsupervised identification of Floquet topological phase boundaries
• Gapless higher-order topology and corner states in Floquet systems
• Multiple topological transitions and spectral singularities in non-Hermitian Floquet systems
• Nonlinear signatures of Floquet band topology
• Scattering theory of higher order topological phases
• Floquet second-order topological insulator in strained graphene
• Dynamical Symmetry Indicators for Floquet Crystals