Universal driving protocol for symmetry-protected Floquet topological phases

Abstract

Universal driving protocol for symmetry-protected Floquet topological phasesWe propose a universal driving protocol for the realization of symmetry-protected topological phases in $2+1$ dimensional Floquet systems. Our proposal is based on the theoretical analysis of the possible symmetries of a square lattice model with pairwise nearest-neighbor coupling terms. Among the eight possible symmetry operators we identify the two relevant choices for topological phases with either time-reversal, chiral, or particle-hole symmetry. From the corresponding symmetry conditions on the protocol parameters, we obtain the universal driving protocol where each of the symmetries can be realized or broken individually. We provide specific parameter values for the different cases, and demonstrate the existence of symmetry-protected copropagating and counterpropagating topological boundary states. The driving protocol especially allows us to switch between bosonic and fermionic time-reversal symmetry, and thus between a trivial and non-trivial symmetry-protected topological phase, through continuous variation of a parameter.

arXiv comment15 pages, 15 figures

References in corpus (30)

• Topological Insulators
• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Topological Insulators in Three Dimensions
• Topological Photonics
• Topological Photonics
• Photonic Floquet Topological Insulators
• Floquet Topological Insulator in Semiconductor Quantum Wells
• Observation of Floquet-Bloch states on the surface of a topological insulator
• Topological characterization of periodically-driven quantum systems
• Transport properties of non-equilibrium systems under the application of light: Photo-induced quantum Hall insulators without Landau levels
• Time Reversal Polarization and a Z_2 Adiabatic Spin Pump
• Observation of photonic anomalous Floquet Topological Insulators
• Experimental reconstruction of the Berry curvature in a topological Bloch band
• Experimental observation of anomalous topological edge modes in a slowly-driven photonic lattice
• Periodic Table for Floquet Topological Insulators
• Topological singularities and the general classification of Floquet-Bloch systems
• Quantum spin Hall effect in three dimensional materials: Lattice computation of Z${}_2$ topological invariants and its application to Bi and Sb
• Topological invariants of Floquet systems: General formulation, special properties, and Floquet topological defects
• Topological index for periodically driven time-reversal invariant 2D systems
• Counter-propagating edge modes and topological phases of a kicked quantum Hall system
• Complex classes of periodically driven topological lattice systems
• Topological Effects in Chiral Symmetric Driven Systems
• Universal sign-control of coupling in tight-binding lattices
• Floquet interface states in illuminated three-dimensional topological insulators
• Scattering matrix invariants of Floquet topological insulators
• Floquet edge states in a harmonically driven integer quantum Hall system
• Topological invariants for Floquet-Bloch systems with chiral, time-reversal, or particle-hole symmetry
• Floquet Quantum Spin Hall Insulator in Cold Atomic Systems
• Efficient computation of the $W_3$ topological invariant and application to Floquet-Bloch systems

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• Realization of Anomalous Floquet Insulators in Strongly-Coupled Nanophotonic Lattices
• Non-Hermitian Pseudo-Gaps
• Non-Hermitian Boundary State Engineering in Anomalous Floquet Topological Insulators
• Topological origin of quantized transport in non-Hermitian Floquet chains
• Counter-propagating edge states in Floquet topological insulating phases
• Unconventional Floquet topological phases from quantum engineering of band inversion surfaces
• Stability of topologically protected edge states in nonlinear quantum walks: Additional bifurcations unique to Floquet systems
• Cutting off the non-Hermitian boundary from an anomalous Floquet topological insulator
• Characterizing Floquet topological phases by quench dynamics: A multiple-subsystem approach
• Controlling the direction of topological transport in a non-Hermitian time-reversal symmetric Floquet ladder
• Quantized charge transport in disordered Floquet topological insulators in the absence of Anderson localization
• Real and imaginary edge states in stacked Floquet honeycomb lattices
• Immutable quantized transport in Floquet chains