Topological invariants for Floquet-Bloch systems with chiral, time-reversal, or particle-hole symmetry

Abstract

We introduce ${\mathbb{Z}}_2$-valued bulk invariants for symmetry-protected topological phases in $2+1$ dimensional driven quantum systems. These invariants adapt the $W_3$-invariant, expressed as a sum over degeneracy points of the propagator, to the respective symmetry class of the Floquet-Bloch Hamiltonian. The bulk-boundary correspondence that holds for each invariant relates a non-zero value of the bulk invariant to the existence of symmetry-protected topological boundary states. To demonstrate this correspondence we apply our invariants to a chiral Harper, time-reversal Kane-Mele, and particle-hole symmetric graphene model with periodic driving, where they successfully predict the appearance of boundary states that exist despite the trivial topological character of the Floquet bands. Especially for particle-hole symmetry, combination of the $W_3$ and the ${\mathbb{Z}}_2$-invariants allows us to distinguish between weak and strong topological phases.

arXiv comment12 pages, 9 figures. Final version as published

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• Universal driving protocol for symmetry-protected Floquet topological phases
• Electronic transport in one-dimensional Floquet topological insulators via topological and nontopological edge states
• Periodic and aperiodic dynamics of flat bands in diamond-octagon lattice
• Driven Hofstadter Butterflies and Related Topological Invariants
• Tuning of Bilayer Graphene Heterostructure by Horizontally Incident Circular Polarized Light
• Floquet states of Valley-Polarized Metal with One-way Spin or Charge Transport in Zigzag Nanoribbons
• Cutting off the non-Hermitian boundary from an anomalous Floquet topological insulator
• Computing Floquet Hamiltonians with Symmetries
• Optically Induced Topological Phase Transition in two dimensional Square Lattice Antiferromagnet
• Quantized charge transport in disordered Floquet topological insulators in the absence of Anderson localization
• Localized Floquet states in gated bilayer graphene induced by a focused optical beam with orbital angular momentum
• Immutable quantized transport in Floquet chains