Edge-state transport in Floquet topological insulators

Floquet topological insulators are systems in which the topology emerges only when a time-periodic perturbation is applied. In these systems one can define quasienergy states which replace the equilibrium stationary states. The system exhibits its nontrivial topology by developing edge-localized quasienergy states which lie in a gap of the quasienergy spectrum. These states represent a nonequilibrium analog of the topologically protected edge states in equilibrium topological insulators which exhibit an edge conductance of 2e(2)/h. Here we explore the transport properties of the edge states in a Floquet topological insulator. In stark contrast to the equilibrium result, we find that the two-terminal conductivity of these edge states is significantly different from 2e(2)/h. This fact notwithstanding, we find that for certain external potential strengths the conductivity is smaller than 2e(2)/h and robust to the effects of disorder and smooth changes to the Hamiltonian's parameters. This robustness is reminiscent of the robustness found in equilibrium topological insulators. We provide an intuitive understanding of the reduction of the conductivity in terms of a picture where electrons in edge states are scattered by photons. We also consider the Floquet sum rule [A. Kundu and B. Seradjeh, Phys. Rev. Lett. 111, 136402 (2013)], which was proposed in a different context. The summed conductivity recovers the equilibrium value of 2e(2)/h whenever edge states are present. We show that this sum rule holds in our system using both numerical and analytic techniques.