Edge State Transport in Floquet Topological Insulators

Abstract: Floquet topological insulators are systems in which the topology emerges out of equilibrium when a time periodic perturbation is applied. In these systems one can define quasi-energy states which replace the quilibrium stationary states. The system exhibits its non-trivial topology by developing edge localized quasi-energy states which lie in a gap of the quasi energy spectrum. These states represent a non-equilibrium analogue of the topologically protected edge-states in equilibrium topological insulators. In equilibrium these edge-states lead to very specific transport properties, in particular the two-terminal conductivity of these systems is $2e^2/h$. 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 scattering by photons. This leads us to consider a previously proposed Floquet sum rule which recovers the equilibrium value of $2e^2/h$ for the conductivity when edge states are present. We show that this sum rule holds in our system using both numerical and analytic techniques.