Disentangling signatures of Floquet topological systems*

Floquet theory helps us find steady state solutions to the time dependent Schrodinger equation when the Hamiltonian is periodic in time. By defining the quasi energy spectrum and quasi energy states one can identify topological features like edge modes and non-zero topological invariants. In some cases, a system which is non-topological at equilibrium becomes topological when a time-periodic perturbation is applied. In this work we take a close look at these non-equilibrium topological states which are induced by the periodic perturbation and characterize their response functions. We find that the splitting into side bands can be seen in transport and suppress the ability to carry current. For example, in a 2D Floquet topological insulator attached to metallic leads at equilibrium the measured conductivity is not quantized although the system exhibits edge modes. This is due to the fact that the edge modes are split into many side bands and the overlap with the lead states at a particular energy reflects the splitting. Nevertheless, the current is carried only by edge modes and is therefore robust against weak perturbations. For certain cases like equilibrium leads or a sudden turn on of the periodic perturbation it is possible to calculate the strength of each side band and predict the transport properties. Results for DC and AC transport in driven systems will be presented.