Characterization {\&} Transport Signatures of Periodically Driven Topological Phases

The discovery of the Quantum Hall Effect in the 80's opened the field of topological phases of matter, which has been renewed by the discovery of a new kind of topological insulator in 2005, this time in a time-reversal invariant system. In order to obtain a material with tunable topological properties, research were carried out on out-of-equilibrium systems subject to a periodic drive. Such periodically driven topological phases turn out to be richer that their equilibrium counterparts. We consider a 2D crystal subject to a drive periodic in time, constrained so that is is time-reversal invariant and show that such a system is characterized by Z2 indices attached to a gap (and not to a band), which we explicitly construct. To probe these out-of-equilibrium phases in a phase coherent regime, we use standard transport measurements. With the help of numerical simulations, we show that the running time-averaged differential conductances are quantized in a topological gap, and that multi-terminal setups enable to probe the chirality of the out-of-equilibrium topological states.