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Manipulating controlling topological states using time-periodic (Floquet) drives

Topological insulators and superconductors have been extensively studied in the past decade and represent a paradigm shift in our classification of matter states.  In particular, non-zero topological invariants in the bulk result in protected surface states at low energy, within the bulk gap.

In this talk I will discuss topological states out of equilibrium.  In particular, when the system is subject to a time-periodic field (such as light), Floquet theory can be used to find steady state solutions and analyze topological properties.  In some cases, a system which is non-topological in equilibrium becomes topological when a time-periodic perturbation is applied; in other cases a topological system changes its transport properties when the perturbation is applied.

We will discuss two examples - a driven two dimensional insulator and a driven one dimensional topological superconductor.  In the insulator case we find that the existence edge modes does not necessarily imply quantized conductivity.  In the superconductor case we propose braiding of Majorana fermions on a single wire, a protocol which can not be realized at equilibrium.