Topology and Transport in Periodically Driven Systems

One way to introduce topological phases in certain systems is periodic driving. For example, an 1D p-wave superconductor, driven periodically, can go through a Floquet transition to become topologically non-trivial. Such Floquet topological superconductor can host exotic steady states, which are called Floquet Majorana fermions. Whereas, graphene, under the application of circularly polarized laser is an example of Floquet topological insulator. Such topological insulators, like the quantum-hall systems, have non-trivial topology and chiral edge states. Such systems present potential applications to various fields from quantum computation to valleytronics. In this talk I\'ll present our recent works on topological classification and some novel transport characteristics of such driven systems.