Synthesizing exotic topological states of matter by periodic driving

Periodic driving has become one useful and versatile tool in quantum engineering. In this talk, I will report that interesting nonequilibrium quantum phase transitions (QPTs) can be synthesized by engineering the formation of midgap bound state in Floquet quasienergy spectrum using periodic driving. I will clarify this idea by two examples. One example is to induce more colorful topological QPT in one-dimensional Kitaev model. A tunable number of topologically protected Majorana modes are generated in Kitaev model by a well-designed periodic driving, which may supply a novel way to identify the formation of the Majorana modes in the system. The other example is to induce large-Chern-number topological insulator phases in two-dimensional two-band model. The topological insulator phases with large and widely tunable Chern numbers can be triggered by periodic driving, which is exemplified in Haldane model. Our approach may lift experimental difficulties in material fabrication to realize the large-Chern-number topological phases.