Two dimensional Floquet topological states in a driven graphene lattice

The study of topological phase transitions induced by external fields in quantum systems is of significant interest in physics, as it enables the exploration of various topological nontrivial phenomena in a controllable manner. This paper investigates the induced topological states of a graphene lattice subjected to an in-plane time-periodic electric field. The time-independent effective Hamiltonian in the high-frequency approximation is obtained under the Floquet theory. The results show that the graphene lattice can be turned into a chiral symmetric protection architectures by a specially designed periodic driving, which thus fulfills a topological phase transition. The topological invariant is found to confirm the transition in the corresponding nanoribbons. The controlled topological transition is impressively demonstrated by two distinct edge states in a nanosheet with different edges in two directions, achieved simply by adjusting the external field. This type of driven lattice, which can be easily realized in quantum photonics, shaken optical lattices, or other systems, provides a feasible theoretical foundation for experimental studies of the controllable topological phase of matter.