Inducing and controlling superconductivity in Hubbard honeycomb model using an electromagnetic drive

The recent successful experimental observation of quantum anomalous Hall effect in graphene under laser irradiation demonstrates the feasibility of controlling single-particle band structure by lasers. Here we study superconductivity in a Hubbard honeycomb model in the presence of an electromagnetic drive. We start with the Hubbard honeycomb model in the presence of an electromagnetic field drive; both, (a) circularly and (b) linearly polarized light, and map it onto a Floquet t-J model. We study the Floquet t-J model within the mean-field theory in the singlet pairing channel and explore superconductivity for small doping in the system using the Bogoliubov-de Gennes approach. We uncover several superconducting phases, which break lattice or time-reversal symmetries. We show that the unconventional chiral SC order parameter (d+id) can be driven to a nematic SC order parameter (s+d) in the presence of a circularly polarized light. We further show that the three-fold nematic degeneracy can be lifted using linearly polarized light. Our work, therefore, provides a generic framework for inducing and controlling SC in the Hubbard honeycomb model, with possible application to graphene and other two-dimensional materials.