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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 Hubbard honeycomb model in the presence of an electromagnetic field drive, both circularly and linearly polarized light and map it onto a Floquet $t$-$J$ model. We explore conditions on the drive under which one can induce superconductivity (SC) in the system. 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 in addition to the standard $U(1)$ symmetry. We show that the unconventional chiral SC order parameter ($d \pm id$) can be driven to a nematic SC order parameter ($s+d$) in the presence of a circularly polarized light. The $d+id$ SC order parameter breaks time reversal symmetry and is topologically nontrivial, and supports chiral edge modes. 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.