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The recent successful experimental observation of quantum anomalous Halleffect in graphene under laser irradiation demonstrates the feasibility ofcontrolling single particle band structure by lasers. Here we studysuperconductivity in a Hubbard honeycomb model in the presence of anelectromagnetic drive. We start with Hubbard honeycomb model in the presence ofan electromagnetic field drive, both circularly and linearly polarized lightand map it onto a Floquet $t$-$J$ model. We explore conditions on the driveunder which one can induce superconductivity (SC) in the system. We study theFloquet $t$-$J$ model within the mean-field theory in the singlet pairingchannel and explore superconductivity for small doping in the system using theBogoliubov-de Gennes approach. We uncover several superconducting phases, whichbreak lattice or time reversal symmetries in addition to the standard $U(1)$symmetry. We show that the unconventional chiral SC order parameter ($d \pmid$) can be driven to a nematic SC order parameter ($s+d$) in the presence of acircularly polarized light. The $d+id$ SC order parameter breaks time reversalsymmetry and is topologically nontrivial, and supports chiral edge modes. Wefurther show that the three-fold nematic degeneracy can be lifted usinglinearly polarized light. Our work, therefore, provides a generic framework forinducing and controlling SC in the Hubbard honeycomb model, with possibleapplication to graphene and other two-dimensional materials.

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