  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.
