Time-dependent Gutzwiller simulation of Floquet topological superconductivity

Periodically driven systems provide a novel route to control the topology of quantum materials. In particular, Floquet theory allows an effective band description of periodically-driven systems through the Floquet Hamiltonian. Here, we study the time evolution of $d$-wave superconductors irradiated with intense circularly-polarized laser light. We consider the Floquet $t$-$J$ model with time-periodic interactions, and investigate its mean-field dynamics by formulating the time-dependent Gutzwiller approximation. We observe the development of the $id_{xy}$-wave pairing amplitude along with the original $d_{x^2-y^2}$-wave order upon gradual increasing of the field amplitude. We further numerically construct the Floquet Hamiltonian for the steady state, with which we identify the system as the fully-gapped $d+id$ superconducting phase with a nonzero Chern number. We explore the low-frequency regime where the perturbative approaches in the previous studies break down, and find that the topological gap of an experimentally-accessible size can be achieved at much lower laser intensities.