Topological properties of photon-mediated interacting fermions in the presence of honeycomb optical lattice.

We study the effect of cavity-induced long-range interactions and laser-induced tunneling on the topological properties of fermions subjected to an optical lattice. We integrate out the bosonic degrees of freedom and use a mean-field theory to develop an effective fermionic Hamiltonian. Further, treating the attractive onsite interaction using a mean-field level, we study the band structure to investigate the topological properties of the system. We categorize the topological features by calculating the Chern number.