Inverse Faraday effect in massive Dirac electrons

We study the inverse Faraday effect (IFE) in a Dirac Hamiltonian with random impurities using Keldysh formalism and diagrammatic perturbation theory. The mass term in the Dirac Hamiltonian is essential for IFE, where the spin magnetic moment induced by circularly polarized light is proportional to the frequency of the incident light within the THz regime. For massive Dirac electrons, the corrections due to short-range impurities on spin magnetic moment vertex exhibits mixing of the spin magnetic moment vertex and spin angular momentum vertex. The spin magnetic density response is divergently enhanced by the vertex corrections near the band edge, indicting a long-range diffusion of spin density profile in massive Dirac electrons.