Photo-induced tunable Anomalous Hall and Nernst effects in tilted Weyl Semimetals using Floquet theory

In this paper, we discuss the effect of a periodically driving circularly polarized laser beam in the high frequency limit, on the band structure and thermal transport properties of type-I and type-II Weyl semimetals (WSMs). We develop the notion of an effective Fermi surface stemming from the time-averaged Floquet Hamiltonian and discuss its effects on the steady-state occupation numbers of electrons and holes in the linearized model. In order to compute the transport coefficients averaged over a period of the incident laser source, we employ the Kubo formalism for Floquet states and show that the Kubo formula for the conductivity tensor retains its well known form with the difference that the eigenstates and energies are replaced by the Floquet states and their quasi-energies. We find that for type-I WSMs the anomalous thermal Hall conductivity grows quadratically with the amplitude $A_{0}$ of the U(1) gauge field for low tilt, while the Nernst conductivity remains unaffected. For type-II WSMs, the Hall conductivity decreases non-linearly with $A_{0}$ due to the contribution from the physical momentum cutoff, required to keep finite electron and hole pocket sizes, and the Nernst conductivity falls of logarithmically with $A_{0}^2$. These results may serve as a diagnostic for material characterization and transport parameter tunability in WSMs, which are currently the subject of a wide range of experiments.