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In this paper, we discuss the effect of a periodically driving circularlypolarized laser beam in the high frequency limit, on the band structure andthermal transport properties of type-I and type-II Weyl semimetals (WSMs). Wedevelop the notion of an effective Fermi surface stemming from thetime-averaged Floquet Hamiltonian and discuss its effects on the steady-stateoccupation numbers of electrons and holes in the linearized model. In order tocompute the transport coefficients averaged over a period of the incident lasersource, we employ the Kubo formalism for Floquet states and show that the Kuboformula for the conductivity tensor retains its well known form with thedifference that the eigenstates and energies are replaced by the Floquet statesand their quasi-energies. We find that for type-I WSMs the anomalous thermalHall conductivity grows quadratically with the amplitude $A_{0}$ of the U(1)gauge field for low tilt, while the Nernst conductivity remains unaffected. Fortype-II WSMs, the Hall conductivity decreases non-linearly with $A_{0}$ due tothe contribution from the physical momentum cutoff, required to keep finiteelectron and hole pocket sizes, and the Nernst conductivity falls oflogarithmically with $A_{0}^2$. These results may serve as a diagnostic formaterial characterization and transport parameter tunability in WSMs, which arecurrently the subject of a wide range of experiments.

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