Photoinduced tunable anomalous Hall and Nernst effects in tilted Weyl semimetals using Floquet theory

Abstract

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 A0 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 A0 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 2 0 . 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.Weyl Semimetals (WSMs) have been identified as materials with nontrivial topological structure having a variety of physical properties stemming from a Hamiltonian possessing a gapless spectrum with at least one of the time reversal and inversion symmetries broken [1][2][3][4]. The minimal model, obtained by breaking time reversal symmetry, consists of a Dirac-like dispersion around two distinct points in the first Brillouin zone, where the conduction and the valence bands touch. These Weyl points or Weyl nodes are topological charges acting as a source or a sink for Berry curvature [2, 5, 6], as reflected by their occurrence in opposite chirality pairs, and by contrast, the inversion symmetry breaking minimal model requires four Weyl points [1, 4]. Such materials, classed as type-I WSMs, exhibit a number of phenomena including chiral magnetic waves [7], chiral anomaly induced plasmon modes [8], and chirality induced negative magneto resistance [9]. The addition of a SO(3,1) symmetry breaking term to the low energy Hamiltonian coupled to the momentum leads to a tilt in the dispersion. For sufficiently large tilts, it can be shown [1, 10] that a Lifshitz phase transition occurs, leading to a new phase i.e. type-II WSMs, with different physical properties. Type-I WSMs have a single Fermi surface, whereas in type-II WSMs, the Fermi surface splits into two, one each for electrons and holes, such that the density of states at each Weyl points is finite. Reports on the experimental realizations of type-I Weyl semimetals have been presented in [11, 12], * Electronic address: amenon@ucdavis.edu † Electronic address: debashreephys@g...

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