Magneto-optical conductivity in the type-I and type-II phases of Weyl/multi-Weyl semimetals

Abstract

Magneto-optical conductivity is a very widely studied transport coefficient, useful to understand and characterize the behaviour of materials under magnetic fields. Using the Kubo formula, we compute the components of the conductivity tensor σμν transverse to a uniform magnetic field B, for a single node of a multi-Weyl semimetal (with monopole charge J equal to two or three). We also include the results for a Weyl semimetal (with J=1), and identify peaks in the conductivity profile which were not reported in earlier studies. In our analysis, we explore how the tilting of the Weyl/multi-Weyl cone affects σμν, focussing on both type-I and type-II phases. All these systems have a linear-in-momentum dispersion along the tilting axis, which is chosen to align with B. In the type-II phases, open Fermi pockets appear as artifacts of the low-energy effective continuum models, which ignore higher-order momentum terms of the actual bandstructures. Hence, we supplement the linear power term with a cubic term, which closes the Fermi pockets, thus eliminating any need for an ad hoc cutoff for the momentum integrals. Our results reveal that the absorptive parts of σμν display multiple peaks as functions of the frequency, whose locations are determined by an energy scale ∼|B|J/2.