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

Magneto-optical conductivity is a very widely studied transport coefficient to understand and characterize the behaviour of materials. In this paper, we compute this magneto-optical response for an isolated node of a multi-Weyl semimetal (with monopole charge $J$ equal to two or three), using the Kubo formula. We employ the low energy effective Hamiltonian in the continuum limit, and consider both the type-I and type-II phases. For the type-II phase, instead of using just a linear dispersion along the tilting direction, we supplement it with a cubic term, which eliminates the need to impose ad hoc momentum/energy cutoffs, while evaluating the integrals involved in the calculations. Our results show that in the absorption spectrum, the optical response shows peaks, with the $n^{\text{th}}$ peak appearing at a frequency value proportional to $ B^{J/2} \left (\sqrt{ ^{n+1}P_J } + \sqrt{ ^nP_J } \right )$, where $B$ is the magnitude of the applied magnetic field. This feature holds for all values of tilt and irrespective of the type of multi-Weyl semimetal under consideration. But the density of peaks increase as we transition from type-I phase to type-II phase, due to the appearance of secondary peaks. This is caused by the fact that there are higher number of allowed intraband scatterings in the type-II phase than in the type-I phase, which results from over-tilting.Comment: 9 pages, 6 figure