Novel electric field effects on Landau levels in multi- Weyl semimetals

Multi-Weyl semimetals(WSMs) have an anisotropic non-linear dispersion along a 2-D plane and a linear dispersion in an orthogonal direction. They have topological charge $\mathrm{‘}n$’ and are created when two or multiple Weyl points or nodes with nonzero net monopole charge are brought together onto a high-symmetry point. We study the perturbation corrections up to second order of such multi-WSMs in crossed electric($\mathcal{E}$) and magnetic (B) fields in the low electric field approximation. As a result, the first order correction lifts only n-fold degeneracy of the lowest Landau levels(LLs) while the higher Landau levels are modified due to the second order perturbation. We study the signatures of these corrections due to electric fields on the density of states (DOS) subjected to a magnetic field.