Transport phenomena of multi-Weyl semimetals in co-planar setups

Tanay Nag, Snehasish Nandy

Published 2018-12-20Version 1

The chiral anomaly induced magneto-transport phenomena has been extensively studied in single Weyl semimetal ($n=1$), transport properties for multi-Weyl semimetals (m-WSMs) with $n>1$ (i.e., topological charge larger than one) so far have not been studied. Using semiclassical Boltzmann transport formalism with the relaxation time approximation, we investigate several intriguing transport properties such as longitudinal magneto-conductivity (LMC), planar Hall effect (PHE), thermo-electric coefficients (TEC) and planar Nernst coefficient (PNE) in m-WSMs considering coplanar magnetic field and electric field or temperature gradient setup. Starting from the linearized model, we show analytically that at zero temperature both LMC and planar Hall conductivity (PHC) vary cubically with topological charge ($n^3$) while the finite temperature ($T \neq 0$) correction is proportional to $(n+n^2)T^2$. Interestingly, we find that both the longitudinal and transverse TECs vary quadratically with topological charge (i.e., $n^2$). We find universal magnetic field and angular dependencies of all the above transport coefficients. Moreover, in order to verify the analytical findings, we simultaneously investigate their behavior with magnetic field, angle, temperature and chemical potential numerically using the lattice model for m-WSMs. Our analysis with temperature and chemical potential suggests that the chiral anomaly and chiral magnetic effect terms dominate in the transverse part of electrical conductivity and TEC, respectively, while Drude contribution becomes significant for the longitudinal coefficients. We comment also on the possible lattice effects for the deviation of numerical results from the analytical one.