Magneto-conductivity of Weyl semimetals: the roles of inter-valley scattering and high-order Feynman diagrams

Abstract

Within the theoretical framework of Kubo formula and self-consistent Born approximation, we theoretically study the transversal and longitudinal magneto-conductivity of a type-I Weyl semimetal. We focus mainly on the peculiar role of inter-valley scattering on linear transversal magnetoresistance (LTMR) and negative longitudinal magnetoresistance (NLMR). At first, we find that the contributions of high-order Feynman diagrams to the transversal magneto-conductivity play the distinct roles between the cases of intra- and inter-valley scatterings. The former suppresses the transversal conductivity whereas the latter enhances it. Then, with the increase of scattering strength, the LTMR is destroyed, accompanying a sizable increase of transversal conductivity, in particular, in the case of the tilted cone. For longitudinal magneto-transport, inter-valley scattering contributes only trivial magnetoresistance. In contrast, intra-valley scattering is invalid for longitudinal magneto-transport which means a very large NLMR. In addition, the high-order Feynman diagrams always play the nontrivial role on the longitudinal conductivity even in the weak scattering limit. Finally, when altering the Fermi energy among low-lying Landau level, the peaks of transversal conductivity just correspond to the valleys of the longitudinal conductivity.