A comparative study on the influence of intra- and inter-valley scattering to Hall conductivity of Dirac semimetals

Abstract

Within the theoretical framework of Kubo linear response theory as well as the self-consistent Born approximation(SCBA), we perform a comparative study about the Hall conductivities of a Dirac semimetal(DSM) subject to, respectively, the intra- and inter-valley scattering. By calculating the Hall conductivity as a function of Fermi level, we find that when the Fermi level lies in the region around the Dirac node, the Hall conductivities between the two cases, i.e. subject to intra- and inter-valley scattering respectively, do not show appreciable difference, regardless of the scattering strength. As the Fermi level goes away from the Dirac node, the Hall conductivity in the case of inter-valley scattering is smaller than that in the case of intra-valley scattering if the scattering has relatively weak or moderate strength. In contrast, as scattering strength increases further, the Hall conductivity spectra between the two cases look almost identical no matter whether the Fermi level is close to or far away from the Dirac node. The underlying physics of these numerical results is that the Fermi surface has nontrivial contribution to the Hall conductivity in the case of weak or moderate scattering. However, in the case of strong scattering, it becomes much smaller than the contribution arising from all the occupied states. In addition, our study indicates that the cone tilt brings about the effective enhancement of Hall conductivity of DSMs.