Anomalous DC Hall response in noncentrosymmetric tilted Weyl semimetals

Abstract

Weyl nodes come in pairs of opposite chirality. For broken time reversal symmetry (TR) they are displaced in momentum space by $\bf{Q}$ and the anomalous DC Hall conductivity $\sigma_{xy}$ is proportional to $\bf{Q}$ at charge neutrality. For finite doping there are additive corrections to $\sigma_{xy}$ which depend on the chemical potential as well as on the tilt ($C$) of the Dirac cones and on their relative orientation. If inversion symmetry (I) is also broken the Weyl nodes are shifted in energy by an amount $Q_{0}$. This introduces further changes in $\sigma_{xy}$ and we provide simple analytic formulas for these modifications for both type I ($C<1$) and type II ($C>1$, overtilted) Weyl. For type I when the Weyl nodes have equal magnitude but oppositely directed tilts, the correction to $\sigma_{xy}$ is proportional to the chemical potential $\mu$ and completely independent of the energy shift $Q_{0}$. When instead the tilts are parallel, the correction is linear in $Q_{0}$ and $\mu$ drops out. For type II the corrections involve both $\mu$ and $Q_{0}$, are nonlinear and also involve a momentum cut off. We discuss the implied changes to the Nernst coefficient and to the thermal Hall effect of a finite $Q_{0}$.