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 [Formula: see text] and the anomalous DC Hall conductivity [Formula: see text] is proportional to [Formula: see text] at charge neutrality. For finite doping there are additive corrections to [Formula: see text] which depend on the chemical potential as well as on the tilt ([Formula: see text]) 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 [Formula: see text]. This introduces further changes in [Formula: see text] and we provide simple analytic formulas for these modifications for both type I ([Formula: see text]) and type II ([Formula: see text], overtilted) Weyl. For type I when the Weyl nodes have equal magnitude but oppositely directed tilts, the correction to [Formula: see text] is proportional to the chemical potential μ and completely independent of the energy shift [Formula: see text]. When instead the tilts are parallel, the correction is linear in [Formula: see text] and μ drops out. For type II the corrections involve both μ and [Formula: see text], 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 [Formula: see text].