Large enhancement of conductivity in Weyl semimetals with tilted cones: Pseudorelativity and linear response

We study the conductivity of two-dimensional graphene-type materials with tilted cones as well as their three-dimensional Weyl counterparts and show that a covariant quantum Boltzmann equation is capable of providing an accurate description of these materials' transport properties. The validity of the covariant Boltzmann approach is corroborated by calculations within the Kubo formula. We find a strong anisotropy in the conductivities parallel and perpendicular to the tilt direction upon an increase of the tilt parameter η, which can be interpreted as the boost parameter of a Lorentz transformation. While the ratio between the two conductivities is √1−η2 in the two-dimensional case where only the conductivity perpendicular to the tilt direction diverges for η→1, both conductivities diverge in three-dimensional Weyl semimetals, where η=1 separates a type-I (for η<1) from a type-II Weyl semimetal (for η>1).