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

## TL;DR

This paper demonstrates that tilted Weyl cones significantly enhance conductivity, with a covariant Boltzmann approach accurately describing anisotropic transport properties and diverging conductivities at critical tilt parameters.

## Contribution

It introduces a covariant quantum Boltzmann framework for tilted Weyl semimetals and graphene, revealing anisotropic conductivity behavior and divergence at the transition between type-I and type-II phases.

## Key findings

- Conductivity becomes highly anisotropic with increasing tilt.
- Perpendicular conductivity diverges as tilt approaches critical value in 2D.
- Both conductivities diverge in 3D Weyl semimetals at the transition point.

## Abstract

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 increase of the tilt parameter $\eta$, which can be interpreted as the boost parameter of a Lorentz transformation. While the ratio between the two conductivities is $\sqrt{1-\eta^2}$ in the two-dimensional case where only the conductivity perpendicular to the tilt direction diverges for $\eta\rightarrow 1$, both conductivities diverge in three-dimensional Weyl semimetals, where $\eta=1$ separates a type-I (for $\eta<1$) from a type-II Weyl semimetal (for $\eta>1$).