Tilted disordered Weyl semimetals

TL;DR

This paper studies how tilting in Weyl semimetals affects the disorder-driven phase transition, revealing that tilt reduces the critical disorder needed for the transition and obscures the Lifshitz transition to type-II Weyl phases.

Contribution

It provides a combined analytical and numerical analysis of tilt effects on disorder-induced phase transitions in Weyl semimetals, highlighting the suppression of the Lifshitz transition.

Findings

Tilt reduces the critical disorder strength for the phase transition.

Increasing tilt drives the system into a diffusive phase at lower disorder.

Tilt obscures the Lifshitz transition to type-II Weyl phases at finite disorder.

Abstract

Although Lorentz invariance forbids the presence of a term that tilts the energy-momentum relation in the Weyl Hamiltonian, a tilted dispersion is not forbidden and, in fact, generic for condensed matter realizations of Weyl semimetals. We here investigate the combined effect of such a tilted Weyl dispersion and the presence of potential disorder. In particular, we address the influence of a tilt on the disorder-induced phase transition between a quasi-ballistic phase at weak disorder, in which the disorder is an irrelevant perturbation, and a diffusive phase at strong disorder. Our main result is that the presence of a tilt leads to a reduction of the critical disorder strength for this transition or, equivalently, that increasing the tilt at fixed disorder strength drives the system through the phase transition to the diffusive strong-disorder phase. Notably this obscures the tilt induced Lifshitz transition to an over tilted type-II Weyl phase at any finite disorder strength. Our results are supported by analytical calculations using the self-consistent Born approximation and numerical calculations of the density of states and of transport properties.