Weyl Geometry in Weyl Semimetals

TL;DR

This paper explores how vacancies in Weyl semimetals induce a geometric gauge field related to non-metricity, affecting their conductivity and possibly modifying the chiral magnetic effect.

Contribution

It introduces a geometric interpretation of vacancy-induced effects in Weyl semimetals, linking non-metricity to emergent gauge fields and their influence on physical phenomena.

Findings

Vacancies induce a magnetic-like geometric field in Weyl semimetals.

The geometric gauge field relates to non-metricity caused by vacancies.

Vacancies can influence the chiral magnetic effect.

Abstract

A novel oscillatory behaviour of the DC conductivity in Weyl semimetals with vacancies has recently been identified, occurring in the absence of external magnetic fields. Here, we argue that this effect has a geometric interpretation in terms of a magnetic-like field induced by an emergent Weyl connection. This geometric gauge field is related to the non-metricity of the underlying effective geometry, which is physically induced by vacancies in the lattice system. Finally, we postulate that the chiral magnetic effect in Weyl semimetals can be affected by the presence of dynamical vacancies.