Axion response in Weyl semimetals

TL;DR

This paper demonstrates that the electromagnetic response of Weyl semimetals includes a $ heta$-term identical to that of relativistic chiral fermions, confirming the full analogy despite previous doubts.

Contribution

The authors explicitly derive the $ heta$-term for a microscopic Weyl semimetal model, establishing its equivalence to the relativistic case.

Findings

The $ heta$-term in Weyl semimetals matches the relativistic form.

The analogy between solid state Weyl fermions and quantum field theory holds fully.

The derivation confirms the presence of the $ heta$-term in microscopic models.

Abstract

Weyl semimetal is a new phase of matter that provides the first solid state realization of chiral Weyl fermions. Most of its unique physics is a consequence of chiral anomaly, namely nonconservation of the number of particles of a given chirality. Mathematically, this is expressed in the appearance of the so called $\theta$-term in the action of the electromagnetic field, when the Weyl fermions are integrated out. Recently, however, it has been suggested that the analogy between the chiral fermions of quantum field theory with unbounded linear dispersion, and their solid state realization with a dispersion naturally bounded by the bandwidth and crystal momentum defined only within the first Brillouin zone, holds only in a restricted sense, with parts of the $\theta$-term absent. Here we demonstrate that this is not the case. We explicitly derive the $\theta$-term for a microscopic model of a Weyl semimetal by integrating out fermions coupled to electromagnetic field, and show that the result has exactly the same form as in the case of relativistic chiral fermions.