Chiral gauge field and axial anomaly in a Weyl semimetal

TLDR

Weyl fermions are two‑component chiral fermions in (3+1) dimensions that exhibit an axial anomaly when coupled to a gauge field, and they have recently been proposed in condensed‑matter systems known as Weyl semimetals. The authors propose a Weyl semimetal phase in magnetically doped topological insulators and aim to study the axial anomaly in this system. They model the magnetic fluctuations as a chiral gauge field that couples minimally to Weyl fermions with opposite charges for the two chiralities. The anomaly equation is derived and its physical consequences are discussed, revealing one‑dimensional chiral modes along ferromagnetic vortex lines and a novel plasmon‑magnon coupling.

Abstract

Weyl fermions are two-component chiral fermions in $(3+1)$ dimensions. When coupled to a gauge field, the Weyl fermion is known to have an axial anomaly, which means the current conservation of the left-handed and right-handed Weyl fermions cannot be preserved separately. Recently, Weyl fermions have been proposed in condensed-matter systems named ``Weyl semimetals.'' In this paper we propose a Weyl semimetal phase in magnetically doped topological insulators, and study the axial anomaly in this system. We propose that the magnetic fluctuation in this system plays the role of a ``chiral gauge field'' which minimally couples to the Weyl fermions with opposite charges for two chiralities. We study the anomaly equation of this system and discuss its physical consequences, including one-dimensional chiral modes in a ferromagnetic vortex line, and a novel plasmon-magnon coupling.