Axions and Superfluidity in Weyl Semimetals

TL;DR

This paper develops an effective field theory predicting a dynamical axion mode in Weyl semimetals, linking superfluidity, chiral symmetry breaking, and the axial anomaly, with potential experimental implications.

Contribution

It introduces a novel EFT framework for dynamical axions in Weyl semimetals, connecting superfluidity and axial anomaly effects in a unified model.

Findings

Prediction of a pseudoscalar axion excitation in WSMs at low temperatures.

Identification of axion as a Goldstone boson or collective mode depending on coupling strength.

Verification of 't Hooft anomaly matching within the EFT framework.

Abstract

An effective field theory (EFT) for dynamical axions in Weyl semimetals (WSMs) is presented. A pseudoscalar axion excitation is predicted in WSMs at sufficiently low temperatures, independently of the strength of the Weyl fermion self-coupling. For strong fermion self-coupling the axion is the gapless Goldstone boson of chiral $U(1)^{\text{ch}}$ spontaneous symmetry breaking. For weak fermion self-coupling an axion is also generated at non-zero chiral density for Weyl nodes displaced in energy, as a gapless collective mode of correlated fermion pair excitations of the Fermi surface. This is an explicit example of the extension of Goldstone's theorem to symmetry breaking by the axial anomaly itself. In both cases the axion is a chiral density wave or phason mode of the superfluid state of the WSM, and the Weyl fermions form a chiral condensate $\langle\bar{\psi}\psi\rangle$ at low temperatures. In the presence of an applied magnetic field the axion mode becomes gapped, in analogy to the Anderson-Higgs mechanism in a superconductor. 't Hooft anomaly matching from ultraviolet to infrared scales is directly verified in the EFT approach. WSMs thus provide an interesting quantum system in which superfluid, non-Fermi liquid behavior, and a dynamical axion are predicted to follow directly from the axial anomaly in a consistent EFT that may be tested experimentally.