Finite-momentum instability of a dynamical axion insulator

Abstract

Due to the chiral anomaly, Weyl semimetals can exhibit a signature topological magnetoelectric response known as an axion term which is determined by the microscopic band structure. In the presence of strong interactions Weyl fermions may form a chiral condensate, with the intrinsic dynamics and fluctuations of the associated condensate phase producing a dynamical contribution to the axion response. Here we show that an imbalance in the density of right- and left-handed electrons drives an instability of the chiral condensate towards finite momentum and leads to strong fluctuations in the axion response. We derive a long-wavelength theory of Lifschitz type governing the dynamics of the Goldstone mode and use this to characterize its associated spatial fluctuations, which manifest as an inhomogeneous anomalous Hall effect. We show that these fluctuations produce signatures in inelastic light-scattering experiments across a broad spectrum of frequencies, and can be used to determine the structure factor for the axionic collective mode.