Interaction robustness of the chiral anomaly in Weyl semimetals and Luttinger liquids from a mixed anomaly approach

Abstract

The chiral anomaly is one of the robust quantum effects in relativistic field theories with a chiral symmetry where charges in chiral sectors appear to be separately conserved. The chiral anomaly, which is often associated with a renormalization-invariant topological term, is a violation of this conservation law due to quantum effects. Such anomalies manifest in Weyl materials as an electromagnetic field-induced transfer of charge between Fermi pockets. However, the emergent nature of the conservation of chiral charge leads to manifestations of the chiral anomaly response that depend on the details of the system such as the strength of interactions. In this paper, we apply an approach where the chiral symmetry in solid materials is replaced by the combination of charge $U(1)$ gauge and spatial translation symmetry. The chiral anomaly in this case is replaced by a mixed anomaly between the two symmetries and the chiral charge can be defined as being proportional to the total momentum. We show that the chiral anomaly associated with this chiral charge is unrenormalized by interactions in contrast to other chiral charges in $(1+1)D$ whose renormalization is regularization dependent. In $(3+1)$D Weyl systems, this chiral anomaly is equivalent to the charge transferred between Fermi surfaces which can be measured through changes in Fermi-surface-enclosed volume. We propose a pump-probe technique to measure this.

Figures (4)

• Figure 1: Illustration of the chiral anomaly in the Sine-Gordon model. The energy spectrum is sketched as two curves with an energy gap of $2m$, where $m$ is the soliton mass. In the presence of an $E$, solitons and antisolitons are generated and are shown by black dots in the top band and white dots in the bottom band, respectively. The range between two dashed lines in the middle corresponds to low-speed moving (anti)solitons. The minimum highest-level momentum of soliton pairs is labeled by $\zeta$.
• Figure 2: Schematic of a scattering pattern around the Fermi surface at finite $T$.
• Figure 3: Band structure of Weyl model ($k_0=1$) in the Sec.\ref{['sec:6d']} with a small spin-obit coupling $v=1.5$ under the magnetic field $B=0.1$. The chemical potentials are set away from the Weyl nodes, and the low energy states are basically multiply LLs.
• Figure 4: The second order conductivity $\sigma_{xy}^{(2)}$ v.s. the parameter $m$. It is not quantized and non-universal