Regularization of a massless Dirac model to describe anomalous electromagnetic response of Weyl semimetals

TL;DR

This paper addresses the inconsistency in the Dirac model for Weyl semimetals' electromagnetic response by redefining operators to include quantum anomaly effects, enabling accurate description of the chiral magnetic and anomalous Hall effects.

Contribution

It introduces a regularization method for the Dirac model that incorporates quantum anomaly contributions, resolving previous inconsistencies in electromagnetic response predictions.

Findings

Redefinition of current and charge operators to include anomaly contributions.

Proper description of CME and AHE using the regularized Dirac model.

Clarification that CME results from a balance between anomaly and low-energy electron contributions.

Abstract

An unbounded massless Dirac model with two nondegenerate Dirac cones is the simplest model for Weyl semimetals, which show the anomalous electromagnetic response of chiral magnetic effect (CME) and anomalous Hall effect (AHE). However, if this model is naively used to analyze the electromagnetic response within a linear response theory, it gives the result apparently inconsistent with the persuasive prediction based on a lattice model. We show that this serious difficulty is related to the breaking of current conservation in the Dirac model due to quantum anomaly and can be removed if current and charge operators are redefined to include the contribution from the anomaly. We demonstrate that the CME as well as the AHE can be properly described using newly defined operators, and clarify that the CME is determined by the competition between the contribution from the anomaly and that from low-energy electrons.