Electromagnetic Response of Weyl Semimetals

TL;DR

This paper constructs a lattice model of Weyl semimetals to analyze their electromagnetic response, confirming the anomalous Hall effect but finding no evidence of the chiral magnetic effect, thus clarifying theoretical discrepancies.

Contribution

It provides a minimal lattice model and combines analytical and numerical methods to study Weyl semimetals' electromagnetic responses, addressing previous theoretical debates.

Findings

Confirmed the anomalous Hall effect in Weyl semimetals.

Found the absence of the chiral magnetic effect in the model.

Clarified discrepancies between field theory predictions and lattice results.

Abstract

It has been suggested recently, based on subtle field-theoretical considerations, that the electromagnetic response of Weyl semimetals and the closely related Weyl insulators can be characterized by an axion term E.B with space and time dependent axion angle. Here we construct a minimal lattice model of the Weyl medium and study its electromagnetic response by a combination of analytical and numerical techniques. We confirm the existence of the anomalous Hall effect expected on the basis of the field theory treatment. We find, contrary to the latter, that chiral magnetic effect (that is, ground-state charge current induced by the applied magnetic field) is absent in both the semimetal and the insulator phase. We elucidate the reasons for this discrepancy.