Magnetization energy current in the axial magnetic effect

TL;DR

This paper investigates the axial magnetic effect (AME) in relativistic and semimetal models, revealing that the AME current is mainly a magnetization energy current, not observable in transport experiments.

Contribution

It provides a numerical study of the AME in Wilson fermions and twisted Dirac semimetals, clarifying the origin of the AME current as a magnetization energy current.

Findings

AME current density is nonzero in the bulk for low-energy regimes.

Surface contributions cause the average AME current to vanish.

The AME is due to magnetization energy current, not transport phenomena.

Abstract

The axial magnetic effect (AME) is one of the anomalous transport phenomena in which the energy current is induced by an axial magnetic field. Here, we numerically study the AME for the relativistic Wilson fermion in the axial magnetic field and a twisted Dirac semimetal. The AME current density inside the bulk is nonzero, and particularly in the low-energy regime for the former model, it is explained by the field-theoretical results without any fitting parameter. However, for both models, the average AME current density vanishes owing to the surface contribution. The axial gauge field is regarded as the spatially modulated (effective) Zeeman field and induces the spatially modulated energy magnetization. The AME is attributed to the magnetization energy current and hence cannot be observed in transport experiments.