Magnetization energy current in the axial magnetic effect

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