Abstract
A gauge invariant effective lagrangian for the fermion axial anomaly is constructed. The dynamical degree of freedom for fermion field is preserved. Using the anomaly lagrangian, the scattering cross section of pair production γγ → e−e+ in Dirac or Weyl semimetal is computed. The result is compared with the corresponding result from Dirac lagrangian. It is found that anomaly lagrangain and Dirac lagrangian exhibit the same E ⋅ B pattern, therefore the E ⋅ B signature may not serve a good indicator of the existence of axial anomaly. Because anomaly generates excessive right-handed electrons and positrons, pair production can give rise to spin current by applying gate voltage and charge current with depositing spin filters. These experiments are able to discern genuine anomaly phenomena.
Highlights
Axial anomaly[1,2], sometimes referred to as chiral anomaly in proper context, arises from the non-invariance of fermion measure under axial γ5 transformation[3], it is a generic property of quantum fermion field theory, massive or massless
This approach leaves very little room for the study of electron transport properties as the degree of freedom for electron has been frozen out. It is the purpose of this work to construct an effective lagrangian which describes the axial anomaly in a fermion system, and keep the fermion field dynamical
The axial anomaly can be considered as a source generating axial current
Summary
A gauge invariant effective lagrangian for the fermion axial anomaly is constructed. The dynamical degree of freedom for fermion field is preserved. Previous studies used Chern-Simons term[6] to construct an effective lagrangian for axial anomaly in Weyl semimetals by integrating out the fermion degree of freedom, and treats the fermion field as a mean field of the background. The residual Chern-Simons term exhibits E ⋅ B form and is used to argue that it is a signature of axial anomaly in condensed matter This approach leaves very little room for the study of electron transport properties as the degree of freedom for electron has been frozen out. It is the purpose of this work to construct an effective lagrangian which describes the axial anomaly in a fermion system, and keep the fermion field dynamical. Such an effective lagrangian which contains dynamical fermion field, it is easy to account for the effect of anomaly while keeping fermion dynamics explicit
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