Axion-like Quasiparticles and Topological States of Matter: Finite Density Corrections of the Chiral Anomaly Vertex
arxiv(2024)
摘要
We investigate the general structure of the chiral anomaly AVV/AAA and
(LLL, RRR) vertices, in the presence of chemical potentials in perturbation
theory. The study finds application in anomalous transport, whenever chirally
unbalanced matter is present, with propagating external currents that are
classically conserved. Examples are topological materials and the chiral
magnetic effect in the plasma state of matter of the early universe. We
classify the minimal number of form factors of the AVV parameterization, by a
complete analysis of the Schouten identities in the presence of a heat bath. We
show that the longitudinal (anomaly) sector in the axial-vector channel, for
on-shell and off-shell photons, is protected against corrections coming from
the insertion of a chemical potential in the fermion loop. When the photons are
on-shell, we prove that also the transverse sector, in the same channel, is
μ-independent and vanishes. The related effective action is shown to be
always described by the exchange of a massless anomaly pole, as in the case of
vanishing chemical potentials. The pole is interpreted as an interpolating
axion-like quasiparticle generated by the anomaly. In each axial-vector
channel, it is predicted to be a correlated fermion/antifermion pseudoscalar
(axion-like) quasiparticle appearing in the response function, once the
material is subjected to an external chiral perturbation. The cancellation of
the μ dependence extends to any chiral current within the Standard Model,
including examples like B (baryon), L (lepton), and B-L. This holds true
irrespective of whether these currents exhibit anomalies.
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