Anomal transport in spin-orbit and Weyl systems- normally explained

A quantum kinetic theory is developed for interacting systems with spin-orbit coupling and electric and magnetic fields. Using a linear spin-orbit coupling, As special cases, graphene and Weyl systems can be realized as infinite-mass limit. These systems possess chiral symmetry where quantum fluctuations cause an anomaly. This has been recently observed in Weyl systems and is frequently interpreted as caused by gravitational anomaly. It is demonstrated that this anomaly arises from the quantum kinetic equations not violating conservation laws. The inter-, intraband conductivities and anomalous Hall effects of graphene are calculated and compared with the experimental values. For large Zeeman fields the dynamical conductivities become independent of the density and are universal. The density and pseudospin response functions to an external electric field show a frequency and wave-vector range where the dielectric function changes sign and the repulsive Coulomb potential becomes effectively attractive allowing for Cooper pairing. New modes due to magnetic fields and spin-orbit coupling are found and terahertz out-of plane resonances are predicted.

[1] spin-orbit transport:
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Phys. Rev. B 92 (2015) 245425 errata: Phys. Rev. B93 (2016)239904(E),
Phys. Rev. B 92 (2015) 245426
[2] graphene:
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[3] anomaly:
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Phys. Lett. A 383 (2019) 1362, arXiv:2004.01507