Anomalous transport model with axial magnetic fields

The transport properties of massless fermions in spacetime dimension have been in the focus of recent theoretical and experimental research. New transport properties appear as consequences of chiral anomalies. The most prominent is the generation of a current in a magnetic field, the so-called chiral magnetic effect leading to an enhancement of the electric conductivity (negative magnetoresistivity). We study the analogous effect for axial magnetic fields that couple with opposite signs to fermions of different chirality. We emphasize local charge conservation and study the induced magneto-conductivities proportional to an electric field and a gradient in temperature. We find that the magnetoconductivity is enhanced whereas the magneto-thermoelectric conductivity is diminished. As a side result we interpret an anomalous contribution to the entropy current as a generalized thermal Hall effectThe research of K.L. has been supported by FPA2015-65480-P and by the Centro de Excelencia Severo Ochoa Programme under grant SEV-2012-0249 and SEV-2016-0597. The research of Y.L. has been supported by the Thousand Young Talents Program of China and grants ZG216S17A5 and KG12003301 from Beihang Universit