Fermion self-energy in magnetized chirally asymmetric QED matter

The fermion self-energy is calculated for a cold QED plasma with chiral chemical potential in a magnetic field. It is found that a momentum shift parameter dynamically generated in such a plasma leads to a modification of the chiral magnetic effect current. It is argued that the momentum shift parameter can be relevant for the evolution of magnetic field in the chirally asymmetric primordial plasma in the early Universe.