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We report on a mean-field study of spontaneous breaking of chiral symmetryfor Dirac fermions with contact interactions in the presence of chiralimbalance, which is modelled by nonzero chiral chemical potential. We point outthat chiral imbalance lowers the vacuum energy of Dirac fermions, which leadsto the increase of the renormalized chiral chemical potential upon chiralsymmetry breaking. The critical coupling strength for the transition to thebroken phase is slightly lowered as the chiral chemical potential is increased,and the transition itself becomes milder. Furthermore, we study the chiralmagnetic conductivity in different phases and find that it grows both in theperturbative weak-coupling regime and in the strongly coupled phase with brokenchiral symmetry. In the strong coupling regime the chiral magnetic effect issaturated by vector-like bound states (vector mesons) with mixed transversepolarizations. General pattern of meson mixing in the presence of chiralimbalance is also considered. We discuss the relevance of our study for Weylsemimetals and strongly interacting QCD matter. Finally, we comment on theambiguity of the regularization of the vacuum energy of Dirac fermions in thepresence of chirality imbalance.

Spontaneous chiral symmetry breaking and the Chiral Magnetic Effect for interacting Dirac fermions with chiral imbalance