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