  We compute the QCD phase diagram in the plane of the chiral chemical
potential and temperature using the linear sigma model coupled to quarks and to
the Polyakov loop. The chiral chemical potential accounts for effects of
imbalanced chirality due to QCD sphaleron transitions which may emerge in
heavy-ion collisions. We found three effects caused by the chiral chemical
potential: the imbalanced chirality (i) tightens the link between deconfinement
and chiral phase transitions; (ii) lowers the common critical temperature;
(iii) strengthens the order of the phase transition by converting the crossover
into the strong first order phase transition passing via the second order
end-point. Since the fermionic determinant with the chiral chemical potential
has no sign problem, the chirally imbalanced QCD matter can be studied in
numerical lattice simulations.
