  The effects of chiral imbalance and external magnetic field on pion
superfluidity and color superconductivity are investigated in extended
Nambu--Jona-Lasinio models. We take Schwinger approach to treat the interaction
between charged pion condensate and magnetic field at finite isospin density
and include simultaneously the chiral imbalance and magnetic field at finite
baryon density. For the superfluidity, the chiral imbalance and magnetic field
lead to catalysis and inverse catalysis effects, respectively. For the
superconductivity, the chiral imbalance enhances the critical baryon density,
and the magnetic field results in a de Haas--van Alphan oscillation on the
phase transition line.
