  In this paper the duality correspondence between fermion-antifermion and
difermion interaction channels is established in two (2+1)-dimensional
Gross-Neveu type models with a fermion number chemical potential $\mu$ and a
chiral chemical potential $\mu_5$. The role and influence of this property on
the phase structure of the models are investigated. In particular, it is shown
that the chemical potential $\mu_5$ promotes the appearance of dynamical chiral
symmetry breaking, whereas the chemical potential $\mu$ contributes to the
emergence of superconductivity.
