Competition and duality correspondence between chiral and superconducting channels in (2+1)-dimensional four-fermion models with fermion number and chiral chemical potentials

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.