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. 
D. Ebert, T.G. Khunjua, K.G. Klimenko, and V.C. Zhukovsky
hep-th hep-ph