Superconductivity phenomenon induced by external in-plane magnetic field in (2+1)-dimensional Gross--Neveu type model

Understand

Phase structure of the (2+1)-dimensional model with four-fermion interaction of spin-1/2 quasiparticles (electrons) both in the fermion-antifermion (or chiral) and fermion-fermion (or superconducting) channels is considered at nonzero chemical potential $\mu$ and under the influence of an in-plane, i.e.

• parallel to a system sheet, external magnetic field $\vec B_\parallel$.
• It is shown that at sufficiently large values of $\mu$ and/or $\vec B_\parallel$ the Cooper pairing (or superconducting) phase appears in the system at arbitrary relation between coupling constants, provided that there is an (arbitrary small) attractive interaction in the superconducting channel.
• In particular, at sufficiently weak attractive interaction in the chiral channel, the Cooper pairing occurs even at infinitesimal values of $\mu$ and/or $\vec B_\parallel$.