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

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 $μ$ 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 $μ$ 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 $μ$ and/or $\vec B_\parallel$. The superconducting phase of the model is always a paramagnetic one.