On the Meissner effect in a superconductor with 4-fermion attraction

A presence of a Meissner-Ochsenfeld effect in a gas of spin 1/2 fermions with an interaction $V_4=-|\Lambda|^{-1}\sum\limits_{{\bf k},{\bf k}'}g_{{\bf k},{\bf k}'}b_{{\bf k}}^\ast b_{-{\bf k}}^\ast b_{{\bf k}'}b_{-{\bf k}'}$, where $|\Lambda|$ is a volume of a region Λ in real space which is taken by the system and $b_{{\bf k}}=a_{{\bf k}+}a_{{\bf k}-}$ with $a_{{\bf k}\sigma}$, $a_{{\bf k}'\sigma'}^\ast$ satisfying Fermi anticommutation relations, is investigated. The effect proves to be weaker than in BCS by a factor 3/4 at T=0, implying a greater penetration depth λ of external magnetic field. V4 is nonzero only within a thin layer of 1-fermion energies around the chemical potential μ