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

Abstract.

A presence of a Meissner-Ochsenfeld effect in a gas of spin 1/2 fermions with an interaction $V_4 = -\vert\Lambda\vert^{-1}\sum\limits_{{\bf k},{\bf k}'}g_{{\bf k},{\bf k}'}b_{{\bf k}}^* b_{-{\bf k}}^* b_{{\bf k}'}b_{-{\bf k}'}$, where $\vert\Lambda\vert$ is a volume of a region $\Lambda$ in real space which is taken by thesystem and $b_{{\bf k}} = a_{{\bf k} + }a_{{\bf k}-}$ with $a_{{\bf k}\sigma}$, $a_{{\bf k}'\sigma'}^*$ 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 $\lambda$ of external magnetic field. V ₄ is nonzero only within a thin layer of 1-fermion energies around the chemical potential μ.