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 <InlineEquation ID="Equ1"> <EquationSource Format="TEX">$V_4=-\vert\Lambda\vert^{-1}\sum\limits_{{\bf k},{\bf k}'}g_{{\bf k},{\bf k}'}b_{{\bf k}}^* b_{-{\bf k}}^* b_{{\bf k}'}b_{-{\bf k}'}$</EquationSource> </InlineEquation>, where <InlineEquation ID="Equ2"> <EquationSource Format="TEX">$\vert\Lambda\vert$</EquationSource> </InlineEquation> is a volume of a region <InlineEquation ID="Equ3"> <EquationSource Format="TEX">$\Lambda$</EquationSource> </InlineEquation> in real space which is taken by thesystem and <InlineEquation ID="Equ4"> <EquationSource Format="TEX">$b_{{\bf k}}=a_{{\bf k} + }a_{{\bf k}-}$</EquationSource> </InlineEquation> with <InlineEquation ID="Equ5"> <EquationSource Format="TEX">$a_{{\bf k}\sigma}$</EquationSource> </InlineEquation>, <InlineEquation ID="Equ6"> <EquationSource Format="TEX">$a_{{\bf k}'\sigma'}^*$</EquationSource> </InlineEquation> 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 <InlineEquation ID="Equ7"> <EquationSource Format="TEX">$\lambda$</EquationSource> </InlineEquation> of external magnetic field. V <Subscript>4</Subscript> is nonzero only within a thin layer of 1-fermion energies around the chemical potential μ. Copyright Springer-Verlag Berlin/Heidelberg 2004