BCS theory with the external pair potential

We consider a hypothetical substance, where interaction between (within) structural elements of condensed matter (molecules, nanoparticles, clusters, layers, wires etc.) depends on state of Cooper pairs: an additional work must be made against this interaction to break a pair. Such a system can be described by BCS Hamiltonian with the external pair potential term. In this model the potential essentially renormalizes the order parameter: if the pairing lowers energy of the structure the energy gap is slightly enlarged at zero temperature and asymptotically tends to zero as temperature rises. Thus the critical temperature of such a superconductor is equal to infinity formally. For this case the effective Ginzburg-Landau theory is formulated, where the coherence length decreases as temperature rises, the GL parameter and the second critical field are increasing functions of temperature unlike the standard theory. If the pairing enlarges energy of the structure then suppression of superconductivity and the first order phase transition occur.