  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.
