Cooper instability in the occupation dependent hopping Hamiltonians

A generic Hamiltonian, which incorporates the effect of the orbital contrac tion on the hopping amplitude between nearest sites, is studied both analyt ically at the weak coupling limit and numerically at the intermediate and s trong coupling regimes for a finite atomic cluster. The effect of the orbit al contraction due to hole localization at atomic sites is specified with t wo coupling parameters V and W (multiplicative and additive contraction ter ms). The singularity of the vertex part of the two-particle Green's functio n determines the critical temperature T-c and the relaxation rate Gamma(T) of the order parameter at temperature above T-c. Unlike the case in convent ional BCS superconductors, Gamma has a non-zero imaginary part which may in fluence the fluctuation conductivity of the superconductor above T-c. We co mpute the ground state energy as a function of the particle number and magn etic flux through the cluster, and show the existence of the parity gap Del ta appearing at the range of system parameters consistent with the appearan ce of the Cooper instability. Numeric calculation of the Hubbard model (wit h U > 0) at arbitrary occupation does not show any sign of superconductivit y in a small cluster. (C) 1999 American Institute of Physics.