Hole superconductivity in the dilute limit

F. Marsiglio, J.E. Hirsch, Physica C 171, 554 (1990)

We study the mechanism of hole superconductivity in the limit where the number of holes in the band goes to zero. The model describes a single band with on-site and nearest-neighbor Coulomb repulsions as well as a hopping interaction that gives rise to pairing of holes. The Schrödinger equation for a single pair of holes yields an analytic condition on the parameters to give rise to binding. In one and two dimensions this conditions coincides with the condition for non-zero Tc obtained from BCS theory in the limit where the density of holes approaches zero, while in three dimensions it is more stringent. The dependence of the pair binding energy on the parameters in the Hamiltonian is discussed. We study also the behavior of pair susceptibilities in the ladder sum approximation, which is expected to be accurate in the dilute limit. This expectation is checked by comparison between the ladder sum approximation and Monte Carlo results for the attractive Hubbard model. For the parameter regime where pairing originates in the hopping interaction, the on-site pair susceptibility is suppressed by the interactions at intermediate temperatures and only increases significantly very close to the transition temperature. In contrast, the “extended s-wave” pair susceptibility is enhanced over a large temperature range.