Superconductivity, hole motion, and spin-charge correlations in thet-Jmodel in two dimensions

We study the ‘‘t-J’’ model with strongly correlated electrons (infinite-U Hubbard-model kinetic energy plus superexchange J) by exact diagonalization on small two-dimensional clusters of six, eight, and twelve sites on a square lattice with periodic boundary conditions. We find an attractive pairing potential for two holes when J/t≥(J/t${)}_{\mathit{c}}$≃0.2, with t the hopping matrix element. Ground-state calculations show that extended s-wave and d-wave pairing susceptibilities and equal-time pairing correlations grow weakly with increasing J and system size at fixed filling n. Pairing correlations may be enhanced for (J/t)>(J/t${)}_{\mathit{c}}$≊0.2. We compare equal-time pairing correlations to a mean-field theory for J=0 and note potential difficulties with interpreting numerical results for such small systems. The widths of one- and two-hole energy bands in low-spin states are of order J; the one-hole effective mass is larger than the two-hole effective mass in such states. Spin-charge correlation functions for a single hole in the eight- and twelve-site lattices are consistent with the spin-charge decoupling scenario for resonating-valence-bond states.