Static-hole energies in thet-Jmodel and at-J-ε model of the high-temperature superconductors

We present Monte Carlo results for the energies of static holes in the t-J model. We consider the cases of zero, one, two, and four holes on square lattices of side L=4, 6, and 8 and extrapolate these results to give estimates for the bulk limit. We find that the hole energies and finite-size effects are in good agreement with spin-wave theory. Our results are consistent with phase separation in the static limit of the t-J model, but indicate that the incorporation of long-range Coulomb repulsion between holes prevents phase separation. We find that hole pairs alone are bound for a certain range of dielectric constant ε, which is 52<ε<104 in the static limit of a t-J-ε model with 1/r Coulomb repulsion, given the currently accepted value of J. The large observed value of the in-plane dielectric constant of ${\mathrm{La}}_2$ ${\mathrm{CuO}}_4$, ε=30±3, is not far from the lower limit of this theoretical pairing range, so the t-J-ε model may provide a useful approximate description of the mechanism of hole pairing in the high-temperature superconductors. Hole Cooper pairs that act as mediators of high-temperature superconductivity may thus arise from a competition between the large antiferromagnetic coupling J, which encourages hole clustering, and the ε-suppressed hole Coulomb repulsion, which restricts hole binding to pairs.