Superconducting pairing of spin polarons in the t-J model

The pairing of quasiparticles in a CuO$_2$ plane is studied within a spin polaron formulation of the $t$-$t^{'}$-$J$ model. Our numerical solution of the Eliashberg equations unambiguously shows d-wave pairing between spin polarons on different sublattices mediated by the exchange of spin-fluctuations, and a strong doping dependence of the quasiparticle bandwidth. The transition temperature $T_c$ is an increasing function of $J/t$ and crosses a maximum at an optimal doping concentration $\delta_{opt}$. For the t-J model with $J/t=0.4$ we obtain $T_c\simeq 0.013 t$ at $\delta_{opt}\simeq 0.2$.