Superconductivity Induced by the Proximity Effect of Singlet Resonating   Valence Bond Order in High-$T_c$ Superconductors
  Effects of inhomogeneous doping on the high-$T_c$ cuprate superconductors are studied within the framework of the t-J model. Especially, the boundary between two non-superconducting regions with doping rates much higher and lower than the optimal one is examined. It is found that, although there is no superconductivity in the bulk, a superconducting region appears at the boundary because singlet resonating valence bond order and holon condensation occur simultaneously in this region. The critical temperature of the induced superconductivity can be higher than that of the optimally doped sample and the critical current density can be the same order as that in the superconducting state below the critical temperature. We also point out an experimental possibility to observe this phenomenon. 
M. Hayashi and H. Ebisawa