Reduction of Electron Repulsion and Enhancement of T_{c} in Small Diffusive Superconducting Grains.

The superconducting properties of small metallic grains has been a topic of active research for half a century now. Early experiments demonstrated a remarkable rise in the critical temperature, T_{c}, with reducing grain size in a variety of materials. In two-dimensional diffusive superconductors, T_{c} is decreased due to enhanced Coulomb repulsion. We propose that in finite-size grains the diffusive enhancement of the Coulomb repulsion is weakened and leads ultimately to an increase in T_{c} in isolated, disordered two-dimensional grains. Our mechanism is superimposed on the possible enhancement in T_{c} due to the change in the density of states of finite-size systems.