Enhancement of Superconducting $T_c$ due to the Spin-orbit Interaction

We calculate the superconducting $T_c$ for a system which experiences Rashba spin-orbit interactions. Contrary to the usual case where the electron-electron interaction is assumed to be wave vector-independent, where superconductivity is suppressed by the spin-orbit interaction (except for a small region at low electron or hole densities), we find an enhancement of the superconducting transition temperature when we include a correlated hopping interaction between electrons. This interaction originates in the expansion of atomic orbitals due to electron-electron repulsion and gives rise to superconductivity only at high electron (low hole) densities. When superconductivity results from this interaction it is enhanced by spin-orbit coupling, in spite of a suppression of the density of states. The degree of electron-hole asymmetry about the Fermi surface is also enhanced.