Bound state, phase separation and superconductivity in presence of Rashba spin-orbit coupling

We have investigated the phase diagram for the t−J model at low electronic densities in presence of Rashba spin-orbit coupling (RSOC). We have rigorously derived a bound state criterion which arises out of a competition between the kinetic energy of the electrons and the exchange coupling between them. Further, we have obtained that the phase diagram consists of three phases, namely, a gas of electrons, a gas of bound pairs, and a fully phase separated state. Subsequently an extension of the pairing scenario is done at finite densities by solving a BCS gap equation. Finite superconducting correlations are observed for J values much lower than that required for the formation of a single bound pair, thereby indicating that pairing in a many particle environment requires weaker interaction strengths than that in the dilute case. We have further obtained that the RSOC increases the transition temperature for a p-wave pairing state, while it diminishes the same for an s-wave pairing correlations.