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In this thesis we study short Josephson junctions which include a region withRashba spin-orbit coupling effect. Our junctions consists of twosuperconductors (S) and a 2-dimensional electron gas (2DEG) layer between them:S/2DEG/S junction. We also include two thin insulating interfaces between thesuperconductors and the 2DEG, which are capable of both normal and spin-flipscattering. The junctions we study are assumed to be in the ballistic limit andso, we do not consider the effects of impurities. The basic equations we usefor our model are the Bogoliubov-de Gennes equations. We give particularemphasis in the relation between the supercurrent of the junction as a functionof difference of the phase parameters of the two superconductors. We studythoroughly how this relation differs to the change of the junction's length,the spin-orbit coupling constant, the normal scattering strength and thespin-flip scattering strength and direction. We are also interested in the0-$\pi$ transition and the second harmonic appearance, as well as thesymmetries which occur in the current-phase relation, for different geometriesof the two spin-flip interfaces. In addition, we show how the Critical currentof our junction is affected to the change of the above parameters and underwhich conditions it is optimized. Finally, we study the supercurrent flowing atzero phase difference (ZPC) of the two superconductors. We emphasize theconditions under which it is non-zero and also examine the cases it becomesmaximized.

Josephson junctions with spin-orbit and spin-flip interactions