  In this thesis we study short Josephson junctions which include a region with
Rashba spin-orbit coupling effect. Our junctions consists of two
superconductors (S) and a 2-dimensional electron gas (2DEG) layer between them:
S/2DEG/S junction. We also include two thin insulating interfaces between the
superconductors and the 2DEG, which are capable of both normal and spin-flip
scattering. The junctions we study are assumed to be in the ballistic limit and
so, we do not consider the effects of impurities. The basic equations we use
for our model are the Bogoliubov-de Gennes equations. We give particular
emphasis in the relation between the supercurrent of the junction as a function
of difference of the phase parameters of the two superconductors. We study
thoroughly how this relation differs to the change of the junction's length,
the spin-orbit coupling constant, the normal scattering strength and the
spin-flip scattering strength and direction. We are also interested in the
0-$\pi$ transition and the second harmonic appearance, as well as the
symmetries which occur in the current-phase relation, for different geometries
of the two spin-flip interfaces. In addition, we show how the Critical current
of our junction is affected to the change of the above parameters and under
which conditions it is optimized. Finally, we study the supercurrent flowing at
zero phase difference (ZPC) of the two superconductors. We emphasize the
conditions under which it is non-zero and also examine the cases it becomes
maximized.

Superconductivity;Mesoscale and Nanoscale Physics