Josephson current in low-dimensional proximity systems and the field effect

The system S_α-M_β-S_γ (S_α and S_γ are superconductors, M_β is a semiconductor, a semimetal, or a normal metal) is studied. Particular attention is paid to the case when M_β contains a two-dimensional electron gas (e.g., an inversion layer). A one-dimensional (1D) case is also considered. The Josephson current is evaluated and the main factors determining the field effect are studied. A special diagrammatic method allowing one to calculate the thermodynamic Green's function and, consequently, the Josephson current, has been developed. The current depends strongly on the electron concentration which leads to a noticeable field effect. The dependence of jₘ on other factors, such as temperature, mobility, effect mass, etc. is also studied. The field effect appears to be stronger for low-dimensional systems. An analysis of the experimental data obtained recently for the Nb-InAs-Nb system is carried out.