Critical currents and supercurrent oscillations in Josephson field-effect transistors

Abstract

The dc Josephson effect of a superconductor/two-dimensional electron gas/superconductor (S/2DEG/S junction in the clean limit is investigated with emphasis on the field-effect dependence of the critical current. Calculation of the Josephson current is based on solving the Bogoliubov--de Gennes equations for a steplike variation of the pair potential. In the normal conducting region, the motion of electrons is quantized in one direction by means of a triangular-well potential. The 2DEG is contained in a semiconductor treated within the effective-mass approximation. We assume an abrupt band-edge jump at the interfaces, and additional scattering is taken into account by \ensuremath{\delta}-function potential barriers. Normal scattering leads to the formation of resonant states, which are visible in critical current oscillations. The ratio of Fermi velocities in the 2DEG and the S regions determines the rates of Andreev and normal scattering and has a large influence on the field-effect dependence of the critical current. We take an effective mass suitable for the inversion layer on p-type InAs and consider Nb for the superconducting contacts. Typical magnitudes of the calculated critical current are some \ensuremath{\mu}A-per-\ensuremath{\mu}m junction width for experimentally accessible values of junction length, temperature, and surface carrier density of the 2DEG.