The approach applicable for spatially inhomogeneous and time-dependent problems associated with the induced superconductivity in low dimensional electronic systems is developed. This approach is based on the Fano--Anderson model which describes the decay of a resonance state coupled to a continuum. We consider two types of junctions made of a ballistic 2D electron gas placed in a tunnel finite-length contact with a bulk superconducting leads. We calculate the spectrum of the bound states, supercurrent, and the current-voltage curve which show a rich structure due to the presence of induced gap and dimensional quantization.
@article{arxiv.1105.1903,
title = {Induced superconductivity in 2D electronic systems},
author = {N. B. Kopnin and A. S. Melnikov},
journal= {arXiv preprint arXiv:1105.1903},
year = {2011}
}