HAMILTONIAN APPROACH TO THE TRANSPORT-PROPERTIES OF SUPERCONDUCTING QUANTUM POINT

A microscopic theory of the transport properties of quantum point cont acts giving a unified description of the normal conductor-superconduct or (N-S) and superconductor-superconductor (S-S) cases is presented. I t is based on a model Hamiltonian describing charge transfer processes in the contact region and makes use of nonequilibrium Green function techniques for the calculation of the relevant quantities. It is expli citly shown that when calculations are performed up to infinite order in the coupling between the electrodes, the theory contains all known results predicted by the more usual scattering approach for N-S and S- S contacts. For the latter we introduce a specific formulation for dea ling with the nonstationary transport properties. An efficient algorit hm is developed for obtaining the de and ac current components, which allows a detailed analysis of the different current-voltage characteri stics for all range of parameters. We finally address the less underst ood small bias limit, for which some analytical results can be obtaine d within the present formalism. It is shown that four different physic al regimes can be reached in this limit depending on the values of the inelastic scattering rate and the contact transmission. The behavior of the system in these regimes is discussed together with the conditio ns for their experimental observability.