Hamiltonian approach to the transport properties of superconducting quantum point contacts

TL;DR

This paper develops a microscopic Hamiltonian-based theory for transport in superconducting quantum point contacts, unifying normal-superconductor and superconductor-superconductor cases, and introduces an efficient algorithm for analyzing current-voltage characteristics.

Contribution

It presents a comprehensive microscopic model using non-equilibrium Green functions that reproduces known results and extends understanding of non-stationary and small bias transport regimes.

Findings

Unified description of N-S and S-S contacts.

Efficient algorithm for dc and ac current analysis.

Analytical insights into small bias regimes.

Abstract

A microscopic theory of the transport properties of quantum point contacts giving a unified description of the normal conductor- superconductor (N-S) and superconductor-superconductor (S-S) cases is presented. It is based on a model Hamiltonian describing charge transfer processes in the contact region and makes use of non-equilibrium Green function techniques for the calculation of the relevant quantities. It is explicitly 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 dealing with the non-stationary transport properties. An efficient algorithm is developed for obtaining the dc and ac current components, which allows a detailed analysis of the different current-voltage characteristics for all range of parameters. We finally address the less understood small bias limit, for which some analytical results can be obtained within the present formalism. It is shown that four different physical 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 conditions for their experimental observability.