Hamiltonian approach to the transport properties of superconducting quantum point contacts

TLDR

The authors present a microscopic theory that unifies the transport properties of normal‑conductor–superconductor and superconductor–superconductor quantum point contacts, introduces a formulation for nonstationary transport, and analytically addresses the small‑bias limit. The theory employs a Hamiltonian model of charge transfer and nonequilibrium Green‑function techniques, and includes an efficient algorithm for computing dc and ac current components to analyze current‑voltage characteristics across all parameter ranges, including nonstationary transport. The model reproduces all known scattering‑approach results when expanded to infinite order and reveals four distinct regimes in the small‑bias limit determined by inelastic scattering rate and transmission, with their behaviors and experimental observability conditions discussed. © 1996 The American Physical Society.

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 nonequilibrium 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 nonstationary 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. \textcopyright{} 1996 The American Physical Society.