Scattering theory of superconductive tunneling in quantum junctions

TL;DR

This paper develops a scattering-based theory for superconductive tunneling in quantum junctions, explaining Josephson effects, quasiparticle transport, and subgap currents with a focus on inelastic scattering and Andreev states.

Contribution

It introduces a unified scattering formulation for both elastic and inelastic quasiparticle processes in superconducting junctions, advancing understanding of tunneling phenomena.

Findings

Derived a general expression for inelastic scattering amplitudes.

Calculated quasiparticle current across all voltages.

Clarified the role of Andreev bound states in Josephson transport.

Abstract

We present a consistent theory of superconductive tunneling in single-mode junctions within a scattering formulation of Bogoliubov-de Gennes quantum mechanics. Both dc Josephson effect and dc quasiparticle transport in voltage biased junctions are considered. Elastic quasiparticle scattering by the junction determines equilibrium Josephson current. We discuss the origin of Andreev bound states in tunnel junctions and their role in equilibrium Josephson transport. In contrast, quasiparticle tunneling in voltage biased junctions is determined by inelastic scattering. We derive a general expression for inelastic scattering amplitudes and calculate the quasiparticle current at all voltages with emphasis on a discussion of the properties of subgap tunnel current and the nature of subharmonic gap structure.