Self-consistent scattering description of transport in normal-superconductor structures

TL;DR

This paper develops a scattering theory for transport in normal-superconductor structures, highlighting how self-consistency and current conservation influence transport regimes, quasiparticle thresholds, and conductance features, especially under non-negligible superconductor currents.

Contribution

It introduces a self-consistent scattering framework that captures the impact of superconductor current on transport properties, revealing new regimes and effects not accounted for in previous models.

Findings

Identification of voltage ranges with only Andreev transmission

Discovery of gapless superconductivity at high voltages at low temperatures

Shift of conductance peaks due to current conservation effects

Abstract

We present a scattering description of transport in several normal-superconductor structures. We show that the related requirements of self-consistency and current conservation introduce qualitative changes in the transport behavior when the current in the superconductor is not negligible. The energy thresholds for quasiparticle propagation in the superconductor are sensitive to the existence of condensate flow ($v_s\neq 0$). This dependence is responsible for a rich variety of transport regimes, including a voltage range in which only Andreev transmission is possible at the interfaces, and a state of gapless superconductivity which may survive up to high voltages if temperature is low. The two main effects of current conservation are a shift towards lower voltages of the first peak in the differential conductance and an enhancement of current caused by the greater availability of charge transmitting scattering channels.