Multiple Andreev reflections as a transport problem in energy space

TL;DR

This paper introduces a novel approach to analyze dc current in voltage-biased superconducting junctions by mapping multi-particle processes to wave transport problems, revealing the relation between resonances and subgap structures.

Contribution

It presents a method to analyze multiple Andreev reflections as a transport problem in energy space, applicable to general SXS-junctions with arbitrary non-superconducting regions.

Findings

Only processes creating real excitations contribute at zero temperature.

The n-particle current maps onto wave transport through n-barrier structures.

Resonances in these structures relate to subgap features in the I-V characteristics.

Abstract

We present an approach for analyzing the dc current in voltage biased quantum superconducting junctions. By separating terms from different $n$-particle processes, we find that the $n$-particle current can be mapped on the problem of wave transport through a potential structure with $n$ barriers. We discuss the relation between resonances in such structures and the subgap structures in the current-voltage characteristics. At zero temperature we find, exactly, that only processes creating real excitations contribute to the current. Our results are valid for a general SXS-junction, where the X-region is an arbitrary non-superconducting region described by an energy-dependent transfer matrix.