Conductances in normal and normal-superconductor structures

TL;DR

This paper explores the concept of conductance in normal-superconductor interfaces, revealing multiple definitions and their dependence on chemical potential choices, challenging traditional interpretations of Andreev reflection effects.

Contribution

It introduces multiple conductance definitions for NS interfaces and analyzes their physical implications, offering a new perspective on the standard conductance value of 2.

Findings

Multiple conductance definitions depend on chemical potential choices.

The standard conductance of 2 is linked to specific chemical potential selection.

An alternative conductance diverges in the transmissive limit due to Andreev reflection limitations.

Abstract

We study theoretically electronic transport through a normal metal-- superconductor (NS) interface and show that more than one conductance may be defined, depending on the pair of chemical potentials whose difference one chooses to relate linearly to the current. We argue that the situation is analogous to that found for purely normal transport, where different conductance formulae can be invoked. We revisit the problem of the "right" conductance formula in a simple language, and analyze its extension to the case of mesoscopic superconductivity. The well-known result that the standard conductance of a NS interface becomes 2 (in units of $2e^2/h$) in the transmissive limit, is viewed here in a different light. We show that it is not directly related to the presence of Andreev reflection, but rather to a particular choice of chemical potentials. This value of 2 is measurable because only one single-contact resistance is involved in a typical experimental setup, in contrast with the purely normal case, where two of them intervene. We introduce an alternative NS conductance that diverges in the transmissive limit due to the inability of Andreev reflection to generate a voltage drop. We illustrate numerically how different choices of chemical potential can yield widely differing I--V curves for a given NS interface.