Scattering matrix approach to the description of quantum electron transport

TL;DR

This paper reviews the scattering matrix approach for quantum electron transport, highlighting its advantages in analyzing coherent mesoscopic conductors, including current, noise, and full counting statistics, with applications to superconducting contacts.

Contribution

It introduces the scattering matrix method as an efficient and transparent alternative to traditional approaches for analyzing quantum transport in meso- and nano-conductors, including superconducting systems.

Findings

Provides a comprehensive description of time-averaged transport properties.

Analyzes current fluctuations and noise characteristics.

Extends the approach to superconducting contacts and Josephson junctions.

Abstract

We consider the scattering matrix approach to quantum electron transport in meso- and nano-conductors. This approach is an alternative to the more conventional kinetic equation and Green's function approaches, and often is more efficient for coherent conductors (especially for proving general relations) and typically more transparent. We provide a description of both time-averaged quantities (for example, current-voltage characteristics) and current fluctuations in time -- noise, as well as full counting statistics of charge transport in a finite time. In addition to normal conductors, we consider contacts with superconductors and Josephson junctions.