Josephson and Andreev transport through quantum dots

TL;DR

This review discusses the theoretical understanding of transport phenomena in quantum dots connected to superconducting and normal leads, highlighting key physical effects, methods, and recent extensions to complex systems.

Contribution

It provides a comprehensive overview of theoretical models and methods for quantum dot transport, including recent advances in multi-dot and multi-terminal systems.

Findings

Analysis of competition between pairing and Kondo effects

Identification of -junction behavior

Insights into Andreev bound states and their spectral role

Abstract

In this article we review the state of the art on the transport properties of quantum dot systems connected to superconducting and normal electrodes. The review is mainly focused on the theoretical achievements although a summary of the most relevant experimental results is also given. A large part of the discussion is devoted to the single level Anderson type models generalized to include superconductivity in the leads, which already contains most of the interesting physical phenomena. Particular attention is paid to the competition between pairing and Kondo correlations, the emergence of \pi-junction behavior, the interplay of Andreev and resonant tunneling, and the important role of Andreev bound states which characterized the spectral properties of most of these systems. We give technical details on the several different analytical and numerical methods which have been developed for describing these properties. We further discuss the recent theoretical efforts devoted to extend this analysis to more complex situations like multidot, multilevel or multiterminal configurations in which novel phenomena is expected to emerge. These include control of the localized spin states by a Josephson current and also the possibility of creating entangled electron pairs by means of non-local Andreev processes.