Josephson and Andreev transport through quantum dots

Abstract

Esta es la versión de autor del artículo publicado en: This is an author produced version of a paper published in:Advances in Physics 60.6 (2011): 899-958 DOI: http://dx.doi.org/10.1080/00018732.2011.624266 Copyright: © 2011 Taylor & FrancisEl acceso a la versión del editor puede requerir la suscripción del recurso Access to the published version may require subscription Josephson and Andreev transport through quantum dotsA. Martín-Rodero and A. Levy Yeyati Departamento de Física Teórica de la Materia Condensada C-05 Universidad Autónoma de Madrid, E-28049; Madrid, SpainIn 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 π-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. Contents VII. Concluding remarks 36Acknowledgements 37References 37 I. INTRODUCTIONThe field of electronic transport in nanoscale devices is experiencing a fast evolution driven both by advances in fabrication techniques and by the interest in potential applications like spintronics or quantum information processing. Within this context quantum dot (QD) systems are playing a central role. These devices have several different physical realizations including semiconducting heterostructures, small metallic particles, carbon nanotubes or other molecules connected to metallic electrodes. In spite of this variety a very attractive feature of these devices is that they can usually be described theoretically by simple "universal-like" models characterized by a few parameters. In addition to their potential applications, these systems provide a unique test-bed for analyzing the interplay of electronic correlations and transport properties in nonequilibrium conditions. Electron transport in semiconducting QDs has been studied since the early 90's when phenomena like Coulomb blockade (CB) was first observed (Kastner, 1993). It soon became clear that QDs could all...

Subgap features due to quasiparticle tunneling in quantum dots coupled to superconducting leads

“…In order to observe the Josephson effect and Andreev reflections, the theory must be extended to higher order perturbation theory. 20,22 …”

“…(22). Further we assume that the leads have so many degrees of freedom that they stay in thermal equilibrium up to a correction 155439-3 of orderĤ T .…”

Nonequilibrium transport through a Josephson quantum dot

“…[16][17][18][19][20][21][22][23][28][29][30][31][32][34][35][36]38 As later on we will mainly consider regimes in which the Kondo effect does not develop, we do not describe the details of these physics. Beautiful spectroscopic data [49][50][51][52][53] triggered much current effort to study the parameter dependencies of the energy of the Andreev bound states (ABS) 1,35,37 which mainly carry the current.…”

“…In the case in which the dots charging energy or equivalently the local Coulomb repulsion U vanishes, the Josephson current, MAR as well as the AC Josephson effect are well understood and all parameter dependencies can straightforwardly be computed. 1,2,4,12,13,15 In MAR, an electron passing the dot gains an energy of V > 0 and is then reflected at the superconductor as a hole which once more aquires an energy of V as it passes the dot. Then the hole is reflected and the process starts again with an electron.…”

“…For example, the interplay between the superconducting gap ∆ and the Coulomb energy triggers for V = 0 and T = 0 a first order level-crossing quantum phase transition between a singlet and a doublet phase. 1 The phase boundary can be crossed by variation of the two-particle interaction U , the superconducting phase difference φ, and the dot level energy. In the context of bulk superconductors with magnetic impurities this phase transition was revealed and qualitatively understood already decades ago.…”