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 π-junction behavior, the interplay of Andreev and resonant tunneling, and the important role of Andreev bound states that 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.

中文翻译：

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Josephson 和 Andreev 通过量子点传输

在本文中，我们回顾了连接到超导和普通电极的量子点系统的传输特性的最新技术。综述主要集中在理论成果上，但也给出了最相关的实验结果的总结。讨论的很大一部分致力于将超导性包括在导联中的单级安德森型模型，该模型已经包含了大部分有趣的物理现象。特别关注配对和 Kondo 相关性之间的竞争、π 结行为的出现、Andreev 和共振隧穿的相互作用以及表征大多数这些系统光谱特性的 Andreev 束缚态的重要作用。我们给出了为描述这些特性而开发的几种不同分析和数值方法的技术细节。我们进一步讨论了最近致力于将这种分析扩展到更复杂的情况的理论工作，例如预计会出现新现象的多点、多级或多终端配置。这些包括通过约瑟夫森电流控制局部自旋状态，以及通过非局部安德烈夫过程产生纠缠电子对的可能性。