Interaction effects on quantum transport in superconducting nanoscale junctions

本文拟从理论上研究附着在一对超导电极上的各种相互作用量子点（约瑟夫森点）的平衡约瑟夫森电流-相位关系和非平衡电流-电压特性。在这样的约瑟夫森点中，超导相关性（由附着电极引起的接近性）和相互作用（库仑或振动模式相互作用）之间的相互作用产生了丰富的和实验上可接近的物理。特别地，我们计划解决：(i)由于自旋轨道耦合引起的效应，包括自发破缺的时间反转对称性；（ii）耦合到两能级系统的Josephson点的非平衡动力学，包括Cooper对人工Kondo筛选的可能性以及Cooper对动力学对两能级系统的反作用，以及（iii）在超净碳纳米管中放大SU(4)对称性对Josephson效应和相应相图的影响。我们将使用两种分析方法（基于路径积分的场论和图解摄动理论）和量子蒙特卡罗模拟。

We propose to theoretically study the equilibrium Josephson current-phase relation and the nonequilibrium current-voltage characteristics for various models of interacting quantum dots attached to a pair of superconducting electrodes (Josephson dot). The interplay between superconducting correlations (proximityinduced by the attached electrodes) and the interactions (either Coulomb or vibrational mode interactions) in such Josephson dots gives rise to rich and experimentally accessible physics. In particular, we plan to address: (i) effects due to the spin-orbit coupling, including the spontaneously broken time reversal symmetry; (ii) the nonequilibrium dynamics of a Josephson dot coupled to a two-level system, including the possibility of artificial Kondo screening by Cooper pairs and the backaction of the Cooper pair dynamics on the two-level system, and (iii) the effects of an enlarged SU(4) symmetry on the Josephson effect and the corresponding phase diagram realized in ultraclean carbon nanotubes. We will use both analytical methods (path-integral based field theory and diagrammatic perturbation theory) and quantum Monte Carlo simulations.