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arXiv 1610.08366cond-mat.mes-hall
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超导导线上的量子点:对称耦合与非对称耦合的关系

Quantum dot attached to superconducting leads: Relation between symmetric and asymmetric coupling

Alžběta Kadlecová, Martin Žonda, Tomáš Novotný

摘要:

我们研究了两个BCS超导导线上的Anderson单能级量子点,导线具有相同的带隙尺寸。我们发现,具有不对称隧道耦合到电极导线($Γ_{L}\neqΓ_{R}$)的系统可以与具有相同净耦合强度$Γ=Γ_{L}+Γ_{R}$的对称系统相关。令人惊讶的是,对称的情况是最普遍的,这意味着在非对称耦合的情况下,所有的物理量都完全由对称的物理量决定。我们给出了$0-π$相变边界、点上量和约瑟夫森电流的现成转换公式,并在Oguri、Tanaka和Bauer [Phys. Rev. B 87,075432(2013)]的NRG结果上对三端设置进行了说明。我们将我们的理论应用于Delagrange等人最近的$0-π$跃迁测量[Phys. Rev. B 93,196437(2016)],并从测量的跃迁宽度确定实验装置的不对称性。最后,我们建立了广泛假设的Kondo "普适性"的物理量仅取决于Kondo温度和超导间隙的比率$T_{K}/Δ$不能举行非对称结。

英文摘要:

We study the Anderson single-level quantum dot attached to two BCS superconducting leads with the same gap size. We reveal that a system with asymmetric tunnel coupling to the leads ($Γ_{L}\neqΓ_{R}$) can be related to the symmetric system with the same net coupling strength $Γ=Γ_{L}+Γ_{R}$. Surprisingly, it is the symmetric case which is the most general, meaning that all physical quantities in case of asymmetric coupling are fully determined by the symmetric ones. We give ready-to-use conversion formulas for the $0-π$ phase transition boundary, on-dot quantities, and the Josephson current, and illustrate them on the NRG results of Oguri, Tanaka and Bauer [Phys. Rev. B 87, 075432 (2013)] for the three-terminal setup. We apply our theory to the recent $0-π$ transition measurement of Delagrange et al. [Phys. Rev. B 93, 196437 (2016)] and determine the asymmetry of the experimental setup from the measured transition width. Finally, we establish that the widely assumed Kondo "universality" of physical quantities depending only on the ratio of the Kondo temperature and the superconducting gap $T_{K}/Δ$ cannot hold for asymmetric junctions.

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