Abstract

The charge transport has been analyzed theoretically across a T-shaped and series-configured double quantum dots Josephson junction by implementing the Slave Boson mean field approximation at an infinite-\(\textit{U}\) limit. It has been shown that Andreev bound states and Josephson current can be tuned by varying the interdot tunneling (t) and quantum dots energy level. For the T-shape configuration of the quantum dots, an extra path is available for the transport of electrons which causes the interference destruction between two paths. For decoupled quantum dots with energy level \(\epsilon _{d1}=\epsilon _{d2}=0\), the energy of Andreev bound states crosses at Fermi energy, and Josephson current shows a discontinuity at phase difference \(\phi =\pm \pi \). On the other hand, for coupled quantum dots the lower and upper Andreev bound states have a finite spacing, the Josephson current exhibits a sinusoidal nature and its magnitude suppresses with increasing interdot tunneling strength. While in the series configuration, with increment in interdot tunneling, Josephson current increases and shows a discontinuity at phase difference \(\phi =\pm \pi \), once the system gets resonant tunneling for \(t=0.5\Gamma \) with quantum dots energy level \(\epsilon _{d1}=\epsilon _{d2}=0.5\Gamma \). Further, we also analyze the nature of the energy of Andreev bound states and Josephson current with the quantum dots energy level in both configurations.

Graphical Abstract

中文翻译：

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约瑟夫森在无限 $$\textit{U}$$ 极限下穿越 T 形串联配置的双量子点系统

摘要

通过在无限\(\textit{U}\)极限下实现从玻色子平均场近似，对 T 形串联双量子点约瑟夫森结上的电荷传输进行了理论分析。研究表明，安德烈夫束缚态和约瑟夫森电流可以通过改变点间隧道效应 (t) 和量子点能级来调节。对于量子点的T形结构，有一条额外的路径可用于电子传输，这会导致两条路径之间的干扰破坏。对于能级为\(\epsilon _{d1}=\epsilon _{d2}=0\) 的解耦量子点，Andreev 束缚态的能量在费米能级处交叉，约瑟夫森电流在相位差\(\ phi =\pm \pi \)。另一方面，对于耦合量子点，下安德烈夫束缚态和上安德烈夫束缚态具有有限的间距，约瑟夫森电流表现出正弦特性，并且其幅度随着点间隧道强度的增加而受到抑制。而在串联配置中，随着点间隧道效应的增加，一旦系统获得谐振隧道效应\ (t=0.5\Gamma \ )，约瑟夫森电流就会增加，并在相位差 \(\phi =\pm \pi \ ) 处显示出不连续性。量子点能级\(\epsilon _{d1}=\epsilon _{d2}=0.5\Gamma \)。此外，我们还分析了两种配置中量子点能级的安德烈夫束缚态和约瑟夫森电流的能量性质。

图形概要