Abstract Kitaev chain (KC) is a prototypical model for the study of Majorana fermions (MFs). In the topological phase, a KC hosts two MFs at its ends. Being separated in space, these two MFs are nonlocal. The nonlocal transport in a KC biased between two normal metal leads is mediated by electron tunneling (ET) and crossed Andreev reflection (CAR). ET contributes positively while CAR contributes negatively to the nonlocal conductance. Enhanced CAR and hence a negative nonlocal conductance is a hallmark of nonlocality of MFs. But simple conductance measurements in the above setup cannot probe the nonlocality of MFs due to the almost cancellation of currents from ET and CAR. On the other hand, a Josephson junction between two KCs hosts two Andreev bound states (ABSs) at the junction formed by a recombination of Majorana fermions of the individual KCs. The energies of the ABSs are away from zero and can be changed by altering the superconducting phase difference. A Josephson junction between two finitely long KCs hosts two MFs at the two ends and two ABSs at the junction. We show that when normal metal leads are connected to two ends of such a Josephson junction, the nonlocal conductance of the setup can be negative for bias values equal to the energies of the ABSs. Thus the nonlocal conductance in such setup can probe the nonlocality of the constituent MFs.

中文翻译：

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探测连接到正常金属引线的基塔耶夫链约瑟夫森结中马约拉纳费米子的非定域性

摘要 Kitaev 链（KC）是研究马约拉纳费米子（MF）的典型模型。在拓扑阶段，KC 在其两端承载两个 MF。在空间上分开，这两个 MF 是非本地的。在两个正常金属引线之间偏置的 KC 中的非局部传输是由电子隧道 (ET) 和交叉安德列夫反射 (CAR) 介导的。ET 对非局部电导有积极贡献，而 CAR 对非局部电导有负面贡献。增强的 CAR 以及负的非局部电导是 MF 非局部性的标志。但是由于几乎抵消了来自 ET 和 CAR 的电流，上述设置中的简单电导测量无法探测 MF 的非定域性。另一方面，两个 KC 之间的约瑟夫森结在由单个 KC 的马约拉纳费米子重组形成的结处承载两个安德列夫束缚态 (ABS)。ABS 的能量远离零，可以通过改变超导相位差来改变。两个有限长 KC 之间的约瑟夫森连接在两端承载两个 MF，在连接处承载两个 ABS。我们表明，当普通金属引线连接到此类约瑟夫森结的两端时，装置的非局部电导对于等于 ABS 能量的偏置值可能为负。因此，这种设置中的非局域电导可以探测组成 MF 的非局域性。两个有限长 KC 之间的约瑟夫森连接在两端承载两个 MF，在连接处承载两个 ABS。我们表明，当普通金属引线连接到这种约瑟夫森结的两端时，装置的非局部电导对于等于 ABS 能量的偏置值可能为负。因此，这种设置中的非局域电导可以探测组成 MF 的非局域性。两个有限长 KC 之间的约瑟夫森连接在两端承载两个 MF，在连接处承载两个 ABS。我们表明，当普通金属引线连接到此类约瑟夫森结的两端时，装置的非局部电导对于等于 ABS 能量的偏置值可能为负。因此，这种设置中的非局域电导可以探测组成 MF 的非局域性。