Cayao Jorge, Black-Schaffer Annica M, Prada Elsa, Aguado Ramón
Department of Physics and Astronomy, Uppsala University, Box 516, S-751 20 Uppsala, Sweden.
Departamento de Física de la Materia Condensada, Condensed Matter Physics Center (IFIMAC) & Instituto Nicolás Cabrera, Universidad Autónoma de Madrid, E-28049 Madrid, Spain.
Beilstein J Nanotechnol. 2018 May 3;9:1339-1357. doi: 10.3762/bjnano.9.127. eCollection 2018.
Hybrid superconductor-semiconductor nanowires with Rashba spin-orbit coupling are arguably becoming the leading platform for the search of Majorana bound states (MBSs) in engineered topological superconductors. We perform a systematic numerical study of the low-energy Andreev spectrum and supercurrents in short and long superconductor-normal-superconductor junctions made of nanowires with strong Rashba spin-orbit coupling, where an external Zeeman field is applied perpendicular to the spin-orbit axis. In particular, we investigate the detailed evolution of the Andreev bound states from the trivial into the topological phase and their relation with the emergence of MBSs. Due to the finite length, the system hosts four MBSs, two at the inner part of the junction and two at the outer one. They hybridize and give rise to a finite energy splitting at a superconducting phase difference of π, a well-visible effect that can be traced back to the evolution of the energy spectrum with the Zeeman field: from the trivial phase with Andreev bound states into the topological phase with MBSs. Similarly, we carry out a detailed study of supercurrents for short and long junctions from the trivial to the topological phases. The supercurrent, calculated from the Andreev spectrum, is 2π-periodic in the trivial and topological phases. In the latter it exhibits a clear sawtooth profile at a phase difference of π when the energy splitting is negligible, signalling a strong dependence of current-phase curves on the length of the superconducting regions. Effects of temperature, scalar disorder and reduction of normal transmission on supercurrents are also discussed. Further, we identify the individual contribution of MBSs. In short junctions the MBSs determine the current-phase curves, while in long junctions the spectrum above the gap (quasi-continuum) introduces an important contribution.
具有 Rashba 自旋轨道耦合的混合超导 - 半导体纳米线，可以说是在人工拓扑超导体中寻找马约拉纳束缚态（MBS）的主要平台。我们对由具有强 Rashba 自旋轨道耦合的纳米线制成的短和长超导 - 正常 - 超导结中的低能安德列夫谱和超电流进行了系统的数值研究，其中垂直于自旋轨道轴施加了外部塞曼场。特别是，我们研究了安德列夫束缚态从平凡相到拓扑相的详细演化及其与 MBS 出现的关系。由于长度有限，该系统包含四个 MBS，两个在结的内部，两个在外部。它们发生杂化，并在超导相差为 π 时产生有限的能量分裂，这是一个清晰可见的效应，可追溯到能谱随塞曼场的演化：从具有安德列夫束缚态的平凡相到具有 MBS 的拓扑相。同样，我们对短和长结从平凡相到拓扑相的超电流进行了详细研究。根据安德列夫谱计算的超电流在平凡相和拓扑相中都是 2π 周期的。在后者中，当能量分裂可忽略不计时，它在相差为 π 时呈现出清晰的锯齿形轮廓，这表明电流 - 相位曲线强烈依赖于超导区域的长度。还讨论了温度、标量无序和正常传输降低对超电流的影响。此外，我们确定了 MBS 的个体贡献。在短结中，MBS 决定电流 - 相位曲线，而在长结中，能隙以上的谱（准连续谱）引入了重要贡献。
