Majorana fermions and transport in quantum wires with strong spin-orbit coupling

最近，人们发现半导体自旋电子学的一个标准系统——即具有强自旋轨道耦合的一维或二维半导体线——为拓扑量子计算提供了一个很有前途的平台。结果表明，当这些系统接近s波超导体时，可以承载马约拉纳费米子。最重要的是，对于一维导线，我们发现这些马约拉纳费米子可以被制造出来，并且可以很好地操纵äs äs通过对导线段施加栅极电压来融合。在有线网络上，马约拉纳费米子服从非阿贝尔量子统计，尽管没有超导涡旋，而超导涡旋是马约拉纳费米子非阿贝尔统计的核心论点。在这个项目中，我们的目标是研究承载马约拉纳费米子的量子线的输运性质。具体来说，我们计划讨论由拓扑(T)和非拓扑(S)超导相，（正常）螺旋(H)相或正常(N)相区域组成的多段导线。该项目的核心动机是为量子线中马约拉纳费米子的特征提供理论预测，以指导正在进行的实验工作。

Recently, it became clear that one of the Standard Systems of semiconductor spintronics - namely one- or two-dimensional semiconductor wires with strong spinorbit coupling - offer a promising platform for topological quantum computation. It was shown that these Systems, when brought into proximity with s-wave superconductors, can host Majorana fermions. Most importantly, it was found for one-dimensional wires that these Majorana fermions can be created, manipulated äs well äs fused by the application of gate voltages to segments of the wire. On wire networks, the Majorana fermions obey non-Abelian quantum statistics despite the absence of superconducting vortices which were at the heart of previous arguments for non-Abelian statistics of Majorana fermions. In this project, we aim to investigate the transport properties of quantum wires hosting Majorana fermions. Specifically, we plan to discuss multi-segment wires which consist of regions in the topological (T) and nontopological (S) superconducting phase, the (normal) helical (H) phase, or the normal (N) phase. A central motivation for this project is to provide theoretical predictions for signatures of Majorana fermions in quantum wires to guide ongoing experimental work.