基于Schrödinger-Poisson方程的半导体-超导混合纳米线电学性质的数值模拟

理论预言，通过调控电场和磁场可驱动半导体-超导混合纳米线进入拓扑超导相，在其两端诱导出服从非阿贝尔统计的Majorana束缚态，有望用于实现容错拓扑量子计算。目前，通过电子输运测量已在混合纳米线系统中探测到Majorana束缚态的一些迹象，但均存在争议。受近期理论进展启发，本项目拟采用求解Schrödinger-Poisson方程的方法对实际混合纳米线系统进行数值模拟，探究实验可调参数如何影响其电学性质，包括自旋-轨道耦合强度、电子态密度和电子浓度的空间分布。以此为基础，本项目将系统研究如何优化和调控混合纳米线，以及如何区分混合纳米线中的Majorana束缚态和拓扑平庸的近零能Andreev束缚态。本项目将与清华大学混合纳米线实验团队紧密合作，充分探讨实验细节和最新实验数据，有助于对混合纳米线中Majorana束缚态的准确探测和精准操控，为实现拓扑量子计算做铺垫。

It was predicted that applying electric and magnetic fields can drive a semiconductor-superconductor hybrid nanowire into the topological superconducting phase harboring boundary Majorana bound states (MBSs), which obey non-Abelian statistics and thus are promising for realizing fault-tolerant topological quantum computation. Currently, electronic transport experiments in hybrid nanowires have detected a few signatures of MBSs, however, all of them remain controversial. Motivated by recent theoretical progress, we plan to simulate realistic hybrid nanowires by solving the Schrödinger-Poisson equantion to study the effects of the experimentally tunable parameters on the electronic properties, such as the spin-orbit coupling strength, density of states, and electron density distribution. Based on these, we will systematically explore how to improve and control hybrid nanowires, and how to distinguish MBSs from topologically trivial near-zero energy Andreev bound states in hybrid nanowires. The project will be carried out in cooperation with the group in Tsinghua University to share experimental details and latest data, facilitating the unambiguous detection and accurate control of the MBSs in hybrid nanowires, which paves the way to topological quantum computation.