强自旋轨道耦合系统中的拓扑超导以及Majorana费米子

Topological superconductor (TSC) with Majorana fermions (MFs) in it is a new topic in condensed matter physics in recent years. Because of its attractive prospect for application(for example, it can be used to design quantum computer, which is topologically protected and very robust to local disorders and impurities, so has strong fault tolerance compared to other quantum computing proposals) and its exotic properties, TSC and MFs attract growing attention and the related researches become very hot and popular. In the last year, some top experimental groups have reported some evidences of Majorana fermions in semiconductor/superconductor heterostructures. But people still have lots of concerns about the experiments, because lots of other physical effects can cause similar experimental results, so it is necessary and important to do some further theoretical and experimental works. The applicant prepares to study the effects of disorders and impurities to hole doped nanowire/s-wave superconductor heterostructures with numerical simulation(hole doped systems have topological phases and Majorana fermions are firstly proposed by the applicant), and search new materials and structures which can effectively support Majorana fermions(such as core-shell semiconductor nanowires, ultra cold fermions, and so on).

拓扑超导体以及其中的Majorana费米子是近年凝聚态物理的新兴方向。由于其非常诱人的应用前景（例如可以利用它来设计量子计算机，由于受到拓扑保护此类量子计算机对于局部的扰动和杂质不敏感，因此容错能力比其它方案更好），以及其本身的新奇特性，使得关于拓扑超导与Majorana费米子的研究变得十分热门。去年世界上几个顶级实验小组在电子型纳米线与超导体复合结构中观测到了Majorana费米子存在的证据，但是物理学界对实验本身还存在争议，因为不少其它的物理效应也能产生类似的实验结果，所以进一步的理论和实验研究显得必不可少。申请人准备利用数值方法研究空穴型纳米线与超导体复合结构中杂质对实验信号的影响（空穴型系统也有拓扑超导相以及Majorana费米子由申请人首次提出），同时进一步寻找其它更有效的纳米材料或者结构（例如具有core-shell结构的半导体纳米线、超冷费米原子等）。

在短暂的一年时间中发展了一套数值计算程序，并在此基础上研究了准一维超冷费米气体，得到了系统详细的相图。我们发现在存在自旋轨道耦合的情况下系统可以存在暗孤子，并且更有趣的是在暗孤子中能够存在两个无相互作用的Majorana费米子。提出了通过测量两组分密度差来判断系统是否进入拓扑非平庸相的方法。相关文章发表在Physical Review Letters上（项目负责人为共同第一作者，详见文章Phys. Rev. Lett. 113, 130404最后一句话）。