Self-consistent study of topological superconductors

自十年前首次对三维（3D）拓扑绝缘体进行理论预测以及随后在铋基化合物中的实验发现以来，拓扑材料这一新的广阔领域一直在以非常快的速度发展和扩展。虽然在体中绝缘，但3D拓扑绝缘体具有受拓扑保护的新颖金属表面态，并且在载流子掺杂时，可以转变为3D拓扑超导体或在其表面上呈现二维（2D）拓扑超导性（TSC）。也有工程二维TSC在各种各样的系统，如传统材料制成的半导体异质结构的有前途的建议。TSC的结果，使这一领域显着的是拓扑保护的出现，拓扑超导体中的零能量激发的马约拉纳费米子。马约拉纳费米子--它们是自己的反粒子，并且服从非阿贝尔交换统计--长期以来一直在高能物理领域受到追捧，但直到今天，马约拉纳费米子作为基本粒子的探测仍然难以捉摸。因此，在凝聚态系统中产生马约拉纳费米子的能力不仅可能导致基础物理学的突破，而且还可能实现可扩展的容错拓扑量子计算。拟议研究计划的主要目标是全面了解马约拉纳费米子在各种拓扑超导体家族中的性质。了解它们如何被创建和稳定，以及如何控制和操纵它们，以便设计可用作量子计算量子位的固态设备，这是至关重要的。拟议的研究还旨在探索新发现的拓扑半金属中的TSC，这不仅为各种技术应用带来了新的可能性，而且还为在桌面实验中探索基础量子物理带来了新的可能性。为了加快这一竞争非常激烈的领域的研究项目，将利用最近开发的高效数值算法和大规模并行计算。通过在拟议的研究计划中的项目工作，学生将获得尖端材料科学的优秀研究培训，这将是学生未来职业生涯的资产-在学术界或工业界-无论学生选择追求什么领域。

Since the first theoretical prediction of three-dimensional (3D) topological insulators a decade ago and their subsequent experimental discovery in bismuth-based compounds, there has been a burst of theoretical and experimental activities in this new and vast field of topological materials, which keeps advancing and expanding at a very fast rate. Though insulating in the bulk, a 3D topological insulator hosts novel metallic surface states protected by topology and upon carrier doping, can turn into a 3D topological superconductor or present two-dimensional (2D) topological superconductivity (TSC) on its surfaces. There have also been promising proposals for engineering 2D TSC in a wide variety of systems such as semiconductor heterostructures made of conventional materials.One of the consequences of TSC that makes this field significant is the emergence of Majorana fermions as topologically protected, zero-energy excitations in topological superconductors. Majorana fermions -- which are their own antiparticles and obey the non-Abelian exchange statistics -- have long been sought after in the area of high-energy physics, yet detection of Majorana fermions as elementary particles remains elusive to this day. Thus, the capability of creating Majorana fermions in condensed matter systems will potentially lead to not only a breakthrough in fundamental physics, but also realisation of scalable, fault-tolerant topological quantum computation.The major goal of the proposed research program is to have a comprehensive understanding of the properties of Majorana fermions in various families of topological superconductors. It is essential to understand how they can be created and stabilised, and how to control and manipulate them, so as to design solid-state devices that can be used as qubits for quantum computing. The proposed research also aims to explore TSC in newly discovered topological semimetals, which have brought about new possibilities not only for various technological applications, but also for exploring fundamental quantum physics in table-top experiments. To expedite the research projects in this very competitive field, recently developed, efficient numerical algorithms and large-scale parallel computation will be utilised. Through working on a project in the proposed research program, students will receive excellent research training in cutting-edge materials science, which will be an asset for the student's future career -- in academia or industry -- no matter what area the student chooses to pursue.