Properties of Majorana fermions in topological superconductors

2011年是超导（在一定温度下无电阻流动的电流）发现一百周年，但在世界范围内寻找更高温度下超导材料的竞赛中，新的超导体不断出现。就在几年前，人们发现了一类具有拓扑超导性的新型材料，这种材料在纳米电子学中具有很高的应用潜力，为凝聚态物质研究和材料科学开辟了一个全新的令人兴奋的领域。拓扑超导的一个不寻常的特征是马约拉纳费米子的可能存在，这是一种基本粒子，它可能是解开支配宇宙的对称性的关键，但至今仍是假设。在凝聚态系统中创造马约拉纳费米子不仅是基础物理学的突破，也是计算机技术的突破，因为马约拉纳费米子可以用来实现容错量子计算。

Year 2011 marked the centennial anniversary of the discovery of superconductivity -- the flow of electric currents without resistance below a certain temperature -- but in the worldwide race for finding superconducting materials at ever higher temperature, new superconductors continue to emerge. The discovery of a new class of materials that exhibit the so-called topological superconductivity and have a high potential for applications in nanoelectronics only few years ago has opened up a brand-new exciting field in condensed matter research and materials science. One of the unusual features of topological superconductivity that makes this field significant is the possible existence of Majorana fermions -- elementary particles which may hold a key to unravelling the symmetry that governs the universe, but remain hypothetical to this day. Creating Majorana fermions in condensed matter systems will be a breakthrough not only in fundamental physics, but also for computer technology, as Majorana fermions can be used to realise fault-tolerant quantum computation. The major goal of the proposed research is to have a comprehensive understanding of the properties of Majorana fermions in topological superconducting states. 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 materials that can be turned into a topological superconductor. To expedite the research projects in this very competitive field, the powerful technique of massively parallel computation using graphics cards will be utilised.