Self-consistent study of topological superconductors

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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.