Properties of Majorana fermions in topological superconductors

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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.