Topological insulators and superconductor - effects of disorder and interactions

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Topology is a branch of mathematics that deals with the shape and connectivity of objects. Recently, the field of topology has intersected condensed matter physics and helped to define a new class of materials. These are topological insulators and superconductors. Their remarkable properties are a result of their unusual microscopic structure which displays non-trivial topology. In particular, a topological insulator, is similar to a regular insulator in its bulk - it simply can not conduct electrons. On its surface, however, not only does it conduct electrons but it also does so without any dissipation. In the past few years many theoretical models and experimental systems that display this unusual phenomenon have been found. A topological superconductor, is another example of a topological state of matter. It has been predicted to exist theoretically and the community is currently hard at work to realize this prediction experimentally. The amazing property of a topological superconductor is that it can support Majorana Fermions. These are peculiar particles that have been predicted in 1937 and have never been seen. A majorana fermion is its own antiparticle and in the topological superconductor may be used as a building block for quantum computation. In my research I investigate these novel materials. One of my objectives is to propose a feasible way to realize a topological superconductor while my other objectives have to do with understanding topological insulators and superconductors. I describe these materials by theoretical models and take into account the effects of disorder and strong interactions.