Topological insulators and superconductor - effects of disorder and interactions

拓扑学是研究物体形状和连通性的数学分支。最近，拓扑学领域与凝聚态物理相交，并帮助定义了一类新的材料。这些是拓扑绝缘体和超导体。其非凡的性质是由于其不寻常的微观结构显示出非平凡的拓扑结构。 特别是，拓扑绝缘体在体积上类似于常规绝缘体--它只是不能传导电子。然而，在它的表面，它不仅传导电子，而且没有任何耗散。在过去的几年里，许多理论模型和实验系统被发现显示了这种不寻常的现象。 拓扑超导体是物质拓扑态的另一个例子。已经从理论上预测了它的存在，目前社区正在努力实现这一预测的实验。拓扑超导体的惊人性质是它可以支持马约拉纳费米子。这些奇特的粒子早在1937年就被预言过，但从未被发现过。Majorana费米子是它自己的反粒子，在拓扑超导体中可以用作量子计算的积木。 在我的研究中，我调查了这些新奇的材料。我的目标之一是提出一种实现拓扑超导体的可行方法，而我的另一个目标是了解拓扑绝缘体和超导体。我用理论模型来描述这些材料，并考虑了无序和强相互作用的影响。

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.