Topology is the study of the properties of geometric forms that remain invariant under certain continuous transformations like bending or stretching. Topology plays a central role in our understanding of electronic properties of many solid-state materials. Systems as varied as fractional quantum Hall liquids, 3D topological insulators, px+ipy superconductors, superconductor/semiconductor hybrids and 2D spin-Hall effect liquids all possess unusual topological properties. Beyond providing a new paradigm for understanding fundamental electronic processes, the unusual topology of several materials holds promise for the realization of fault-tolerant quantum computing in scalable solid-state systems.
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