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In an introductory part I will discuss the relation between topological insulators and the architectural challenge of building a bridge between Hongkong and mainland China. Then I discuss how a magnetic field induces one-dimensional edge channels when the two-dimensional surface states of three-dimensional topological insulators become gapped. Remarkably, the Hall effect remains quantized even in situations, where the theta-term characteristic of the bulk and the associated surface Hall conductivities are not quantized due to the breaking of time-reversal symmetry. The quantization arises as the theta-term changes by integer multiples along a loop around n edge channels. Model calculations show how an interplay of orbital and Zeeman effects leads to quantum Hall transitions, where channels get redistributed along the edges of the crystal. The network of edges opens new possibilities to investigate the coupling of edge channels. In a last part I will shortly discuss aspects of strongly disordered topological insulators as well as interaction effects on the surfaces.

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Dr. Lars Fritz, University of Cologne
Seminarraum Theoretische Physik
Contact: not specified