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Topological phases, Anderson localization, and anomalous transport law

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Mathematics and Physics of Anderson localization: 50 Years After

Topological phases of matter are a very quantum, highly entangled state of matter. While topological phases and Anderson localization are a quite big research field by themselves and can be discussed independently, they have a very close connection. I will discuss a cross fertilization of both fields by focusing on, in particular, physics at a boundary of topological phases. Due to the “bulk-boundary correspondence”, well known in the quantum Hall effect, quantum transport phenomena mediated by modes appearing at the boundary have a strong stability against impurities. I will extend this idea to a wider class of topological phases in higher dimensions and with the Altland-Zirnbauer discrete symmetries. In topological superconductors in two and three spatial dimensions, I will derive a new thermodynamic relation (“Streda-like” formula) due to the non-zero thermal Hall conductance, and a thernal analogue of the axion electrodynamics.

This talk is part of the Isaac Newton Institute Seminar Series series.

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