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Topology, symmetry and localization – an alliance on average

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In topological states of matter, topology imposes constraints on the localization properties of electrons. For example, in the quantum Hall effect a quantized value of the Hall resistivity requires localization at the Fermi energy, while a transition between two quantized values requires delocalization. In this talk I will discuss topological states of a weaker type, those in which the topological protection relies on the preservation of a symmetry. I will examine how – and when – their topological nature affects their localization properties when they are subjected to a disordered potential that satisfies the symmetry only on average. I will start by reviewing the case of the quantum Hall effect, and then proceed to analyze topological states that rely on spatial symmetries such as translation invariance and inversion. The talk is not technical, and a broad introduction will be given.

This talk is part of the Theory of Condensed Matter series.

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