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## Condensed Matter / Biophysics Seminar – Wei Chen, Pontifical Catholic University

**Seeing topological charge by naked eyes**

We uncover that the opacity of graphene, which is known to be given by the fine structure constant, is actually protected by the topological charge of the Dirac point owing to a correspondence between quantum metric and topological charge. As a result, one can literally see the topological charge by naked eyes, and moreover it implies that the fine-structure constant is topologically protected. We further predict that the opacity of 3D topological insulators in the infrared region is also given by the fine structure constant, implying that one can see the topological surface states through an infrared lens. These optical observation of topological order can be generalized to atomic scale measurements through utilizing the concept of topological markers, which allow the effect of disorder to be quantified. Based on these markers, we will present an analytical proof for the conditions under which the topological invariant remains quantized in the presence of disorder, which reminisces Anderson’s theorem in disordered superconductors.