In the presence of crystalline symmetries, certain topological insulators present a filling anomaly: a mismatch between the number of electrons in an energy band and the number of electrons required for charge neutrality. This seminar will show how a "corner-induced filling anomaly" is at the core of the bulk-boundary correspondence of higher-order topology in two dimensions. In crystalline insulators, the consequence of higher-order topology is the quantized fractionalization of corner electronic charge. I will discuss the connection between fractional corner charge and topological corner states. The latter is a feature that transcends insulators and allows for higher-order topological protection in superconductors and synthetic materials. In particular, I will discuss higher-order topological protection in crystalline photonic systems.
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