Measurement of fractional charge at disclination defects in higher-order topological crystalline insulators

Topological crystalline insulators (TCIs) are known to host quantized fractional charge at boundaries and defects, which is topologically protected by bulk crystalline symmetries. Recently, this bulk-boundary correspondence was extended by the discovery of higher-order TCIs, which may host quantized fractional charge at a boundary of their boundary. Here, we use arrays of microwave resonators to experimentally study higher-order TCIs on lattices with disclination defects. Introducing a disclination defect to a finite lattice is equivalent to inserting or removing one or more sectors, changing the total number of corners and consequently introducing an overall fractional charge. Since the total charge in a lattice must remain an integer, the disclination core is expected to also host fractional charge to compensate. We experimentally measure C4-symmetric higher-order TCIs on square lattices having disclinations with positive and negative Frank angles, which respectively have 5 and 3 corners. We find that, in both cases, the disclination core does indeed host fractional charge, such that the total charge of the lattice is an integer. Furthermore, we show that there are gapless bound states associated with the defect.