Measurement of fractional corner charges in rotationally symmetric crystalline topological insulator metamaterials*

Topological crystalline insulators (TCIs) with bulk dipole and higher multipole moments can host quantized fractional charges at their boundaries. Recently, it was shown that rotationally symmetric TCIs with vanishing bulk electric moments can also host quantized fractional electric charges at their corners. We used arrays of coupled microwave frequency resonators to experimentally investigate the local density of states (LDOS) in C3- and C4-symmetric crystalline topological lattices. We find that the LDOS is indeed fractionally quantized, in an analogous way as what is expected for the corner charge in their fermionic counterparts. Moreover, we show experimentally that these fractional LDOS are associated with corner-localized states that, although initially may be hidden within bulk energy bands, can be pulled out of them and be spectrally isolated. When these arrays are transitioned into their topological trivial phase, on the other hand, no fractionalization is observed, and consequently, corner-localized states cannot be isolated.