The topological phases of matter are characterized using the Berry phase, a geometrical phase associated with the energy-momentum band structure. The quantization of the Berry phase and the associated wavefunction polarization manifest as remarkably robust physical observables, such as quantized Hall conductivity and disorder-insensitive photonic transport. Recently, a novel class of topological phases, called higher-order topological phases, were proposed by generalizing the fundamental relationship between the Berry phase and quantized polarization, from dipole to multipole moments.
In a recent article published in Nature Photonics, we demonstrated the photonic realization of the quantized quadrupole topological phase, using 2D lattice of ring resonators. In this lattice, the quantization of the bulk quadrupole moment manifests as zero-dimensional corner states which are robust against disorders in the coupling strength between resonators.
The article has been featured in JQI press release and in Nature News and Views.