Topological Disclination States and Charge Fractionalization in a Non-Hermitian Lattice

We show that a non-Hermitian lattice with a disclination can host topological disclination states that are induced by on-site gain and loss. The disclination states are inherently non-Hermitian as they do not exist in the limit of zero gain or loss. They arise from charge fractionalization in the non-Hermitian lattice, which we establish using non-Hermitian Wilson loops calculated with biorthogonal products. The model is suitable for realization on established experimental platforms, such as arrays of photonic or polaritonic resonators. The emergence of the topological disclination states can manifest as an abrupt shift in emission intensity and frequency with varying gain or loss.