Exceptional robustness and anomalous topology in non-reciprocal scattering networks

Back-scattering free transport, robust to defects and disorder, is a pivotal characteristic of topological insulators. However, such resilience to physical parameters variations or structural defects is typically limited to weak perturbations. In Chern insulators, for example, on-site energy fluctuations cannot exceed the band-gap size. Here, we demonstrate that non-reciprocal scattering networks exhibit an anomalous topological phase, distinct from the usual Chern phase, capable of withstanding extremely strong levels of disorder, in both periodic (crystalline) and aperiodic (amorphous) settings. Experiments are carried using non-reciprocal microwave networks, validating the exceptional resilience of anomalous edge transport. We provide a direct confirmation of the anomalous topology of our prototypes by measuring the topological invariant in a topological pump experiment, performed both on periodic and amorphous samples. Our results pave the way for robust two-dimensional (2D) wave manipulation with complete topological protection.