Bound states at partial dislocation defects in multipole higher-order topological insulators.

The bulk-boundary correspondence, which links a bulk topological property of a material to the existence of robust boundary states, is a hallmark of topological insulators. However, in crystalline topological materials the presence of boundary states in the insulating gap is not always necessary since they can be hidden in the bulk energy bands, obscured by boundary artifacts of non-topological origin, or, in the case of higher-order topology, they can be gapped altogether. Crucially, in such systems the interplay between symmetry-protected topology and the corresponding symmetry defects can provide a variety of bulk probes to reveal their topological nature. For example, bulk crystallographic defects, such as disclinations and dislocations, have been shown to bind fractional charges and/or robust localized bound states in insulators protected by crystalline symmetries. Recently, exotic defects of translation symmetry called partial dislocations have been proposed as a probe of higher-order topology. However, it is a herculean task to have experimental control over the generation and probing of isolated defects in solid-state systems; hence their use as a bulk probe of topology faces many challenges. Instead, here we show that partial dislocation probes of higher-order topology are ideally suited to the context of engineered materials. Indeed, we present the first observations of partial-dislocation-induced topological modes in 2D and 3D higher-order topological insulators built from circuit-based resonator arrays. While rotational defects (disclinations) have previously been shown to indicate higher-order topology, our work provides the first experimental evidence that exotic translation defects (partial dislocations) are bulk topological probes.