Trapped state at a dislocation in a weak magnetomechanical topological insulator

Topological insulators (TIs) are characterized by an insulating bulk and symmetry protected bound state on their boundaries. A strong topological insulator is characterized by robust conducting states on emph{all} boundaries protected by certain internal symmetries. A weak topological insulator (WTI) however, requires lattice translation symmetry, making it more sensitive to disorder. However, this sensitivity gives rise to interesting characteristics such as anisotropic edge modes, quantized charge polarization, and bound states appearing at dislocation defects. Despite hosting interesting features, the sensitivity of WTIs to disorder poses an experimental confirmation challenge. Here we realize a 2D magneto-mechanical metamaterial and demonstrate experimentally the unique features of a WTI. Specifically, we show that the 2D WTI is anisotropic and hosts edge modes only on certain edges, as well as hosting a bound state at a dislocation defect. We construct the 2D WTI from stacked 1D SSH chains for which we show experimentally the different gapped phases of the 1D model.