Edge-Dependent Topology in Kekulé Lattices

The boundary states of topological insulators are thought not to depend on the precise atomic structure of the boundary. A recent theoretical study showed that, for topological crystalline insulators with given bond strengths, topological states should only emerge for certain edge geometries. We experimentally probe this effect by creating artificial Kekul\'e lattices with different atomically well-defined edge geometries and hopping ratios in a scanning tunneling microscope. Topological edge modes are found to only appear for specific combinations of edge geometry and hopping ratio.