Arbitrary Positioning Higher-Order Topological Boundary States in Fe Breathing-Kagome Lattices on Ag(111)

Higher-order topological insulators, which host topologically protected states at boundaries that are at least two dimensions lower than the bulk, are an emerging class of topological materials. They provide great opportunities for exploring novel topological phenomena and fascinating applications. Utilizing a low-temperature scanning tunneling microscope, we construct breathing-kagome lattices with Fe adatoms on Ag(111) and investigate their electronic properties. We observe the higher-order topological boundary states in the topological phase but not in the trivial one, which is consistent with the theory. These states are found to be robust against the removal of bulk or edge adatoms. Further, we show the arbitrary positioning of these states either at corner, edge, or bulk sites by slightly modifying their neighbors. Our study not only demonstrates the formation and robustness of the electronic higher-order topological boundary states in real atomic systems but also provides a route for controlling their positions.