Higher order topological edge states revealed by unsupervised machine learning technique on Bi(110) thin film

We performed Spectroscopic Imaging Scanning Tunneling Microscopy measurements on the (110) surface of the topological Bi thin film that is synthesized by Molecular Beam Epitaxy technique. We observed enhanced local density of states at particular edges of the Bi(110) islands, exhibiting one dimensional dispersive feature, which is consistent with previously observed higher order topological edge states in this compound. In this study, we introduce the k-means clustering algorithm, which is a non-supervised machine learning technique, to classify electronic structure on the Bi(110) surface and demonstrate that this algorithm can successfully identify the higher order topological edge states. Our results suggest that the k-means clustering technique is powerful and can be used to identify novel quantum electronic states in quantum materials.