Detection of higher order topological phase in a disordered breathing Kagome model by using machine learning

A higher order topological insulator is a new concept of topological states of matter, which is characterized by the emergent boundary states whose dimensionality is lower by more than two compared with that of the bulk, and draws a considerable interest. Yet, its robustness against disorders is still unclear. Here we investigate a phase diagram of higher order topological insulator phases in a breathing Kagome model in the presence of disorders, by using a state-of-the-art machine learning technique. We find that the corner states survive against the finite strength of disorder potential as long as the energy gap is not closed, indicating the stability of the higher order topological phases against the disorders. We also discuss the relation between the higher order topological phase and the Z_3 Berry phase, which is a bulk topological invariant.