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A higher-order topological insulator is a new concept of topological statesof matter, which is characterized by the emergent boundary states whosedimensionality is lower by more than two compared with that of the bulk, anddraws a considerable interest. Yet, its robustness against disorders is stillunclear. Here we investigate a phase diagram of higher-order topologicalinsulator phases in a breathing kagome model in the presence of disorders, byusing a state-of-the-art machine learning technique. We find that the cornerstates survive against the finite strength of disorder potential as long as theenergy gap is not closed, indicating the stability of the higher-ordertopological phases against the disorders.

Phase diagram of disordered higher-order topological insulator: A machine learning study