Realization of semimagnetic and magnetic topological insulators via topological surface states floating

The observation temperatures of quantum anomalous Hall effect in semimagnetic and magnetic topological insulator (MTI) heterostructures are always much lower than Curie temperature. Here, we theoretically demonstrate that floating of topological surface states (TSSs) into magnetic insulators is not only able to produce ideal semi-MTI heterostructures, but also provides insight into the origin of extremely low observation temperature of the quantum anomalous Hall effect in different MTIs. We show that the emergence of diving and floating of TSSs can be observed in MnBi₂Te₄/Bi₂Se₃ family heterostructures. Within the TSSs floating systems, MnBi₂Te₄/Sb₂Te₃ and NiBi₂Te₄/Sb₂Te₃ exhibit characteristics of ideal semi-MTIs, featuring a tunable Fermi level, and MnSb₂Te₄/Bi₂Te₃/NiBi₂Te₄ (NiBi₂Te₄/Sb₂Te₃/VBi₂Te₄) is found to be MTI with weak (strong) long-range ferromagnetic coupling and large (small) surface gap. Our findings reveal that the observation temperature of quantum anomalous Hall effect is governed by the smaller of the two surface gaps, rather than being directly linked to the Curie temperature of MTIs.