Exchange-Driven Chern States in High-Mobility Intrinsic Magnetic Topological Insulators

The layer-dependent Chern number ($C$) in ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$ is characterized by the presence of a Weyl semimetal state in the ferromagnetic coupling. However, the influence of a key factor, namely, the exchange coupling, remains unexplored. This study focuses on characterizing the $C=2$ state in ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$, which is classified as a higher $C$ state resulting from the anomalous $n=0$ Landau levels (LLs). Our findings demonstrate that the exchange coupling parameter strongly influences the formation of this Chern state, leading to a competition between the $C=1$ and 2 states. Moreover, the emergence of odd-even LL sequences, resulting from the breaking of LL degeneracy, provides compelling evidence for the strong exchange coupling strength. These findings highlight the significance of the exchange coupling in understanding the behavior of Chern states and LLs in magnetic quantum systems.