Interplay between quantum anomalous Hall effect and magnetic skyrmions

Quantum anomalous Hall effect (QAHE) and magnetic skyrmion (SK) represent two typical topological states in momentum (K) and real (R) spaces, respectively. However, little is known about the interplay between these two states. Here, we propose that the coexistence of QAHE and SK may generate a previously unknown SK state, named the RK joint topological skyrmion (RK-SK), which is characterized by the SK surrounded by nontrivial chiral boundary states (CBSs). Interestingly, beyond the traditional SK state that can solely be used via creation or annihilation, the number and chirality of CBS in RK-SK can be tunable under external fields as demonstrated in Janus monolayer (ML) MnBi(2)X(2)Te(2) (X [Formula: see text] S, Se), creating additional degrees of freedom for SK-state manipulations. Moreover, it is also found that external fields can induce a continuous topology phase transition from K-space QAHE to R-space SK in ML MnBi(2)X(2)Te(2), providing an ideal platform to understand the cross-over phenomena of multiple-space topologies.