Abstract
SignificanceQuantum anomalous Hall effect (QAHE) and magnetic skyrmion (SK), as two typical topological states in momentum (K) and real (R) spaces, attract much interest in condensed matter physics. However, the interplay between these two states remains to be explored. We propose that the interplay between QAHE and SK may generate an RK joint topological skyrmion (RK-SK), characterized by the SK surrounded by nontrivial chiral boundary states (CBSs). Furthermore, the emerging external field-tunable CBS in RK-SK could create additional degrees of freedom for SK manipulations, beyond the traditional SK. Meanwhile, external field can realize a rare topological phase transition between K and R spaces. Our work opens avenues for exploring unconventional quantum states and topological phase transitions in different spaces.