In this talk, I will explore the emergent physics resulting from the complex interaction between real-space and momentum-space topology in strongly correlated quantum materials, with a particular focus on skyrmions. Using quantum Hall and quantum spin Hall insulators as key examples, I will explain the mechanisms behind skyrmion formation through electron doping in these correlated and gapped topological systems. We provide a detailed analysis of the phase diagrams and the formation of skyrmion lattices within the Kane-Mele-Hubbard model, supported by calculations from both the unrestricted real-space Hartree-Fock and density matrix renormalization group methods. In these systems, the doped electron and skyrmion form a composite object whose density is governed by the doped electron density. This electron-skyrmion bound state is stabilized by the coupling between the orbital magnetization of the Chern band and the emergent magnetic flux generated by the skyrmion. Moreover, we find that doping induces quantum anomalous Hall crystals, which exhibit quantized Hall conductance and broken translational symmetry. Our theory offers an intrinsic mechanism for the experimentally observed robust quantum anomalous Hall insulator over an extended doping range near a filling factor of ν = 1 in twisted transition metal moiré superlattices.

Reference: Miguel Gonçalves and Shi-Zeng Lin, arXiv:2407.12198