Doping-induced Topological Magnetism: from Quantum Anomalous Hall crystals to Topological Domain Walls

Doping carriers into a correlated quantum ground state offers a promising route to generate new quantum states. The recent advent of moiré superlattices provided a versatile platform with great tunability to explore doping physics in systems with strong interplay between strong correlations and nontrivial topology. We explore the effect of electron doping in the quantum anomalous Hall insulator realized in a TMD moiré superlatice at an integer filling, which can be qualitatively described by the canonical Kane-Mele-Hubbard model. Using an unrestricted real-space Hartree-Fock method, we will show that doping can induce rich translational symmetry breaking quantum states, including quantum anomalous Hall crystals (QAHC) and topological domain walls. In the QAHC, doping induces skyrmion spin textures, which can host one or two electrons in each skyrmion. At finite density of doped electrons, the skyrmions can crystallize into a lattice, with a density-tunable lattice parameter. We will finish by showing some preliminary density-matrix-renormalization-group results for the same model, focusing on the stability of the QAHC to quantum fluctuations.