Charge excitations in graphene-based Moire materials

Graphene-based moire materials usually realize correlated insulators in the form of generalized spin, valley, or sublattice ferromagnets at different integer fillings. A key question is, what is the nature of charge carriers associated with doping these generalized Chern ferromagnets? In addition to single electron excitations, more exotic possibilities such as skyrmions are possible due to band topology where bands residing in opposite valleys or sublattices carry opposite Chern numbers. However, the description of skyrmions as real space topological textures is ill-suited to address momentum space features such as dispersion and the distribution of the Berry curvature which are crucial to understand their energy competition with single electrons and their relevance to low-energy physics. Here, I discuss a momentum-space formulation of the problem of charge excitations in a Chern ferromagnets by studying the bound states formed between single-electrons and spin flip excitations. Using this formulation, I will show what parameter regimes in different graphene-based Moire superlattice are most promising to hunt for non-trivial skyrmion-like charge excitations.