From electrons to baby skyrmions in Chern ferromagnets: A topological mechanism for spin-polaron formation in twisted bilayer graphene

Abstract: The advent of Moir\'e materials has galvanized interest in the nature of charge carriers in topological bands. In contrast to conventional materials where charge carriers are electron-like quasiparticles, topological bands allow for more exotic possibilities where charge is carried by nontrivial topological textures, such as skyrmions. However, the real space description of skyrmions is ill-suited to address the limit of small or `baby' skyrmions which consist of an electron and a few spin flips. Here, we study the formation of the smallest skyrmions -- spin polarons, formed as bound states of an electron and a spin flip -- in Chern ferromagnets. We show that, quite generally, there is an attraction between an electron and a spin flip that is purely topological in origin and of $p$-wave symmetry, which promotes the formation of spin polarons. Applying our results to the topological bands of twisted bilayer graphene, we identify a range of parameters where spin polarons are formed and are lower in energy than electrons. In particular, spin polarons are found to be energetically cheaper on doping correlated insulators at integer fillings towards charge neutrality, consistent with the absence of quantum oscillations and the rapid onset of flavor polarization (cascade) transition in this regime. Our study sets the stage for pairing of spin polarons, helping bridge skyrmion pairing scenarios and momentum space approaches to superconductivity.