Skyrmion Fractional Chern Insulator: An Intrinsically Multiband Route to Fractionalization in Rhombohedral Graphene

Abstract

We propose an unconventional microscopic origin for the fractional quantum anomalous Hall (FQAH) effect in rhombohedral graphene moir\'e superlattices: skyrmion fractionalization. We view the state at filling $\nu<1$ as a metal of skyrmion vacancies, charge $+e$ objects formed by removing layer-pseudospin skyrmions from the interaction-generated skyrmion lattice Chern insulator at $\nu=1$. These vacancies are intrinsically multiband degrees of freedom, absent in single Chern band-projected studies. Building on a recently proposed ideal limit, we first develop an effective field theory showing that skyrmion vacancies can themselves fractionalize, thereby inducing charge fractionalization. Focusing on $\nu=\frac{2}{3}$, we then construct explicit variational trial wavefunctions for the resulting skyrmion fractional Chern insulator and provide numerical evidence, together with general arguments, showing that this process is energetically favored. Our results establish a realistic route to the FQAH that does not rely on a partially filled Chern band, but instead arises from fractionalization of collective pseudospin textures.