Mixed-valence Mott insulator and composite excitation in twisted bilayer graphene

The interplay of strong correlation and flat topological bands is a central problem in moir\'e systems such as magic-angle twisted bilayer graphene (TBG). In this work, we construct the ground state wave function and exotic excitations for correlated phases in TBG at even integer fillings. At a filling of $\ensuremath{\nu}=\ensuremath{-}2$, our findings challenge the conventional picture of a simple Mott insulator with local moments on AA sites. We instead identify a mixed-valence Mott insulating phase, where a fraction of AA sites are self-doped, placing them in a quantum superposition of two- and three-electron occupancies. This state exhibits a momentum-space-differentiated electronic structure: a large Mott gap, on the order of the Hubbard $U$, is present throughout most of the Brillouin zone, while a much smaller charge-transfer gap emerges at the $\mathrm{\ensuremath{\Gamma}}$ point. Notably, the top of the lower band at $\mathrm{\ensuremath{\Gamma}}$ point is dominated by a composite excitation, an emergent quasiparticle orthogonal to the microscopic electron operator. A similar approach at charge neutrality ($\ensuremath{\nu}=0$) describes a correlated Mott semimetal. Our work introduces a new framework for understanding Mott physics in topological flat bands, laying a crucial foundation for future investigations of superconductivity upon doping.