Nematic skyrmion crystals in Twisted Double Bilayer Graphene systems

Two-dimensional moire systems have recently emerged as a platform that can be used to study the interplay between topology and strong correlations. In particular, twisted double bilayer graphene (TDBG) is one such system whose topological properties can be changed in a controlled manner by tuning experimental parameters such as an applied displacement field. Spin-polarized correlated gaps have been previously observed in TDBG for half-filled conduction bands. In this work, we investigate the fate of the correlated state as we dope the system away from half-filling. We show that the added electrons form a nematic skyrmion crystal for some commensurate fillings of the conduction band. We report that the stability of the crystal state strongly depends on the localization of the Berry curvature in the moire Brillouin Zone. Lastly, we extend our analysis to higher Chern number cases where we find similar low-energy solutions.