Two dimensional moiré systems have recently emerged as a platform in which the interplay between topology and strong correlations of electrons play out in nontrivial ways. Among these systems, twisted double bilayer graphene (TDBG) is of particular interest as its topological properties may be tuned via both twist angle and applied perpendicular electric field. In this system, energy gaps are observed at half filling of particular bands, which can be associated with correlated spin polarized states. In this work, we investigate the fate of these states as the system is doped away from this filling. We demonstrate that, for a broad range of fractional fillings, the resulting ground state is partially valley polarized, and supports multiple broken symmetries, including a textured spin order indicative of skyrmions, with a stripe ordering that spontaneously breaks $C_3$ symmetry. Experimental signatures of this state are discussed.

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• Skyrmions
• Graphene
• Twisted heterostructures
• Hartree-Fock methods