Tunable superconductivity and M\"obius Fermi surfaces in an inversion-symmetric twisted van der Waals heterostructure

We study theoretically a moir\'e superlattice geometry consisting of mirror-symmetric twisted trilayer graphene surrounded by identical transition metal dichalcogenide layers. We show that this setup allows to switch on/off and control the spin-orbit splitting of the Fermi surfaces via application of a perpendicular displacement field $D_0$, and explore two manifestations of this control: first, we compute the evolution of superconducting pairing with $D_0$; this features a complex admixture of singlet and triplet pairing and, depending on the pairing state in the parent trilayer system, phase transitions between competing superconducting phases. Second, we reveal that, with application of $D_0$, the spin-orbit-induced spin textures exhibit vortices which lead to "M\"obius fermi surfaces'' in the interior of the Brillouin zone: diabatic electron trajectories, which are predicted to dominate quantum oscillation experiments, require encircling the $\Gamma$ point twice, making their M\"obius nature directly observable. We further show that the superconducting order parameter inherits the unconventional, M\"obius spin textures. Our findings suggest that this system provides a promising experimental avenue for studying systematically the impact of spin-orbit coupling on the multitude of topological and correlated phases in near-magic-angle twisted trilayer graphene.