Pairing in twisted double-bilayer graphene and related moiré superlattice systems

We present a systematic classification and analysis of possible pairing instabilities in graphene-based moiré superlattices. Motivated by recent experiments on twisted double-bilayer graphene showing signs of triplet superconductivity, we analyze both singlet and triplet pairing separately, and describe how these two channels behave close to the limit where the system is invariant under separate spin rotations in the two valleys, realizing an SU(2)₊ × SU(2)_- symmetry. Further, we discuss the conditions under which singlet and triplet can mix via two nearly degenerate transitions, and how the different pairing states behave when an external magnetic field is applied. We find that an approximate SU(2)₊ × SU(2)_- symmetry can generically account for the linear increase of the critical temperature with small magnetic fields, and we map out the possible forms of the phase diagram as a function of temperature and magnetic field. Finally, we also detail the differences in the classification when the additional microscopic or emergent symmetries relevant for twisted bilayer graphene and ABC trilayer graphene on hexagonal boron nitride are taken into account.