Flat bands and superconductivity: Applications to ABC-stacked graphite and magic-angle twisted bilayer graphene

Materials with flat energy bands close to the Fermi level generally exhibit extraordinary high critical ordering temperatures for symmetry breaking orders. Here we show that the critical temperatures follow one of two universal phase diagram curves with doping away from the flat band, depending on it being superconducting or magnetic/charge ordering. Notably, we find that superconductivity survives to decisively higher doping, and thus, even if a magnetic or charge order initially dominates, superconducting domes are still likely to exist on the flanks of flat bands. As an example, we illustrate how these results can be applied to the topological surface flat bands of rhombohedral ABC-stacked graphite.

It has recently also been shown that bilayer graphene with small internal twist angles develops large scale moiré patterns with flat bands hosting correlated insulating states flanked by superconducting domes. The large system size and intricate band structure have however hampered investigations into the properties of the superconducting state. Here we use full-scale atomistic modeling and find a highly inhomogeneous superconducting state with nematic ordering on both the atomic and moiré lattice length scales. More specifically, we obtain locally anisotropic real-valued d-wave pairing with a nematic vector winding throughout the moiré cell, generating a three-fold ground state degeneracy. Despite the d-wave nature, the superconducting state has a full energy gap, which we further tie to a π-phase interlayer coupling. We also show that the superconducting nematicity is easily detected through signatures in the local density of states.