Topological flat bands, valley polarization, and interband superconductivity in magic-angle twisted bilayer graphene with proximitized spin-orbit couplings

We study theoretically the magic-angle twisted bilayer graphene with\nproximity-induced Ising and Rashba spin-orbit couplings on the top layer.\nTopological flat bands (with three distinct phases) are generically realized by\nthe spin-orbit couplings. Using a mean field analysis, we find that (partial)\nvalley polarization prevails for a wide range of doping, suppressing the usual\nsuperconductivity with a pairing between time-reversal partners. Remarkably, we\nuncover that observable unconventional intervalley interband phonon-mediated\nsuperconductivity (with the highest $T_c\\approx 1.2$K) can coexist with strong\nvalley imbalance due to the approximate Fermi surface nesting between two flat\nbands not related by time-reversal symmetry, and the dominant pairing is an\nintersublattice Ising pairing, corresponding to a mixture of $p$- and\n$d$-waves. In contrast, the intrasublattice Ising phonon-mediated\nsuperconductivity with $s$- and $f$-wave mixing emerges in the absence of\nvalley imbalance. Our work reveals an unprecedented route of realizing\nunconventional superconductivity.\n