  Magic-angle twisted bilayer graphene displays at different fillings of the
four flat bands lying around the charge neutrality point a wealth of notable
phases that include magnetic Chern insulators, whose magnetization is mostly of
orbital nature, and contiguous superconducting domes. Such rich phase diagram
is here explained through the positive interplay of Coulomb repulsion and the
electron coupling to a twofold optical mode that corresponds to Kekul\`e
distortions localized into the small AA stacked regions of the moir\'e
supercells. A static distortion stabilizes, at any integer filling of the flat
bands, valence-bond insulators that carry finite Chern number away from charge
neutrality. Similarly, a dynamic distortion that resonates between the two
lattice vibrations leads to resonating-valence-bond topological insulators with
built-in chiral d-wave pairs that have finite Chern number equal to the angular
momentum, and thus are prone to turn superconducting upon doping away from
integer filling.
