  Magic-angle twisted bilayer graphene (TBG) exhibits a captivating phase
diagram as a function of doping, featuring superconductivity and a variety of
insulating and magnetic states. The bands host Dirac fermions with a reduced
Fermi velocity; experiments have shown that the Dirac dispersion reappears near
integer fillings of the moir\'e unit cell -- referred to as the $\textit{Dirac
revival}$ phenomenon. The reduced velocity of these Dirac states leads us to
propose a scenario in which the Dirac fermions possess an approximately
quadratic dispersion. The quadratic momentum dependence and particle-hole
degeneracy at the Dirac point results in a logarithmic enhancement of
interaction effects, which does not appear for a linear dispersion. The
resulting non-trivial renormalisation group (RG) flow naturally produces the
qualitative phase diagram as a function of doping -- with nematic and
insulating states near integer fillings, which give way to superconducting
states past a critical relative doping. The RG method further produces
different results to strong-coupling Hartree-Fock treatments: producing T-IVC
insulating states for repulsive interactions, explaining the results of very
recent STM experiments, alongside nodal $A_2$ superconductivity near
half-filling, whose properties explain puzzles in tunnelling studies of the
superconducting state. The model explains a diverse range of additional
experimental observations, unifying many aspects of the phase diagram of TBG.
