  Using the continuum model for low energy non-interacting electronic structure
of moir\'e van der Waals heterostructures developed by Bistritzer and MacDonald
[1], we study the competition between spin, charge, and superconducting order
in twisted bilayer graphene. Surprisingly, we find that for a range of small
angles inclusive of the so-called magic angle, this model features robust Fermi
pockets that preclude any Mott insulating phase at weak coupling. However, a
Fermi surface reconstruction at $\theta \gtrsim 1.2^{\circ}$ gives emergent van
Hove singularities without any Fermi pockets. Using a hot-spot model for Fermi
surface patches around these emergent saddle points, we develop a random-phase
approximation from which we obtain a phase diagram very similar to that
obtained recently by Isobe, Yuan, and Fu using the parquet renormalization
group [2] but with additional insights. For example, our model shows strong
nesting around time-reversal symmetric points at a moderate doping of $\sim 2
\times 10^{11} \text{cm}^{-2}$ away from the van Hove singularity. When this
nesting dominates, we predict that charge-order enhances singlet
superconductivity, while spin-order suppresses superconductivity. Our theory
also provides additional possibilities for the case of unnested Fermi surfaces.
