  We derive a general low-energy theory for twisted moir\'e heterostructures
comprised of Dirac materials. We apply our theory to heterostructures on the
surface of a three dimensional topological insulator (3D TI). First, we
consider the interface between two 3D TIs arranged with a relative twist angle.
We prove that if the two TIs are identical, then a necessary condition for a
magic angle where the Dirac cone velocity vanishes is to have an interlayer
spin-flipping hopping term. Without this term, the Dirac cone velocities can
still be significantly renormalized, decreasing to less than half of their
original values, but they will not vanish. Second, we consider graphene on the
surface of a TI arranged with a small twist angle. Again, a magic angle is only
achievable with a spin-flipping hopping term. Without this term, the Dirac cone
is renormalized, but not significantly. In both cases, our perturbative results
are verified by computing the band structure of the continuum model. The
enhanced density of states that results from decreasing the surface Dirac cone
velocity provides a tunable route to realizing interacting topological phases.
