  The conventional low-energy theory employed to describe twisted bilayer
graphene (TBG) relies on a local interlayer Hamiltonian. According to this
theory, TBG has the same linear-in-momentum dispersion and spinor wave function
at the Dirac point as single-layer graphene (SLG), albeit with a renormalized
velocity that decreases as the rotation angle between the layers decreases,
eventually reaching zero at the magic angle. In this work, I expand upon this
low-energy theory by including nonlocal terms in the interlayer part of the
Hamiltonian, and explore the consequences at the Dirac point. It is found that
the nonlocality predominantly influences the wave function rather than the
energy spectrum: despite the persistence of the linear-in-momentum dispersion
with a renormalized velocity, the wave functions no longer mirror those of SLG.
Instead, an additional contribution to the phase difference between the
sublattice components of the spinor emerges. This gives rise to interesting
effects in scattering which are demonstrated with a simple example.
