  In the presence of a finite interlayer displacement field bilayer graphene
has an energy gap that is dependent on stacking and largest for the stable AB
and BA stacking arrangements. When the relative orientations between layers are
twisted through a small angle to form a moir$\mathrm{\acute{e}}$ pattern, the
local stacking arrangement changes slowly. We show that for non-zero
displacement fields the low-energy physics of twisted bilayers is captured by a
phenomenological helical network model that describes electrons localized on
domain walls separating regions with approximate AB and BA stacking. The
network band structure is gapless and has of a series of two-dimensional bands
with Dirac band-touching points and a density-of-states that is periodic in
energy with one zero and one divergence per period.

Mesoscale and Nanoscale Physics