Helical Network Model for Twisted Bilayer Graphene

Understand

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.