Helical Network Model for Twisted Bilayer Graphene

TL;DR

This paper introduces a helical network model to describe the low-energy electronic properties of twisted bilayer graphene under finite displacement fields, capturing the effects of stacking and moiré patterns.

Contribution

The study develops a phenomenological helical network model that accurately describes the low-energy physics of twisted bilayer graphene with displacement fields, highlighting the role of domain wall states.

Findings

Network band structure is gapless.

Presence of Dirac points in the band structure.

Density of states is periodic with zero and divergence points.

Abstract

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.