17 Apr 2007 | J. M. B. Lopes dos Santos, N. M. R. Peres, and A. H. Castro Neto
This paper investigates the electronic structure of a graphene bilayer with a small angle rotation between the layers, which is different from the conventional AB or Bernal stacking. The authors calculate the electronic structure near zero energy using a continuum approximation and find that the low energy dispersion is linear, similar to a single layer graphene, but with a significantly reduced Fermi velocity. Additionally, an external electric field perpendicular to the layers does not open an electronic gap, in contrast to the AB stacked bilayer.
The study considers a bilayer with a relative small angle rotation, leading to the formation of periodic Moire superlattices. The electronic structure is described using massless Dirac fermions coupled by a slowly varying periodic inter-layer hopping. The results show that the electronic behavior is similar to that of epitaxial graphene, with a reduced Fermi velocity compared to single layer graphene.
The geometry of the system is described with two sublattices in each layer, and the rotation of one layer relative to the other leads to a shift in the wave vector. The authors derive a condition for the angle of a commensurate rotation and formulate a continuum electronic description. The results show that the Dirac cones remain present in the bilayer, but with a significant reduction in Fermi velocity, especially for small angles of rotation.
The study also considers the effect of an electric potential difference between the layers. It is found that a potential difference does not open a gap in the electronic spectrum, unlike in the AB stacked bilayer. The results are consistent with observations in epitaxial graphene, where the electronic behavior is similar to that of single layer graphene, but with a reduced Fermi velocity.
The authors conclude that a small stacking defect, such as a rotation between the layers, can significantly affect the low energy properties of the bilayer. The results are in agreement with several observations in epitaxial graphene, showing that the electronic structure of a bilayer with a twist is distinct from that of a conventional AB stacked bilayer.This paper investigates the electronic structure of a graphene bilayer with a small angle rotation between the layers, which is different from the conventional AB or Bernal stacking. The authors calculate the electronic structure near zero energy using a continuum approximation and find that the low energy dispersion is linear, similar to a single layer graphene, but with a significantly reduced Fermi velocity. Additionally, an external electric field perpendicular to the layers does not open an electronic gap, in contrast to the AB stacked bilayer.
The study considers a bilayer with a relative small angle rotation, leading to the formation of periodic Moire superlattices. The electronic structure is described using massless Dirac fermions coupled by a slowly varying periodic inter-layer hopping. The results show that the electronic behavior is similar to that of epitaxial graphene, with a reduced Fermi velocity compared to single layer graphene.
The geometry of the system is described with two sublattices in each layer, and the rotation of one layer relative to the other leads to a shift in the wave vector. The authors derive a condition for the angle of a commensurate rotation and formulate a continuum electronic description. The results show that the Dirac cones remain present in the bilayer, but with a significant reduction in Fermi velocity, especially for small angles of rotation.
The study also considers the effect of an electric potential difference between the layers. It is found that a potential difference does not open a gap in the electronic spectrum, unlike in the AB stacked bilayer. The results are consistent with observations in epitaxial graphene, where the electronic behavior is similar to that of single layer graphene, but with a reduced Fermi velocity.
The authors conclude that a small stacking defect, such as a rotation between the layers, can significantly affect the low energy properties of the bilayer. The results are in agreement with several observations in epitaxial graphene, showing that the electronic structure of a bilayer with a twist is distinct from that of a conventional AB stacked bilayer.