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General continuum model for twisted bilayer graphene and arbitrary smooth deformations

by Leon Balents

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Submission summary

Authors (as registered SciPost users): Leon Balents
Submission information
Preprint Link:  (pdf)
Date accepted: 2019-10-01
Date submitted: 2019-09-05 02:00
Submitted by: Balents, Leon
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Condensed Matter Physics - Theory
Approach: Theoretical


We present a simple derivation of a continuum Hamiltonian for bilayer graphene with an arbitrary smooth lattice deformation -- technically in a fashion parametrized by displacement fields with small gradients. We show that this subsumes the continuum model of Bistritzer and Macdonald for twisted bilayer grapheneas well as many generalizations and extensions of it. The derivation is carried out entirely in real space.

Published as SciPost Phys. 7, 048 (2019)

Submission & Refereeing History

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Submission 1909.01545v1 on 5 September 2019

Reports on this Submission

Anonymous Report 1 on 2019-9-27 (Invited Report)

  • Cite as: Anonymous, Report on arXiv:1909.01545v1, delivered 2019-09-27, doi: 10.21468/SciPost.Report.1201


Moire patterns can affect the low energy electronic structure in twisted bilayer graphene and provide unprecedented platform for correlated electron physics. A popular method to calculate the low energy electron band structure is the so called continuum model. The original continuum model written in momentum space is hard to use when lattice relaxation and strain effects come in. The current paper derives the continuum model from a real space point of view, which can easily incorporate these effects, hence is very useful for the community. It may also be helpful for future studies of disorder effects in twisted bilayer graphene.

The derivation and presentation is very clear. I would recommend the publication of the paper without any change.

  • validity: top
  • significance: top
  • originality: top
  • clarity: top
  • formatting: perfect
  • grammar: perfect

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