General continuum model for twisted bilayer graphene and arbitrary smooth deformations

Balents, Leon

doi:10.21468/SciPostPhys.7.4.048

Title: General continuum model for twisted bilayer graphene and arbitrary smooth deformations

Abstract

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 graphene as well as many generalizations and extensions of it. The derivation is carried out entirely in real space.

Authors:

Balents, Leon ^[1]

Canadian Institute for Advanced Research, Kavli Institute for Theoretical Physics

Publication Date:: 2019-10-10

Research Org.:: Univ. of California, Santa Barbara, CA (United States)

Sponsoring Org.:: USDOE Office of Science (SC)

OSTI Identifier:: 1570016

Alternate Identifier(s):: OSTI ID: 1800575

Grant/Contract Number:: FG02-08ER46524

Resource Type:: Published Article

Journal Name:: SciPost Physics Proceedings

Additional Journal Information:: Journal Name: SciPost Physics Proceedings Journal Volume: 7 Journal Issue: 4; Journal ID: ISSN 2542-4653

Publisher:: Stichting SciPost

Country of Publication:: Netherlands

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Physics

Citation Formats


                    Balents, Leon. General continuum model for twisted bilayer graphene and arbitrary smooth deformations.  Netherlands: N. p., 2019. 
Web.  doi:10.21468/SciPostPhys.7.4.048.

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                    Balents, Leon. General continuum model for twisted bilayer graphene and arbitrary smooth deformations.  Netherlands.  https://doi.org/10.21468/SciPostPhys.7.4.048

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                    Balents, Leon. Thu .  
"General continuum model for twisted bilayer graphene and arbitrary smooth deformations".  Netherlands.  https://doi.org/10.21468/SciPostPhys.7.4.048.

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@article{osti_1570016,

  title        = {General continuum model for twisted bilayer graphene and arbitrary smooth deformations},

  author       = {Balents, Leon},

  abstractNote = {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 graphene as well as many generalizations and extensions of it. The derivation is carried out entirely in real space.},

  doi          = {10.21468/SciPostPhys.7.4.048},

  journal      = {SciPost Physics Proceedings},

  number       = 4,

  volume       = 7,

  place        = {Netherlands},

  year         = {2019},

  month        = {10}

}

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Works referenced in this record:

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Title: General continuum model for twisted bilayer graphene and arbitrary smooth deformations

Abstract

Citation Formats

Moire bands in twisted double-layer graphene journal, July 2011

Correlated insulator behaviour at half-filling in magic-angle graphene superlattices journal, March 2018

Phonon-induced giant linear-in- T resistivity in magic angle twisted bilayer graphene: Ordinary strangeness and exotic superconductivity journal, April 2019

Atomic and electronic reconstruction at the van der Waals interface in twisted bilayer graphene journal, April 2019

Unconventional superconductivity in magic-angle graphene superlattices journal, March 2018

Tuning superconductivity in twisted bilayer graphene journal, January 2019

Giant oscillations in a triangular network of one-dimensional states in marginally twisted graphene journal, September 2019

Dynamics of the charge-density wave. I. Impurity pinning in a single chain journal, January 1978

Tunable moiré bands and strong correlations in small-twist-angle bilayer graphene journal, March 2017

Emergent ferromagnetism near three-quarters filling in twisted bilayer graphene journal, July 2019

The electronic properties of graphene journal, January 2009

Lattice relaxation and energy band modulation in twisted bilayer graphene journal, August 2017

Strong electron-phonon coupling, electron-hole asymmetry, and nonadiabaticity in magic-angle twisted bilayer graphene journal, December 2018

Electronic correlations in twisted bilayer graphene near the magic angle journal, August 2019

Designing flat bands by strain journal, July 2019

Twisted Bilayer Graphene: A Phonon-Driven Superconductor journal, June 2019

Phonons and electron-phonon scattering in carbon nanotubes journal, May 2002

Maximized electron interactions at the magic angle in twisted bilayer graphene journal, July 2019

Theory of Phonon-Mediated Superconductivity in Twisted Bilayer Graphene journal, December 2018

Electric field depinning of charge density waves journal, April 1979

Moire bands in twisted double-layer graphene
journal, July 2011

Correlated insulator behaviour at half-filling in magic-angle graphene superlattices
journal, March 2018

Phonon-induced giant linear-in- $T$ resistivity in magic angle twisted bilayer graphene: Ordinary strangeness and exotic superconductivity
journal, April 2019

Atomic and electronic reconstruction at the van der Waals interface in twisted bilayer graphene
journal, April 2019

Unconventional superconductivity in magic-angle graphene superlattices
journal, March 2018

Tuning superconductivity in twisted bilayer graphene
journal, January 2019

Giant oscillations in a triangular network of one-dimensional states in marginally twisted graphene
journal, September 2019

Dynamics of the charge-density wave. I. Impurity pinning in a single chain
journal, January 1978

Tunable moiré bands and strong correlations in small-twist-angle bilayer graphene
journal, March 2017

Emergent ferromagnetism near three-quarters filling in twisted bilayer graphene
journal, July 2019

The electronic properties of graphene
journal, January 2009

Lattice relaxation and energy band modulation in twisted bilayer graphene
journal, August 2017

Strong electron-phonon coupling, electron-hole asymmetry, and nonadiabaticity in magic-angle twisted bilayer graphene
journal, December 2018

Electronic correlations in twisted bilayer graphene near the magic angle
journal, August 2019

Designing flat bands by strain
journal, July 2019

Twisted Bilayer Graphene: A Phonon-Driven Superconductor
journal, June 2019

Phonons and electron-phonon scattering in carbon nanotubes
journal, May 2002

Maximized electron interactions at the magic angle in twisted bilayer graphene
journal, July 2019

Theory of Phonon-Mediated Superconductivity in Twisted Bilayer Graphene
journal, December 2018

Electric field depinning of charge density waves
journal, April 1979