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

Journal Article · 09 October 2019 · SciPost Physics

DOI: https://doi.org/10.21468/SciPostPhys.7.4.048 · OSTI ID:1570016

Balents, Leon ^[1]

Canadian Institute for Advanced Research, Kavli Institute for Theoretical Physics

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.

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Sponsoring Organization:: USDOE

Grant/Contract Number:: FG02-08ER46524

OSTI ID:: 1570016

Journal Information:: SciPost Physics, Journal Name: SciPost Physics Journal Issue: 4 Vol. 7; ISSN 2542-4653

Publisher:: Stichting SciPostCopyright Statement

Country of Publication:: Netherlands

Language:: English

References (20)

Correlated insulator behaviour at half-filling in magic-angle graphene superlattices Cao, Yuan; Fatemi, Valla; Demir, Ahmet Nature, Vol. 556, Issue 7699 https://doi.org/10.1038/nature26154	journal	March 2018
Unconventional superconductivity in magic-angle graphene superlattices Cao, Yuan; Fatemi, Valla; Fang, Shiang Nature, Vol. 556, Issue 7699 https://doi.org/10.1038/nature26160	journal	March 2018
Giant oscillations in a triangular network of one-dimensional states in marginally twisted graphene Xu, S. G.; Berdyugin, A. I.; Kumaravadivel, P. Nature Communications, Vol. 10, Issue 1 https://doi.org/10.1038/s41467-019-11971-7	journal	September 2019
Atomic and electronic reconstruction at the van der Waals interface in twisted bilayer graphene Yoo, Hyobin; Engelke, Rebecca; Carr, Stephen Nature Materials, Vol. 18, Issue 5 https://doi.org/10.1038/s41563-019-0346-z	journal	April 2019
Electronic correlations in twisted bilayer graphene near the magic angle Choi, Youngjoon; Kemmer, Jeannette; Peng, Yang Nature Physics, Vol. 15, Issue 11 https://doi.org/10.1038/s41567-019-0606-5	journal	August 2019
Maximized electron interactions at the magic angle in twisted bilayer graphene Kerelsky, Alexander; McGilly, Leo J.; Kennes, Dante M. Nature, Vol. 572, Issue 7767 https://doi.org/10.1038/s41586-019-1431-9	journal	July 2019
Moire bands in twisted double-layer graphene Bistritzer, R.; MacDonald, A. H. Proceedings of the National Academy of Sciences, Vol. 108, Issue 30 https://doi.org/10.1073/pnas.1108174108	journal	July 2011
Tunable moiré bands and strong correlations in small-twist-angle bilayer graphene Kim, Kyounghwan; DaSilva, Ashley; Huang, Shengqiang Proceedings of the National Academy of Sciences, Vol. 114, Issue 13 https://doi.org/10.1073/pnas.1620140114	journal	March 2017
Designing flat bands by strain Bi, Zhen; Yuan, Noah F. Q.; Fu, Liang Physical Review B, Vol. 100, Issue 3 https://doi.org/10.1103/PhysRevB.100.035448	journal	July 2019
Dynamics of the charge-density wave. I. Impurity pinning in a single chain Fukuyama, H.; Lee, P. A. Physical Review B, Vol. 17, Issue 2 https://doi.org/10.1103/PhysRevB.17.535	journal	January 1978
Electric field depinning of charge density waves Lee, P. A.; Rice, T. M. Physical Review B, Vol. 19, Issue 8 https://doi.org/10.1103/PhysRevB.19.3970	journal	April 1979
Phonons and electron-phonon scattering in carbon nanotubes Suzuura, Hidekatsu; Ando, Tsuneya Physical Review B, Vol. 65, Issue 23 https://doi.org/10.1103/PhysRevB.65.235412	journal	May 2002
Lattice relaxation and energy band modulation in twisted bilayer graphene Nam, Nguyen N. T.; Koshino, Mikito Physical Review B, Vol. 96, Issue 7 https://doi.org/10.1103/PhysRevB.96.075311	journal	August 2017
Strong electron-phonon coupling, electron-hole asymmetry, and nonadiabaticity in magic-angle twisted bilayer graphene Choi, Young Woo; Choi, Hyoung Joon Physical Review B, Vol. 98, Issue 24 https://doi.org/10.1103/PhysRevB.98.241412	journal	December 2018
Phonon-induced giant linear-in- T resistivity in magic angle twisted bilayer graphene: Ordinary strangeness and exotic superconductivity Wu, Fengcheng; Hwang, Euyheon; Das Sarma, Sankar Physical Review B, Vol. 99, Issue 16 https://doi.org/10.1103/PhysRevB.99.165112	journal	April 2019
Theory of Phonon-Mediated Superconductivity in Twisted Bilayer Graphene Wu, Fengcheng; MacDonald, A. H.; Martin, Ivar Physical Review Letters, Vol. 121, Issue 25 https://doi.org/10.1103/PhysRevLett.121.257001	journal	December 2018
Twisted Bilayer Graphene: A Phonon-Driven Superconductor Lian, Biao; Wang, Zhijun; Bernevig, B. Andrei Physical Review Letters, Vol. 122, Issue 25 https://doi.org/10.1103/PhysRevLett.122.257002	journal	June 2019
The electronic properties of graphene Castro Neto, A. H.; Guinea, F.; Peres, N. M. R. Reviews of Modern Physics, Vol. 81, Issue 1, p. 109-162 https://doi.org/10.1103/RevModPhys.81.109	journal	January 2009
Tuning superconductivity in twisted bilayer graphene Yankowitz, Matthew; Chen, Shaowen; Polshyn, Hryhoriy Science, Vol. 363, Issue 6431 https://doi.org/10.1126/science.aav1910	journal	January 2019
Emergent ferromagnetism near three-quarters filling in twisted bilayer graphene Sharpe, Aaron L.; Fox, Eli J.; Barnard, Arthur W. Science, Vol. 365, Issue 6453 https://doi.org/10.1126/science.aaw3780	journal	July 2019

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