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 · 10 October 2019 · SciPost Physics

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

Balents, Leon ^[1]

Univ. of California, Santa Barbara, CA (United States). Kavli Inst. for Theoretical Physics; Canadian Inst. for Advanced Research, Toronto, ON (Canada)

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

Sponsoring Organization:: USDOE Office of Science (SC)

Grant/Contract Number:: FG02-08ER46524

OSTI ID:: 1570016

Alternate ID(s):: OSTI ID: 1800575

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

Publisher:: SciPost FoundationCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 25 works

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References (30)

The electronic properties of graphene Neto, A. H. Castro; Guinea, F.; Peres, N. M. R. arXiv https://doi.org/10.48550/arxiv.0709.1163	text	January 2007
Designing Flat Band by Strain Bi, Zhen; Yuan, Noah F. Q.; Fu, Liang arXiv https://doi.org/10.48550/arxiv.1902.10146	text	January 2019
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
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
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
Moire bands in twisted double-layer graphene Bistritzer, R.; MacDonald, A. H. arXiv https://doi.org/10.48550/arxiv.1009.4203	text	January 2010
Phonon-induced giant linear-in-$T$ resistivity in magic angle twisted bilayer graphene: Ordinary strangeness and exotic superconductivity Wu, Fengcheng; Hwang, Euyheon; Sarma, Sankar Das arXiv https://doi.org/10.48550/arxiv.1811.04920	text	January 2018
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
Tuning superconductivity in twisted bilayer graphene Yankowitz, Matthew; Chen, Shaowen; Polshyn, Hryhoriy arXiv https://doi.org/10.48550/arxiv.1808.07865	text	January 2018
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
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
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
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
Theory of phonon-mediated superconductivity in twisted bilayer graphene Wu, Fengcheng; MacDonald, A. H.; Martin, Ivar arXiv https://doi.org/10.48550/arxiv.1805.08735	text	January 2018
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
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
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
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
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
An Information Theory-Inspired Strategy for Design of Re-programmable Encrypted Graphene-based Coding Metasurfaces at Terahertz Frequencies Momeni, Ali; Rouhi, Kasra; Rajabalipanah, Hamid Scientific Reports, Vol. 8, Issue 1 https://doi.org/10.1038/s41598-018-24553-2	journal	April 2018
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
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
Electronic correlations in twisted bilayer graphene near the magic angle Choi, Youngjoon; Oppen, Felix Von; Kemmer, Jeannette Freie Universität Berlin https://doi.org/10.17169/refubium-26581	text	January 2019
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
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
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
Imaging Electronic Correlations in Twisted Bilayer Graphene near the Magic Angle Choi, Youngjoon; Kemmer, Jeannette; Peng, Yang arXiv https://doi.org/10.48550/arxiv.1901.02997	text	January 2019
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
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
Atomic and electronic reconstruction at van der Waals interface in twisted bilayer graphene Yoo, Hyobin; Engelke, Rebecca; Carr, Stephen arXiv https://doi.org/10.48550/arxiv.1804.03806	text	January 2018

Cited By (3)

Fractal non-Fermi liquids from moiré Hofstadter phonons Kumar, Ajesh; Cheng, Zihan; Potter, Andrew C. Physical Review B, Vol. 102, Issue 23 https://doi.org/10.1103/physrevb.102.235120	journal	December 2020
Electrodynamics of Thin Sheets of Twisted Material Nguyen, Dung Xuan; Son, Dam Thanh arXiv https://doi.org/10.48550/arxiv.2008.02812	preprint	January 2020
Magnetism and charge order in the honeycomb lattice Costa, Natanael C.; Seki, Kazuhiro; Sorella, Sandro arXiv https://doi.org/10.48550/arxiv.2009.05586	text	January 2020

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