Theory of phonon-mediated superconductivity in twisted bilayer graphene

Wu, Fengcheng; MacDonald, A. H.; Martin, Ivar

doi:10.1103/PhysRevLett.121.257001

Title: Theory of phonon-mediated superconductivity in twisted bilayer graphene

Journal Article · Mon Dec 17 00:00:00 EST 2018 · Physical Review Letters

DOI:https://doi.org/10.1103/PhysRevLett.121.257001· OSTI ID:1490430

Wu, Fengcheng ^[1]; MacDonald, A. H. ^[2]; Martin, Ivar ^[3]

Argonne National Lab. (ANL), Argonne, IL (United States); Univ. of Maryland, College Park, MD (United States)
Univ. of Texas at Austin, Austin, TX (United States)
Argonne National Lab. (ANL), Argonne, IL (United States)

We present a theory of phonon-mediated superconductivity in near magic angle twisted bilayer graphene. Using a microscopic model for phonon coupling to moire band electrons, we find that phonons generate attractive interactions in both s- and d-wave pairing channels and that the attraction is strong enough to explain the experimental superconducting transition temperatures. Before including Coulomb repulsion, the s-wave channel is more favorable; however, on-site Coulomb repulsion can suppress s-wave pairing relative to d wave. The pair amplitude varies spatially with the moire period, and is identical in the two layers in the s-wave channel but phase shifted by π in the d-wave channel. In conclusion, we discuss experiments that can distinguish the two pairing states.

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Research Organization:: Argonne National Lab. (ANL), Argonne, IL (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). Materials Sciences & Engineering Division; Welch Foundation; USDOE

Grant/Contract Number:: AC02-06CH11357; FG02-02ER45958; TBF1473

OSTI ID:: 1490430

Alternate ID(s):: OSTI ID: 1487188

Journal Information:: Physical Review Letters, Vol. 121, Issue 25; ISSN 0031-9007

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 260 works

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References (38)

Moiré excitons: From programmable quantum emitter arrays to spin-orbit–coupled artificial lattices Yu, Hongyi; Liu, Gui-Bin; Tang, Jianju Science Advances, Vol. 3, Issue 11 https://doi.org/10.1126/sciadv.1701696	journal	November 2017
Strength of Effective Coulomb Interactions in Graphene and Graphite Wehling, T. O.; Şaşıoğlu, E.; Friedrich, C. Physical Review Letters, Vol. 106, Issue 23 https://doi.org/10.1103/PhysRevLett.106.236805	journal	June 2011
Phonon dispersions and vibrational properties of monolayer, bilayer, and trilayer graphene: Density-functional perturbation theory Yan, Jia-An; Ruan, W. Y.; Chou, M. Y. Physical Review B, Vol. 77, Issue 12 https://doi.org/10.1103/PhysRevB.77.125401	journal	March 2008
Graphene Bilayer with a Twist: Electronic Structure Lopes dos Santos, J. M. B.; Peres, N. M. R.; Castro Neto, A. H. Physical Review Letters, Vol. 99, Issue 25 https://doi.org/10.1103/PhysRevLett.99.256802	journal	December 2007
Topological Superconductivity in Twisted Multilayer Graphene Xu, Cenke; Balents, Leon Physical Review Letters, Vol. 121, Issue 8 https://doi.org/10.1103/PhysRevLett.121.087001	journal	August 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
Strained graphene: tight-binding and density functional calculations Ribeiro, R. M.; Pereira, Vitor M.; Peres, N. M. R. New Journal of Physics, Vol. 11, Issue 11 https://doi.org/10.1088/1367-2630/11/11/115002	journal	November 2009
Doped Twisted Bilayer Graphene near Magic Angles: Proximity to Wigner Crystallization, Not Mott Insulation Padhi, Bikash; Setty, Chandan; Phillips, Philip W. Nano Letters, Vol. 18, Issue 10 https://doi.org/10.1021/acs.nanolett.8b02033	journal	September 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
Theory of optical absorption by interlayer excitons in transition metal dichalcogenide heterobilayers Wu, Fengcheng; Lovorn, Timothy; MacDonald, A. H. Physical Review B, Vol. 97, Issue 3 https://doi.org/10.1103/PhysRevB.97.035306	journal	January 2018
Hofstadter’s butterfly and the fractal quantum Hall effect in moiré superlattices Dean, C. R.; Wang, L.; Maher, P. Nature, Vol. 497, Issue 7451 https://doi.org/10.1038/nature12186	journal	May 2013
Evidence for a fractional fractal quantum Hall effect in graphene superlattices Wang, L.; Gao, Y.; Wen, B. Science, Vol. 350, Issue 6265 https://doi.org/10.1126/science.aad2102	journal	December 2015
Model for the metal-insulator transition in graphene superlattices and beyond Yuan, Noah F. Q.; Fu, Liang Physical Review B, Vol. 98, Issue 4 https://doi.org/10.1103/PhysRevB.98.045103	journal	July 2018
Flat bands in slightly twisted bilayer graphene: Tight-binding calculations Suárez Morell, E.; Correa, J. D.; Vargas, P. Physical Review B, Vol. 82, Issue 12 https://doi.org/10.1103/PhysRevB.82.121407	journal	September 2010
Chiral Spin Density Wave and $d + i d$ Superconductivity in the Magic-Angle-Twisted Bilayer Graphene Liu, Cheng-Cheng; Zhang, Li-Da; Chen, Wei-Qiang Physical Review Letters, Vol. 121, Issue 21 https://doi.org/10.1103/PhysRevLett.121.217001	journal	November 2018
Interplay of Coulomb and electron-phonon interactions in graphene Basko, D. M.; Aleiner, I. L. Physical Review B, Vol. 77, Issue 4 https://doi.org/10.1103/PhysRevB.77.041409	journal	January 2008
Phases of a phenomenological model of twisted bilayer graphene Dodaro, J. F.; Kivelson, S. A.; Schattner, Y. Physical Review B, Vol. 98, Issue 7 https://doi.org/10.1103/PhysRevB.98.075154	journal	August 2018
Intrinsic and Rashba spin-orbit interactions in graphene sheets Min, Hongki; Hill, J. E.; Sinitsyn, N. A. Physical Review B, Vol. 74, Issue 16 https://doi.org/10.1103/PhysRevB.74.165310	journal	October 2006
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
Numerical studies of confined states in rotated bilayers of graphene Trambly de Laissardière, G.; Mayou, D.; Magaud, L. Physical Review B, Vol. 86, Issue 12 https://doi.org/10.1103/PhysRevB.86.125413	journal	September 2012
Ab initio theory of moiré superlattice bands in layered two-dimensional materials Jung, Jeil; Raoux, Arnaud; Qiao, Zhenhua Physical Review B, Vol. 89, Issue 20 https://doi.org/10.1103/PhysRevB.89.205414	journal	May 2014
Massive Dirac Fermions and Hofstadter Butterfly in a van der Waals Heterostructure Hunt, B.; Sanchez-Yamagishi, J. D.; Young, A. F. Science, Vol. 340, Issue 6139 https://doi.org/10.1126/science.1237240	journal	May 2013
Migdal's theorem and electron-phonon vertex corrections in Dirac materials Roy, Bitan; Sau, Jay D.; Das Sarma, S. Physical Review B, Vol. 89, Issue 16 https://doi.org/10.1103/PhysRevB.89.165119	journal	April 2014
Origin of Mott Insulating Behavior and Superconductivity in Twisted Bilayer Graphene Po, Hoi Chun; Zou, Liujun; Vishwanath, Ashvin Physical Review X, Vol. 8, Issue 3 https://doi.org/10.1103/PhysRevX.8.031089	journal	September 2018
Symmetry, Maximally Localized Wannier States, and a Low-Energy Model for Twisted Bilayer Graphene Narrow Bands Kang, Jian; Vafek, Oskar Physical Review X, Vol. 8, Issue 3 https://doi.org/10.1103/PhysRevX.8.031088	journal	September 2018
Maximally Localized Wannier Orbitals and the Extended Hubbard Model for Twisted Bilayer Graphene Koshino, Mikito; Yuan, Noah F. Q.; Koretsune, Takashi Physical Review X, Vol. 8, Issue 3 https://doi.org/10.1103/PhysRevX.8.031087	journal	September 2018
Topological Exciton Bands in Moiré Heterojunctions Wu, Fengcheng; Lovorn, Timothy; MacDonald, A. H. Physical Review Letters, Vol. 118, Issue 14 https://doi.org/10.1103/PhysRevLett.118.147401	journal	April 2017
Electrically Controllable Magnetism in Twisted Bilayer Graphene Gonzalez-Arraga, Luis A.; Lado, J. L.; Guinea, Francisco Physical Review Letters, Vol. 119, Issue 10 https://doi.org/10.1103/PhysRevLett.119.107201	journal	September 2017
Correlated electronic phases in twisted bilayer transition metal dichalcogenides Wang, Lei; Shih, En-Min; Ghiotto, Augusto Nature Materials, Vol. 19, Issue 8 https://doi.org/10.1038/s41563-020-0708-6	journal	June 2020
Moire bands in twisted double-layer graphene Bistritzer, R.; MacDonald, A. H. arXiv https://doi.org/10.48550/arxiv.1009.4203	text	January 2010
Numerical studies of confined states in rotated bilayers of graphene de Laissardière, G. Trambly; Mayou, D.; Magaud, L. arXiv https://doi.org/10.48550/arxiv.1203.3144	text	January 2012
Migdal's theorem and electron-phonon vertex corrections in Dirac materials Roy, Bitan; Sau, Jay Deep; Sarma, S. Das arXiv https://doi.org/10.48550/arxiv.1401.5056	text	January 2014
Electronic Structure Theory of Weakly Interacting Bilayers Fang, Shiang; Kaxiras, Efthimios arXiv https://doi.org/10.48550/arxiv.1604.05371	text	January 2016
Topological Superconductivity in Twisted Multilayer Graphene Xu, Cenke; Balents, Leon arXiv https://doi.org/10.48550/arxiv.1803.08057	text	January 2018
Model for Metal-Insulator Transition in Graphene Superlattices and Beyond Yuan, Noah F. Q.; Fu, Liang arXiv https://doi.org/10.48550/arxiv.1803.09699	text	January 2018
Origin of Mott insulating behavior and superconductivity in twisted bilayer graphene Po, Hoi Chun; Zou, Liujun; Vishwanath, Ashvin arXiv https://doi.org/10.48550/arxiv.1803.09742	text	January 2018
Doped Twisted Bilayer Graphene near Magic Angles: Proximity to Wigner Crystallization not Mott Insulation Padhi, Bikash; Setty, Chandan; Phillips, Philip W. arXiv https://doi.org/10.48550/arxiv.1804.01101	text	January 2018

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Theory of correlated insulating behaviour and spin-triplet superconductivity in twisted double bilayer graphene Lee, Jong Yeon; Khalaf, Eslam; Liu, Shang Nature Communications, Vol. 10, Issue 1 https://doi.org/10.1038/s41467-019-12981-1	journal	November 2019
Magic of high-order van Hove singularity Yuan, Noah F. Q.; Isobe, Hiroki; Fu, Liang Nature Communications, Vol. 10, Issue 1 https://doi.org/10.1038/s41467-019-13670-9	journal	December 2019
Large linear-in-temperature resistivity in twisted bilayer graphene Polshyn, Hryhoriy; Yankowitz, Matthew; Chen, Shaowen Nature Physics, Vol. 15, Issue 10 https://doi.org/10.1038/s41567-019-0596-3	journal	August 2019
Possible nodeless s ^± -wave superconductivity in twisted bilayer graphene Liu, Zhe; Li, Yu; Yang, Yi-Feng Chinese Physics B, Vol. 28, Issue 7 https://doi.org/10.1088/1674-1056/28/7/077103	journal	July 2019
Cold atoms in twisted-bilayer optical potentials González-Tudela, A.; Cirac, J. I. Physical Review A, Vol. 100, Issue 5 https://doi.org/10.1103/physreva.100.053604	journal	November 2019
Ferromagnetism and spin-valley liquid states in moiré correlated insulators Wu, Xiao-Chuan; Keselman, Anna; Jian, Chao-Ming Physical Review B, Vol. 100, Issue 2 https://doi.org/10.1103/physrevb.100.024421	journal	July 2019
Quantum Monte Carlo study of magnetic ordering and superconducting pairing symmetry in twisted bilayer graphene Fang, Shi-Chao; Liu, Guang-Kun; Lin, Hai-Qing Physical Review B, Vol. 100, Issue 11 https://doi.org/10.1103/physrevb.100.115135	journal	September 2019
Topological transitions in a model for proximity-induced superconductivity Batra, Navketan; Nayak, Swagatam; Kumar, Sanjeev Physical Review B, Vol. 100, Issue 21 https://doi.org/10.1103/physrevb.100.214517	journal	December 2019
Formation of Bloch Flat Bands in Polar Twisted Bilayers without Magic Angles Zhao, Xing-Ju; Yang, Yang; Zhang, Dong-Bo Physical Review Letters, Vol. 124, Issue 8 https://doi.org/10.1103/physrevlett.124.086401	journal	February 2020
Correlated insulating and superconducting states in twisted bilayer graphene below the magic angle Codecido, Emilio; Wang, Qiyue; Koester, Ryan Science Advances, Vol. 5, Issue 9 https://doi.org/10.1126/sciadv.aaw9770	journal	September 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
General continuum model for twisted bilayer graphene and arbitrary smooth deformations Balents, Leon SciPost Physics, Vol. 7, Issue 4 https://doi.org/10.21468/scipostphys.7.4.048	journal	January 2019
Kohn-Luttinger Superconductivity in Twisted Bilayer Graphene González, J.; Stauber, T. arXiv https://doi.org/10.48550/arxiv.1807.01275	text	January 2018
Tuning superconductivity in twisted bilayer graphene Yankowitz, Matthew; Chen, Shaowen; Polshyn, Hryhoriy arXiv https://doi.org/10.48550/arxiv.1808.07865	text	January 2018
The pseudo-Landau-level representation of twisted bilayer graphene: band topology and the implications on the correlated insulating phase Liu, Jianpeng; Liu, Junwei; Dai, Xi arXiv https://doi.org/10.48550/arxiv.1810.03103	text	January 2018
Nematic superconductivity stabilized by density wave fluctuations: Possible application to twisted bilayer graphene Kozii, Vladyslav; Isobe, Hiroki; Venderbos, Jörn W. F. arXiv https://doi.org/10.48550/arxiv.1810.04159	text	January 2018
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
Coupled Wire description of the Correlated Physics in Twisted Bilayer Graphene Wu, Xiao-Chuan; Jian, Chao-Ming; Xu, Cenke arXiv https://doi.org/10.48550/arxiv.1811.08442	text	January 2018
Enhanced correlations and superconductivity in weakly interacting partially flat band systems: a determinantal quantum Monte Carlo study Huang, Edwin W.; Vaezi, Mohammad-Sadegh; Nussinov, Zohar arXiv https://doi.org/10.48550/arxiv.1811.08848	text	January 2018
Topological chiral superconductivity with spontaneous vortices and supercurrent in twisted bilayer graphene Wu, Fengcheng arXiv https://doi.org/10.48550/arxiv.1811.10620	text	January 2018
Magic of high order van Hove singularity Yuan, Noah F. Q.; Isobe, Hiroki; Fu, Liang arXiv https://doi.org/10.48550/arxiv.1901.05432	text	January 2019
Gauge phonon dominated resistivity in twisted bilayer graphene near magic angle Yudhistira, I.; Chakraborty, N.; Sharma, G. arXiv https://doi.org/10.48550/arxiv.1902.01405	text	January 2019
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
Quantum valley Hall effect, orbital magnetism, and anomalous Hall effect in twisted multilayer graphene systems Liu, Jianpeng; Ma, Zhen; Gao, Jinhua arXiv https://doi.org/10.48550/arxiv.1903.10419	text	January 2019
Valley Jahn-Teller effect in twisted bilayer graphene Angeli, M.; Tosatti, E.; Fabrizio, M. arXiv https://doi.org/10.48550/arxiv.1904.06301	text	January 2019
Identification of superconducting pairing symmetry in twisted bilayer graphene using in-plane magnetic field and strain Wu, Fengcheng; Sarma, Sankar Das arXiv https://doi.org/10.48550/arxiv.1904.07875	text	January 2019
Geometric and conventional contribution to superfluid weight in twisted bilayer graphene Hu, Xiang; Hyart, Timo; Pikulin, Dmitry I. arXiv https://doi.org/10.48550/arxiv.1906.07152	text	January 2019
Superconductor versus insulator in twisted bilayer graphene Chou, Yang-Zhi; Lin, Yu-Ping; Sarma, Sankar Das arXiv https://doi.org/10.48550/arxiv.1906.10141	text	January 2019
General continuum model for twisted bilayer graphene and arbitrary smooth deformations Balents, Leon arXiv https://doi.org/10.48550/arxiv.1909.01545	text	January 2019

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