Pairing symmetry and spontaneous vortex-antivortex lattice in superconducting twisted-bilayer graphene: Bogoliubov-de Gennes approach

Su, Ying; Lin, Shizeng

doi:10.1103/PhysRevB.98.195101

Title: Pairing symmetry and spontaneous vortex-antivortex lattice in superconducting twisted-bilayer graphene: Bogoliubov-de Gennes approach

Journal Article · Thu Nov 01 00:00:00 EDT 2018 · Physical Review B

DOI:https://doi.org/10.1103/PhysRevB.98.195101· OSTI ID:1495154

^[1];

^[1]

Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

Here, we study the superconducting pairing symmetry in twisted bilayer graphene by solving the Bogoliubov-de Gennes equation for all electrons in moiré supercells. With increasing the pairing potential, the system evolves from the mixed nontopological d + i d and p + i p phase to the s + p + d phase via the first-order phase transition. In the time-reversal symmetry breaking d + i d and p + i p phase, vortex and antivortex lattices accompanying spontaneous supercurrent are induced by the twist. The superconducting order parameter is nonuniform in the moiré unit cell. Nevertheless, the superconducting gap in the local density of states is identical in the unit cell. The twist-induced vortices and nontopological nature of the mixed d + i d and p + i p phase are not captured by the existing effective models. Our results suggest the importance of long-range pairing interaction for effective models.

View Accepted Manuscript (DOE)

View Accepted Manuscript (Publisher)

Cite

Export

Save

Research Organization:: Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: USDOE Laboratory Directed Research and Development (LDRD) Program

Grant/Contract Number:: 89233218CNA000001; AC52-06NA25396

OSTI ID:: 1495154

Alternate ID(s):: OSTI ID: 1480366

Report Number(s):: LA-UR-18-26090; PRBMDO

Journal Information:: Physical Review B, Vol. 98, Issue 19; ISSN 2469-9950

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

Citation Metrics:

Cited by: 54 works

Citation information provided by
Web of Science

References (47)

Unraveling the Intrinsic and Robust Nature of van Hove Singularities in Twisted Bilayer Graphene by Scanning Tunneling Microscopy and Theoretical Analysis Brihuega, I.; Mallet, P.; González-Herrero, H. Physical Review Letters, Vol. 109, Issue 19 https://doi.org/10.1103/PhysRevLett.109.196802	journal	November 2012
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
Soliton in Two-Band Superconductor Tanaka, Y. Physical Review Letters, Vol. 88, Issue 1 https://doi.org/10.1103/PhysRevLett.88.017002	journal	December 2001
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
Kekulé valence bond order in an extended Hubbard model on the honeycomb lattice with possible applications to twisted bilayer graphene Xu, Xiao Yan; Law, K. T.; Lee, Patrick A. Physical Review B, Vol. 98, Issue 12 https://doi.org/10.1103/PhysRevB.98.121406	journal	September 2018
Possible correlated insulating states in magic-angle twisted bilayer graphene under strongly competing interactions Ochi, Masayuki; Koshino, Mikito; Kuroki, Kazuhiko Physical Review B, Vol. 98, Issue 8 https://doi.org/10.1103/PhysRevB.98.081102	journal	August 2018
Resonating valence bonds and mean-field $d$ -wave superconductivity in graphite Black-Schaffer, Annica M.; Doniach, Sebastian Physical Review B, Vol. 75, Issue 13 https://doi.org/10.1103/PhysRevB.75.134512	journal	April 2007
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
Hubbard Model Physics in Transition Metal Dichalcogenide Moiré Bands Wu, Fengcheng; Lovorn, Timothy; Tutuc, Emanuel Physical Review Letters, Vol. 121, Issue 2 https://doi.org/10.1103/PhysRevLett.121.026402	journal	July 2018
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
Pairing symmetry of interacting fermions on a twisted bilayer graphene superlattice Guo, Huaiming; Zhu, Xingchuan; Feng, Shiping Physical Review B, Vol. 97, Issue 23 https://doi.org/10.1103/PhysRevB.97.235453	journal	June 2018
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
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
Chiral superconductors Kallin, Catherine; Berlinsky, John Reports on Progress in Physics, Vol. 79, Issue 5 https://doi.org/10.1088/0034-4885/79/5/054502	journal	April 2016
Competing many-body instabilities and unconventional superconductivity in graphene Kiesel, Maximilian L.; Platt, Christian; Hanke, Werner Physical Review B, Vol. 86, Issue 2 https://doi.org/10.1103/PhysRevB.86.020507	journal	July 2012
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
Unconventional topological superconductivity and phase diagram for an effective two-orbital model as applied to twisted bilayer graphene Fidrysiak, M.; Zegrodnik, M.; Spałek, J. Physical Review B, Vol. 98, Issue 8 https://doi.org/10.1103/PhysRevB.98.085436	journal	August 2018
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
Band structure of twisted bilayer graphene: Emergent symmetries, commensurate approximants, and Wannier obstructions Zou, Liujun; Po, Hoi Chun; Vishwanath, Ashvin Physical Review B, Vol. 98, Issue 8 https://doi.org/10.1103/PhysRevB.98.085435	journal	August 2018
Topological Defect-Phase Soliton and the Pairing Symmetry of a Two-Band Superconductor: Role of the Proximity Effect Vakaryuk, Victor; Stanev, Valentin; Lee, Wei-Cheng Physical Review Letters, Vol. 109, Issue 22 https://doi.org/10.1103/PhysRevLett.109.227003	journal	November 2012
Triangular antiferromagnetism on the honeycomb lattice of twisted bilayer graphene Thomson, Alex; Chatterjee, Shubhayu; Sachdev, Subir Physical Review B, Vol. 98, Issue 7 https://doi.org/10.1103/PhysRevB.98.075109	journal	August 2018
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
Superlattice-Induced Insulating States and Valley-Protected Orbits in Twisted Bilayer Graphene Cao, Y.; Luo, J. Y.; Fatemi, V. Physical Review Letters, Vol. 117, Issue 11 https://doi.org/10.1103/PhysRevLett.117.116804	journal	September 2016
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
Electronic structure of turbostratic graphene Shallcross, S.; Sharma, S.; Kandelaki, E. Physical Review B, Vol. 81, Issue 16 https://doi.org/10.1103/PhysRevB.81.165105	journal	April 2010
Observation of Van Hove singularities in twisted graphene layers Li, Guohong; Luican, A.; Lopes dos Santos, J. M. B. Nature Physics, Vol. 6, Issue 2 https://doi.org/10.1038/nphys1463	journal	November 2009
Chiral d -wave superconductivity in doped graphene Black-Schaffer, Annica M.; Honerkamp, Carsten Journal of Physics: Condensed Matter, Vol. 26, Issue 42 https://doi.org/10.1088/0953-8984/26/42/423201	journal	September 2014
Magnetic Response of Mesoscopic Superconducting Rings with Two Order Parameters Bluhm, Hendrik; Koshnick, Nicholas C.; Huber, Martin E. Physical Review Letters, Vol. 97, Issue 23 https://doi.org/10.1103/PhysRevLett.97.237002	journal	December 2006
Single-Layer Behavior and Its Breakdown in Twisted Graphene Layers Luican, A.; Li, Guohong; Reina, A. Physical Review Letters, Vol. 106, Issue 12 https://doi.org/10.1103/PhysRevLett.106.126802	journal	March 2011
Angle-Dependent van Hove Singularities in a Slightly Twisted Graphene Bilayer Yan, Wei; Liu, Mengxi; Dou, Rui-Fen Physical Review Letters, Vol. 109, Issue 12 https://doi.org/10.1103/PhysRevLett.109.126801	journal	September 2012
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
Electronic structure of turbostratic graphene Shallcross, S.; Sharma, S.; Kandelaki, E. arXiv https://doi.org/10.48550/arxiv.0910.5811	text	January 2009
Moire bands in twisted double-layer graphene Bistritzer, R.; MacDonald, A. H. arXiv https://doi.org/10.48550/arxiv.1009.4203	text	January 2010
Single Layer Behavior and Its Breakdown in Twisted Graphene Layers Luican, A.; Li, Guohong; Reina, A. arXiv https://doi.org/10.48550/arxiv.1010.4032	text	January 2010
Optical Absorption in Twisted Bilayer Graphene Moon, Pilkyung; Koshino, Mikito arXiv https://doi.org/10.48550/arxiv.1302.5218	text	January 2013
Chiral d-wave superconductivity in doped graphene Black-Schaffer, Annica M.; Honerkamp, Carsten arXiv https://doi.org/10.48550/arxiv.1406.0101	text	January 2014
Superlattice-induced insulating states and valley-protected orbits in twisted bilayer graphene Cao, Y.; Luo, J. Y.; Fatemi, V. arXiv https://doi.org/10.48550/arxiv.1607.05147	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
Pairing symmetry of interacting fermions on twisted bilayer graphene superlattice Guo, Huaiming; Zhu, Xingchuan; Feng, Shiping arXiv https://doi.org/10.48550/arxiv.1804.00159	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
Unconventional topological superconductivity and phase diagram for an effective two-orbital model as applied to twisted bilayer graphene Fidrysiak, Maciej; Zegrodnik, Michał; Spałek, Józef arXiv https://doi.org/10.48550/arxiv.1805.01179	text	January 2018
Magnetic response of mesoscopic superconducting rings with two order parameters Bluhm, Hendrik; Koshnick, Nicholas C.; Huber, Martin E. arXiv https://doi.org/10.48550/arxiv.cond-mat/0608287	text	January 2006

Cited By (16)

High-TC Superconductivity Originating from Interlayer Coulomb Coupling in Gate-Charged Twisted Bilayer Graphene Moiré Superlattices Harshman, Dale R.; Fiory, Anthony T. Journal of Superconductivity and Novel Magnetism, Vol. 33, Issue 2 https://doi.org/10.1007/s10948-019-05183-9	journal	July 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
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
Bogoliubov Fermi surfaces stabilized by spin-orbit coupling Menke, Henri; Timm, C.; Brydon, P. M. R. Physical Review B, Vol. 100, Issue 22 https://doi.org/10.1103/physrevb.100.224505	journal	December 2019
Experimental consequences of Bogoliubov Fermi surfaces Lapp, Clara J.; Börner, Georg; Timm, Carsten Physical Review B, Vol. 101, Issue 2 https://doi.org/10.1103/physrevb.101.024505	journal	January 2020
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
Ground state superconducting pair correlations in twisted bilayer graphene Zhang, Lufeng; Huang, Tongyun; Liang, Ying Modern Physics Letters B, Vol. 34, Issue 01 https://doi.org/10.1142/s0217984920500165	journal	December 2019
Charge-transfer insulation in twisted bilayer graphene Rademaker, Louk; Mellado, Paula arXiv https://doi.org/10.48550/arxiv.1805.05294	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
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
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
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
Experimental consequences of Bogoliubov Fermi surfaces Lapp, Clara J.; Börner, Georg; Timm, Carsten arXiv https://doi.org/10.48550/arxiv.1909.10370	text	January 2019

Similar Records

Topological chiral superconductivity with spontaneous vortices and supercurrent in twisted bilayer graphene.

Journal Article · Wed May 08 00:00:00 EDT 2019 · Physical Review, B: Condensed Matter · OSTI ID:1495154

Wu, Fengcheng; Martin, Ivar

All Magic Angles in Twisted Bilayer Graphene are Topological

Journal Article · Tue Jul 16 00:00:00 EDT 2019 · Physical Review Letters · OSTI ID:1495154

Song, Zhida; Wang, Zhijun; Shi, Wujun; +3 more

Superconductivity from valley fluctuations and approximate SO(4) symmetry in a weak coupling theory of twisted bilayer graphene

Journal Article · Mon Apr 29 00:00:00 EDT 2019 · npj Quantum Materials · OSTI ID:1495154

You, Yi-Zhuang; Vishwanath, Ashvin

Related Subjects

75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY

Title: Pairing symmetry and spontaneous vortex-antivortex lattice in superconducting twisted-bilayer graphene: Bogoliubov-de Gennes approach

Citation Formats

References (47)

Cited By (16)

Similar Records

Related Subjects