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Atomic scale moiré pattern created by overlapping two skewed sheets of graphene, a hexagonal lattice composed of carbon atoms.

Twistronics (from twist and electronics) is the study of how the angle (the twist) between layers of two-dimensional materials can change their electrical properties.[1][2] Materials such as bilayer graphene have been shown to have vastly different electronic behavior, ranging from non-conductive to superconductive, that depends sensitively on the angle between the layers.[3][4] The term was first introduced by the research group of Efthimios Kaxiras at Harvard University in their theoretical treatment of graphene superlattices.[1][5]


In 2007, National University of Singapore physicist Antonio Castro Neto hypothesized that pressing two misaligned graphene sheets together might yield new electrical properties, and separately proposed that graphene might offer a route to superconductivity, but he did not combine the two ideas.[4] In 2010 researchers in Eva Andrei's laboratory at Rutgers University in Piscataway New Jersey discovered twisted bilayer graphene through its defining moire pattern and demonstrating that the twist angle has a strong effect on the band structure by measuring greatly renormalized van Hove singularities.[6] Also in 2010 researchers from Universidad Técnica Federico Santa María in Chile found that for a certain angle close to 1 degree the band of the electronic structure of twisted bilayer graphene became completely flat,[7] and because of that theoretical property, they suggested that collective behavior might be possible. In 2011 Allan MacDonald (of University of Texas at Austin) and Rafi Bistritzer using a simple theoretical model found that for the previously found "magic angle" the amount of energy a free electron would require to tunnel between two graphene sheets radically changes.[8] In 2017, the research group of Efthimios Kaxiras at Harvard University used detailed quantum mechanics calculations to reduce uncertainty in the twist angle between two graphene layers that can induce extraordinary behavior of electrons in this two-dimensional system.[1] In 2018, Pablo Jarillo-Herrero, an experimentalist at MIT, found that the magic angle resulted in the unusual electrical properties that Allan MacDonald and Rafi Bistritzer had predicted.[9] At 1.1 degrees rotation at sufficiently low temperatures, electrons move from one layer to the other, creating a lattice and the phenomenon of superconductivity.[10]

Publication of these discoveries has generated a host of theoretical papers seeking to understand and explain the phenomena[11] as well as numerous experiments[3] using varying numbers of layers, twist angles and other materials.[4][12] Subsequent works showed that electronic properties of the stack can also be strongly dependent on heterostrain especially near the magic angle[13][14] allowing potential applications in straintronics.


A twistronics animation. Here, we have 2 overlaid sheets, one of which rotates a total of 90 degrees. We see that as the angle of rotation changes, so does the periodicity.

Superconduction and Insulation[edit]

The theoretical predictions of superconductivity were confirmed by Pablo Jarillo-Herrero and his student Yuan Cao of MIT and colleagues from Harvard University and the National Institute for Materials Science in Tsukuba, Japan. In 2018 they verified that superconductivity existed in bilayer graphene where one layer was rotated by an angle of 1.1° relative to the other, forming a moiré pattern, at a temperature of 1.7 K (−271.45 °C; −456.61 °F).[2][15][16] They created two bilayer devices that acted as an insulator instead of a conductor without a magnetic field. Increasing the field strength turned the second device into a superconductor.

A further advance in twistronics is the discovery of a method of turning the superconductive paths on and off by application of a small voltage differential.[17]


Experiments have also been done using combinations of graphene layers with other materials that form heterostructures in the form of atomically thin sheets that are held together by the weak Van der Waals force.[18] For example, a study published in Science in July 2019 found that with the addition of a boron nitride lattice between two graphene sheets, unique orbital ferromagnetic effects were produced at a 1.17° angle, which could be used to implement memory in quantum computers.[19] Further spectroscopic studies of twisted bilayer graphene revealed strong electron-electron correlations at the magic angle.[20]

Electron puddling[edit]

Between 2-D layers for bismuth selenide and a dichalcogenide, researchers at the Northeastern University in Boston, discovered that at a specific degrees of twist a new lattice layer, consisting of only pure electrons, would develop between the two 2-D elemental layers.[21] The quantum and physical effects of the alignment between the two layers appears to create "puddle" regions which trap electrons into a stable lattice. Because this stable lattice consists only of electrons, it is the first non-atomic lattice observed and suggests new opportunities to confine, control, measure, and transport electrons.


A three layer construction, consisting of two layers of graphene with a 2-D layer of boron nitride, has been shown to exhibit superconductivity, insulation and ferromagnetism.[22] In 2021, this was achieved on a single graphene flake.[23]

See also[edit]


  1. ^ a b c Carr, Stephen; Massatt, Daniel; Fang, Shiang; Cazeaux, Paul; Luskin, Mitchell; Kaxiras, Efthimios (17 February 2017). "Twistronics: Manipulating the electronic properties of two-dimensional layered structures through their twist angle". Physical Review B. 95 (7): 075420. arXiv:1611.00649. Bibcode:2017PhRvB..95g5420C. doi:10.1103/PhysRevB.95.075420. S2CID 27148700.
  2. ^ a b Jarillo-Herrero, Pablo; Kaxiras, Efthimios; Taniguchi, Takashi; Watanabe, Kenji; Fang, Shiang; Fatemi, Valla; Cao, Yuan (2018-03-06). "Magic-angle graphene superlattices: a new platform for unconventional superconductivity". Nature. 556 (7699): 43–50. arXiv:1803.02342. doi:10.1038/nature26160. PMID 29512651. S2CID 4655887.
  3. ^ a b Gibney, Elizabeth (2019-01-02). "How 'magic angle' graphene is stirring up physics". Nature. 565 (7737): 15–18. Bibcode:2019Natur.565...15G. doi:10.1038/d41586-018-07848-2. PMID 30602751.
  4. ^ a b c Freedman, David H. (2019-04-30). "How Twisted Graphene Became the Big Thing in Physics". Quanta Magazine. Retrieved 2019-05-05.
  5. ^ Tritsaris, Georgios A.; Carr, Stephen; Zhu, Ziyan; Xie, Yiqi; Torrisi, Steven B.; Tang, Jing; Mattheakis, Marios; Larson, Daniel; Kaxiras, Efthimios (2020-01-30). "Electronic structure calculations of twisted multi-layer graphene superlattices". 2D Materials. 7 (3): 035028. arXiv:2001.11633. Bibcode:2020TDM.....7c5028T. doi:10.1088/2053-1583/ab8f62. S2CID 211004085.
  6. ^ Li, Guohong; Luican, A.; Lopes dos Santos, J. M. B.; Castro Neto, A. H.; Reina, A.; Kong, J.; Andrei, E. Y. (February 2010). "Observation of Van Hove singularities in twisted graphene layers". Nature Physics. 6 (2): 109–113. arXiv:0912.2102. Bibcode:2010NatPh...6..109L. doi:10.1038/nphys1463.
  7. ^ Suárez Morell, E.; Correa, J. D.; Vargas, P.; Pacheco, M.; Barticevic, Z. (13 September 2010). "Flat bands in slightly twisted bilayer graphene: Tight-binding calculations". Physical Review B. 82 (12): 121407. arXiv:1012.4320. Bibcode:2010PhRvB..82l1407S. doi:10.1103/PhysRevB.82.121407. hdl:10533/144840. S2CID 117926220.
  8. ^ Bistritzer, Rafi; MacDonald, Allan H. (26 July 2011). "Moiré bands in twisted double-layer graphene". Proceedings of the National Academy of Sciences. 108 (30): 12233–12237. arXiv:1009.4203. Bibcode:2011PNAS..10812233B. doi:10.1073/pnas.1108174108. PMC 3145708. PMID 21730173.
  9. ^ Cao, Yuan; Fatemi, Valla; Fang, Shiang; Watanabe, Kenji; Taniguchi, Takashi; Kaxiras, Efthimios; Jarillo-Herrero, Pablo (5 March 2018). "Unconventional superconductivity in magic-angle graphene superlattices". Nature. 556 (7699): 43–50. arXiv:1803.02342. Bibcode:2018Natur.556...43C. doi:10.1038/nature26160. PMID 29512651. S2CID 4655887.
  10. ^ Chang, Kenneth (30 October 2019). "New twist on graphene gets materials scientists hot under the collar". New York Times. Retrieved 29 Sep 2020.
  11. ^ Freedman, David H. (2019-05-28). "What's the Magic Behind Graphene's 'Magic' Angle?". Quanta Magazine. Retrieved 2019-05-28.
  12. ^ "Experiments explore the mysteries of 'magic' angle superconductors". 2019-07-31. Retrieved 2019-07-31.
  13. ^ Bi, Zhen; Yuan, Noah F. Q.; Fu, Liang (2019-07-31). "Designing flat bands by strain". Physical Review B. 100 (3): 035448. arXiv:1902.10146. Bibcode:2019PhRvB.100c5448B. doi:10.1103/PhysRevB.100.035448. hdl:1721.1/135558.
  14. ^ Mesple, Florie; Missaoui, Ahmed; Cea, Tommaso; Huder, Loic; Guinea, Francisco; Trambly de Laissardière, Guy; Chapelier, Claude; Renard, Vincent T. (17 September 2021). "Heterostrain Determines Flat Bands in Magic-Angle Twisted Graphene Layers". Physical Review Letters. 127 (12): 126405. arXiv:2012.02475. Bibcode:2021PhRvL.127l6405M. doi:10.1103/PhysRevLett.127.126405. PMID 34597066. S2CID 227305789.
  15. ^ Cao, Yuan; Fatemi, Valla; Demir, Ahmet; Fang, Shiang; Tomarken, Spencer L.; Luo, Jason Y.; Sanchez-Yamagishi, Javier D.; Watanabe, Kenji; Taniguchi, Takashi; Kaxiras, Efthimios; Ashoori, Ray C.; Jarillo-Herrero, Pablo (5 April 2018). "Correlated insulator behaviour at half-filling in magic-angle graphene superlattices". Nature. 556 (7699): 80–84. arXiv:1802.00553. Bibcode:2018Natur.556...80C. doi:10.1038/nature26154. PMID 29512654. S2CID 4601086.
  16. ^ Wang, Brian (2018-03-07). "Graphene superlattices could be used for superconducting transistors". Retrieved 2019-05-03.
  17. ^ "Twisted physics: Magic angle graphene produces switchable patterns of superconductivity". October 30, 2019. Retrieved 2020-02-06.
  18. ^ University of Sheffield (March 6, 2019). "1 + 1 does not equal 2 for graphene-like 2-D materials". Retrieved 2019-08-01.
  19. ^ Than, Ker (2019-07-26). "Physicists discover new quantum trick for graphene: magnetism". Retrieved 2019-07-27.
  20. ^ Scheurer, Mathias S. (2019-07-31). "Spectroscopy of graphene with a magic twist". Nature. 572 (7767): 40–41. Bibcode:2019Natur.572...40S. doi:10.1038/d41586-019-02285-1. PMID 31367024.
  21. ^ Castañón, Laura (February 27, 2020). "Physicists may have accidentally discovered a new state of matter". Retrieved 2020-02-27.
  22. ^ "A talented 2-D material gets a new gig". March 4, 2020. Retrieved 2020-03-04.
  23. ^ Irving, Michael (2021-05-06). "Magic angle makes graphene simultaneously superconducting and insulating". New Atlas. Retrieved 2021-05-09.