Twistronics

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Atomic scale moire pattern created by overlapping two skewed sheets of graphene, a hexagonal lattice composed of carbon atoms. Moire of twisted bilayer graphene.svg
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]

Contents

Pablo Jarillo-Herrero, Allan H. MacDonald and Rafi Bistritzer were awarded the 2020 Wolf Prize in Physics for their theoretical and experimental work on twisted bilayer graphene. [6]

History

In 2007, National University of Singapore physicist Antonio H. 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 moiré pattern and demonstrating that the twist angle has a strong effect on the band structure by measuring greatly renormalized van Hove singularities. [7] Also in 2010 researchers from Federico Santa María Technical University 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, [8] and because of that theoretical property, they suggested that collective behavior might be possible. In 2011 Allan H. 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. [9] 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 Massachusetts Institute of Technology, found that the magic angle resulted in the unusual electrical properties that MacDonald and Bistritzer had predicted. [10] 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. [11]

Publication of these discoveries has generated a host of theoretical papers seeking to understand and explain the phenomena [12] as well as numerous experiments [3] using varying numbers of layers, twist angles and other materials. [4] [13] Subsequent works showed that electronic properties of the stack can also be strongly dependent on heterostrain especially near the magic angle [14] [15] allowing potential applications in straintronics.

Characteristics

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. Animation901.gif
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

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] [16] [17] 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. [18]

Heterostructures

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. [19] 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. [20] Further spectroscopic studies of twisted bilayer graphene revealed strong electron-electron correlations at the magic angle. [21]

Electron puddling

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. [22] 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.

Ferromagnetism

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. [23] In 2021, this was achieved on a single graphene flake. [24]

See also

Related Research Articles

<span class="mw-page-title-main">Superconductivity</span> Electrical conductivity with exactly zero resistance

Superconductivity is a set of physical properties observed in superconductors: materials where electrical resistance vanishes and magnetic fields are expelled from the material. Unlike an ordinary metallic conductor, whose resistance decreases gradually as its temperature is lowered, even down to near absolute zero, a superconductor has a characteristic critical temperature below which the resistance drops abruptly to zero. An electric current through a loop of superconducting wire can persist indefinitely with no power source.

Unconventional superconductors are materials that display superconductivity which is not explained by the usual BCS theory or its extension, the Eliashberg theory. The pairing in unconventional superconductors may originate from some other mechanism than the electron–phonon interaction. Alternatively, a superconductor is called unconventional if the superconducting order parameter transforms according to a non-trivial irreducible representation of the point group or space group of the system.

<span class="mw-page-title-main">High-temperature superconductivity</span> Superconductive behavior at temperatures much higher than absolute zero

High-temperature superconductivity is superconductivity in materials with a critical temperature above 77 K, the boiling point of liquid nitrogen. They are only "high-temperature" relative to previously known superconductors, which function at colder temperatures, close to absolute zero. The "high temperatures" are still far below ambient, and therefore require cooling. The first breakthrough of high-temperature superconductor was discovered in 1986 by IBM researchers Georg Bednorz and K. Alex Müller. Although the critical temperature is around 35.1 K, this new type of superconductor was readily modified by Ching-Wu Chu to make the first high-temperature superconductor with critical temperature 93 K. Bednorz and Müller were awarded the Nobel Prize in Physics in 1987 "for their important break-through in the discovery of superconductivity in ceramic materials". Most high-Tc materials are type-II superconductors.

<span class="mw-page-title-main">Graphene</span> Hexagonal lattice made of carbon atoms

Graphene is an allotrope of carbon consisting of a single layer of atoms arranged in a honeycomb nanostructure. The name is derived from "graphite" and the suffix -ene, reflecting the fact that the graphite allotrope of carbon contains numerous double bonds in a two-dimensional sheet.

A superlattice is a periodic structure of layers of two materials. Typically, the thickness of one layer is several nanometers. It can also refer to a lower-dimensional structure such as an array of quantum dots or quantum wells.

<span class="mw-page-title-main">Hofstadter's butterfly</span> Fractal describing the theorised behaviour of electrons in a magnetic field

In condensed matter physics, Hofstadter's butterfly is a graph of the spectral properties of non-interacting two-dimensional electrons in a perpendicular magnetic field in a lattice. The fractal, self-similar nature of the spectrum was discovered in the 1976 Ph.D. work of Douglas Hofstadter and is one of the early examples of modern scientific data visualization. The name reflects the fact that, as Hofstadter wrote, "the large gaps [in the graph] form a very striking pattern somewhat resembling a butterfly."

<span class="mw-page-title-main">Tungsten ditelluride</span> Chemical compound

Tungsten ditelluride (WTe2) is an inorganic semimetallic chemical compound. In October 2014, tungsten ditelluride was discovered to exhibit an extremely large magnetoresistance: 13 million percent resistance increase in a magnetic field of 60 tesla at 0.5 kelvin. The resistance is proportional to the square of the magnetic field and shows no saturation. This may be due to the material being the first example of a compensated semimetal, in which the number of mobile holes is the same as the number of electrons. Tungsten ditelluride has layered structure, similar to many other transition metal dichalcogenides, but its layers are so distorted that the honeycomb lattice many of them have in common is in WTe2 hard to recognize. The tungsten atoms instead form zigzag chains, which are thought to behave as one-dimensional conductors. Unlike electrons in other two-dimensional semiconductors, the electrons in WTe2 can easily move between the layers.

<span class="mw-page-title-main">Proximity effect (superconductivity)</span> Phenomena that occur when a superconductor is in contact with a non-superconductor

Proximity effect or Holm–Meissner effect is a term used in the field of superconductivity to describe phenomena that occur when a superconductor (S) is placed in contact with a "normal" (N) non-superconductor. Typically the critical temperature of the superconductor is suppressed and signs of weak superconductivity are observed in the normal material over mesoscopic distances. The proximity effect is known since the pioneering work by R. Holm and W. Meissner. They have observed zero resistance in SNS pressed contacts, in which two superconducting metals are separated by a thin film of a non-superconducting metal. The discovery of the supercurrent in SNS contacts is sometimes mistakenly attributed to Brian Josephson's 1962 work, yet the effect was known long before his publication and was understood as the proximity effect.

Pomeranchuk cooling is the phenomenon in which liquid helium-3 will cool if it is compressed isentropically when it is below 0.3 K. This occurs because helium-3 has the unusual property that its solid state can have a higher entropy than its liquid state. The effect was first observed by Yuri Anufriev in 1965. This can be used to construct a cryogenic cooler.

<span class="mw-page-title-main">Graphane</span> Chemical compound

Graphane is a two-dimensional polymer of carbon and hydrogen with the formula unit (CH)n where n is large. Partial hydrogenation results in hydrogenated graphene, which was reported by Elias et al. in 2009 by a TEM study to be "direct evidence for a new graphene-based derivative". The authors viewed the panorama as "a whole range of new two-dimensional crystals with designed electronic and other properties". With the band gap ranges from 0 to 0.8 eV

Superstripes is a generic name for a phase with spatial broken symmetry that favors the onset of superconducting or superfluid quantum order. This scenario emerged in the 1990s when non-homogeneous metallic heterostructures at the atomic limit with a broken spatial symmetry have been found to favor superconductivity. Before a broken spatial symmetry was expected to compete and suppress the superconducting order. The driving mechanism for the amplification of the superconductivity critical temperature in superstripes matter has been proposed to be the shape resonance in the energy gap parameters ∆n that is a type of Fano resonance for coexisting condensates.

Bilayer graphene is a material consisting of two layers of graphene. One of the first reports of bilayer graphene was in the seminal 2004 Science paper by Geim and colleagues, in which they described devices "which contained just one, two, or three atomic layers"

<span class="mw-page-title-main">Allan H. MacDonald</span> Canadian-American physicist (born 1951)

Allan H. MacDonald is a theoretical condensed matter physicist and the Sid W. Richardson Foundation Regents Chair Professor of Physics at The University of Texas at Austin. He is well known for his work on correlated many-electron states in low-dimensional systems. In 2020, he became one of the laureates of the Wolf Prize in Physics, for predicting the magic angle that turns twisted bilayer graphene into a superconductor.

Eva Yocheved Andrei is an American condensed matter physicist, a Distinguished Professor, and a Board of Governors Professor at Rutgers University. Her research focuses on emergent properties of matter arising from the collective behavior of many particles, especially low-dimensional phenomena under low temperatures and high magnetic fields.

<span class="mw-page-title-main">Electronic properties of graphene</span>

Graphene is a semimetal whose conduction and valence bands meet at the Dirac points, which are six locations in momentum space, the vertices of its hexagonal Brillouin zone, divided into two non-equivalent sets of three points. The two sets are labeled K and K′. The sets give graphene a valley degeneracy of gv = 2. By contrast, for traditional semiconductors the primary point of interest is generally Γ, where momentum is zero. Four electronic properties separate it from other condensed matter systems.

Pablo Jarillo-Herrero is a Spanish physicist and current Cecil and Ida Green Professor of Physics at Massachusetts Institute of Technology (MIT).

<span class="mw-page-title-main">Antonio H. Castro Neto</span>

Antonio Helio de Castro Neto is a Brazilian-born physicist. He is the founder and director of the Centre for Advanced 2D Materials at the National University of Singapore. He is a condensed matter theorist known for his work in the theory of metals, magnets, superconductors, graphene and two-dimensional materials. He is a distinguished professor in the Departments of Materials Science Engineering, and Physics and a professor at the Department of Electrical and Computer Engineering. He was elected as a fellow of the American Physical Society in 2003. In 2011 he was elected as a fellow of the American Association for the Advancement of Science.

Rafi Bistritzer is an Israeli physicist, and manager of an algorithms group at Applied Materials. He is the winner of the 2020 Wolf Prize in Physics, together with Pablo Jarillo-Herrero and Allan MacDonald, for "pioneering theoretical and experimental work on twisted bilayer graphene."

The term heterostrain was proposed in 2018 in the context of materials science to simplify the designation of possible strain situations in van der Waals heterostructures where two two-dimensional materials are stacked on top of each other. These layers can experience the same deformation (homostrain) or different deformations (heterostrain). In addition to twist, heterostrain can have important consequences on the electronic and optical properties of the resulting structure. As such, the control of heterostrain is emerging as a sub-field of straintronics in which the properties of 2D materials are controlled by strain. Recent works have reported a deterministic control of heterostrain by sample processing or with the tip of an AFM of particular interest in twisted heterostructures. Heterostrain alone has also been identified as a parameter to tune the electronic properties of van der Waals structures as for example in twisted graphene layers with biaxial heterostrain.

Fractional Chern insulators (FCIs) are lattice generalizations of the fractional quantum Hall effect that have been studied theoretically since 1993 and have been studied more intensely since early 2010. They were first predicted to exist in topological flat bands carrying Chern numbers. They can appear in topologically non-trivial band structures even in the absence of the large magnetic fields needed for the fractional quantum Hall effect. In principle, they can also occur in partially filled bands with trivial band structures if the inter-electron interaction is unusual. They promise physical realizations at lower magnetic fields, higher temperatures, and with shorter characteristic length scales compared to their continuum counterparts. FCIs were initially studied by adding electron-electron interactions to a fractionally filled Chern insulator, in one-body models where the Chern band is quasi-flat, at zero magnetic field. The FCIs exhibit a fractional quantized Hall conductance.

References

  1. 1 2 3 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. 1 2 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. 1 2 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. 1 2 3 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. ↑ "Allan MacDonald Wins Wolf Prize in Physics | College of Natural Sciences". cns.utexas.edu. Retrieved 2024-09-24.
  7. ↑ 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.
  8. ↑ 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.
  9. ↑ 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.
  10. ↑ 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.
  11. ↑ Chang, Kenneth (30 October 2019). "New twist on graphene gets materials scientists hot under the collar". New York Times . Retrieved 29 Sep 2020.
  12. ↑ Freedman, David H. (2019-05-28). "What's the Magic Behind Graphene's 'Magic' Angle?". Quanta Magazine. Retrieved 2019-05-28.
  13. ↑ "Experiments explore the mysteries of 'magic' angle superconductors". Phys.org. 2019-07-31. Retrieved 2019-07-31.
  14. ↑ 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 .
  15. ↑ 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.
  16. ↑ 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.
  17. ↑ Wang, Brian (2018-03-07). "Graphene superlattices could be used for superconducting transistors". NextBigFuture.com. Retrieved 2019-05-03.
  18. ↑ "Twisted physics: Magic angle graphene produces switchable patterns of superconductivity". phys.org. October 30, 2019. Retrieved 2020-02-06.
  19. ↑ University of Sheffield (March 6, 2019). "1 + 1 does not equal 2 for graphene-like 2-D materials". phys.org. Retrieved 2019-08-01.
  20. ↑ Than, Ker (2019-07-26). "Physicists discover new quantum trick for graphene: magnetism". phys.org. Retrieved 2019-07-27.
  21. ↑ 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.
  22. ↑ Castañón, Laura (February 27, 2020). "Physicists may have accidentally discovered a new state of matter". Phys.org. Retrieved 2020-02-27.
  23. ↑ "A talented 2-D material gets a new gig". Phys.org. March 4, 2020. Retrieved 2020-03-04.
  24. ↑ Irving, Michael (2021-05-06). "Magic angle makes graphene simultaneously superconducting and insulating". New Atlas. Retrieved 2021-05-09.
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