Magic, symmetry, and twisted matter

doi:10.1126/science.abg5641

GSTDTAP > 气候变化

DOI	10.1126/science.abg5641
	Magic, symmetry, and twisted matter
	Ali Yazdani
	2021-03-12
发表期刊	Science
出版年	2021
英文摘要	The discovery in 2018 of superconductivity when two layers of graphene are stacked on top of each other at a “magic angle” has opened a new paradigm for studying electronic phenomena ([ 1 ][1]). Now, a pair of studies, one on page 1133 of this issue by Hao et al. ([ 2 ][2]) and the other by Park et al. ([ 3 ][3]), take the twisting magic trick one step further. More robust and tunable superconductivity was realized in three-layer stacks of graphene arranged at an alternating magic twist angle that is a factor of ![Graphic][4] greater than the magic angle for bilayers. The authors also present evidence that superconductivity in twisted graphene is not caused by the conventional weak-coupling Bardeen-Cooper-Schrieffer (BCS) electron-pairing mechanism. The mechanism of pairing remains unknown, but the experiments suggest that the electrons form tightly bound pairs at temperatures above those at which superconductivity is macroscopically detected. ![Figure][5] Alternating twists Superconductivity in twisted graphene layers arises from flat-band structures near zero energy. GRAPHIC: C. BICKEL/ SCIENCE Early theoretical work predicted that the moiré superlattice created by stacking two twisted layers of graphene, at a magic angle of ∼1°, creates electronic bands with vanishing bandwidths ([ 4 ][6], [ 5 ][7]). The quenched kinetic energy of electrons occupying such flat bands creates strong interactions and would make magic angle–twisted bilayer graphene (TBG) a spectacular platform for collective phenomena. for sighting new quantum phases ([ 6 ][8]) including unexpected interaction-driven topological insulators ([ 7 ][9]). Although steady progress is being made in understanding TBG, the mechanism and nature of its superconducting phase remains a mystery. It is tempting to think in terms of a simple weak-coupling BCS scenario in which a large density of states of a nearly flat band can enhance superconductivity. However, superconductivity occurs in the presence of strong Coulomb interactions that are comparable with or larger than the bandwidth of TBG in the noninteracting limit ([ 8 ][10]), and other flat-band moiré systems do not show reliable signs of superconductivity, despite exhibiting other strongly correlated behavior. Twisting three-layer graphene was predicted to possess flat bands if it was constructed with a curious alternating magic twist angle ![Graphic][11] greater than that of the bilayer system ([ 9 ][12]). This trilayer differs from the bilayer in several respects. For example, its flat bands coexist with dispersing Dirac bands, and a perpendicular displacement field can be used to tune its band structure (see the figure). The two experimental studies fabricated trilayer near the predicted greater alternating magic angle and explored trilayer properties as a function of carrier density and perpendicular displacement field. The presence of the Dirac bands circumvents the formation of correlated insulating states, which also slightly screens the interaction between electrons in the flat band of the trilayer. However, the interactions within the trilayer flat bands give rise to cascades of transitions at several of the integer filling (ν) of carriers per moiré unit cell of its flat bands, similar to those observed in TBG ([ 10 ][13], [ 11 ][14]). These transitions signal the propensity for flavor (spin or valley isospin) symmetry–breaking, near-integer fillings, including at ν = ±2, from which superconductivity emerges upon doping. The trilayer appears at a superconducting transition temperature ( T c) of 2 K (twice that of the bilayer) system. The cause of this enhancement is unclear, but the moiré superlattice constant is smaller in the trilayer, which would increase the Coulomb-interaction scale at the same electron density Several experimental findings in the magic trilayer signal unconventional superconductivity. The superconducting coherence length is about the same as the interparticle distance, and T c increases almost linearly with doping. The ratio of T c to the Fermi temperature is also large (0.1). The superconducting state appears to be in the strong-coupling regime and likely driven by Bose condensation of tightly bound Cooper pairs and limited by their density. Pairing might occur at temperatures much higher than when the zero-resistance state is detected. Tuning the trilayer's band structure allows experimental determination of the role of enhanced density of states at the van Hove singularity (vHS) of the flat bands in superconductivity. The new studies monitored the Hall conductivity as a function of doping and displacement field. When the vHS is tuned to the chemical potential, T c in the trilayer is suppressed, opposite of what is expected from the simple BCS weak-coupling mechanism. Superconductivity appears to be strongly tied to flavor-polarized states, which are beginning to be understood in the bilayer [for example, ([ 12 ][15])]. Topological excitations of these states may be responsible for the pairing mechanism ([ 13 ][16]), but the breakdown of weak coupling does not mean phonons are not involved. Some calculations show that in a fully flat band, electrons cannot pair on their own ([ 14 ][17]). The presence of superconductivity in bilayer and alternating trilayer systems, and its absence in the other flat band system, suggests the importance of spatial-time C2 z T symmetry for the emergence of superconductivity. The discovery of superconductivity in this trilayer raises the possibility that the stacking of multilayers of graphene respecting certain symmetry at other magic angles will uncover more and hopefully greater- T c twisted superconductors. The theory that predicted the ![Graphic][18] ratio for trilayer also identified a hierarchy of magic angles for multilayers with alternating layers ([ 8 ][10]). The prediction for quadrilayers with alternating magic angle larger than the bilayer by the golden ratio is that they would have flat bands without dispersing Dirac bands because they have an even number of layers (see the figure). An unspoken rule in the hunt for new superconductors attributed to early Bell Lab pioneer Bernd Matthias ([ 15 ][19]) is to “never listen to the theorists.” However, maybe the signs of symmetry and the elegance of special ratios need to be heeded. Finding superconductivity in twisted matter with a prescribed symmetry related by the golden ratio of twist angles would be pure magic. 1. [↵][20]1. Y. Cao et al ., Nature 556, 43 (2018). [OpenUrl][21][CrossRef][22][PubMed][23] 2. [↵][24]1. Z. Hao et al ., Science 371, 1133 (2021). [OpenUrl][25][Abstract/FREE Full Text][26] 3. [↵][27]1. J. M. Park et al ., Nature 590, 249 (2021). [OpenUrl][28] 4. [↵][29]1. R. Bistritzer, 2. A. H. MacDonald , Proc. Natl. Acad. Sci. U.S.A. 108, 12233 (2011). [OpenUrl][30][Abstract/FREE Full Text][31] 5. [↵][32]1. E. Suárez Morell et al ., Phys. Rev. B Condens. Matter Mater. Phys. 82, 121407 (2010). [OpenUrl][33][CrossRef][34] 6. [↵][35]1. E. Y. Andrei et al ., Nat. Rev. Mater. 10.1038/s41578-021-00284-1 (2020). 7. [↵][36]1. K. P. Nuckolls et al ., Nature 588, 610 (2020). [OpenUrl][37][CrossRef][38][PubMed][39] 8. [↵][40]1. Y. Xie et al ., Nature 572, 101 (2019). [OpenUrl][41] 9. [↵][42]1. E. Khalaf et al ., Phys. Rev. B 100, 085109 (2019). [OpenUrl][43][CrossRef][44] 10. [↵][45]1. D. Wong et al ., Nature 582, 198 (2020). [OpenUrl][46][CrossRef][47][PubMed][48] 11. [↵][49]1. U. Zondiner et al ., Nature 582, 203 (2020). [OpenUrl][50][CrossRef][51][PubMed][52] 12. [↵][53]1. B. Lian et al ., arXiv:1811.11786 [cond-mat.str-el] (2020). 13. [↵][54]1. E. Khalaf et al ., arXiv:2004.00638 [cond-mat.str-el] (2020). 14. [↵][55]1. B. A. Bernevig et al ., arXiv:2009.14200 [cond-mat.str-el] (2020). 15. [↵][56]1. T. H. Geballe, 2. J. K. Hulm , in Biographical Memoirs (National Academies Press, 1996), vol. 70, pp. 240–259. [OpenUrl][57] Acknowledgments: I acknowledge discussions with X. Li and funding from the Gordon and Betty Moore Foundation, the U.S. Department of Energy, and the U.S. National Science Foundation. 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领域	气候变化 ; 资源环境
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文献类型	期刊论文
条目标识符	http://119.78.100.173/C666/handle/2XK7JSWQ/318678
专题	气候变化资源环境科学
推荐引用方式 GB/T 7714	Ali Yazdani. Magic, symmetry, and twisted matter[J]. Science,2021.
APA	Ali Yazdani.(2021).Magic, symmetry, and twisted matter.Science.
MLA	Ali Yazdani."Magic, symmetry, and twisted matter".Science (2021).