Intrinsic superflat bands in general twisted bilayer systems

Hongfei Wang; Shaojie Ma; Shuang Zhang; Dangyuan Lei

doi:10.1038/s41377-022-00838-0

Go to Nature Website

Your Location：

Home >

Browse articles >

Intrinsic superflat bands in general twisted bilayer systems

Articles

- Intrinsic superflat bands in general twisted bilayer systems
- Light: Science & Applications Vol. 11, Issue 7, Pages: 1475-1481(2022)
- Affiliations：
  
  1.Department of Materials Science and Engineering, City University of Hong Kong, Kowloon, Hong Kong, 999077, China
  2.Department of Physics, University of Hong Kong, Hong Kong, 999077, China
  3.Department of Electrical and Electronic Engineering, University of Hong Kong, Hong Kong, 999077, China
- Author bio：
  
  Shuang Zhang (shuzhang@hku.hk)
  Dangyuan Lei (dangylei@cityu.edu.hk)
- Funds：
- DOI：10.1038/s41377-022-00838-0
  CLC：
Scan for full text
Wang, H. F. et al. Intrinsic superflat bands in general twisted bilayer systems. Light: Science & Applications, 11, 1475-1181 (2022).
DOI：

Wang, H. F. et al. Intrinsic superflat bands in general twisted bilayer systems. Light: Science & Applications, 11, 1475-1181 (2022). DOI： 10.1038/s41377-022-00838-0.

摘要

Abstract

Twisted bilayer systems with discrete magic angles, such as twisted bilayer graphene featuring moiré superlattices, provide a versatile platform for exploring novel physical properties. Here, we discover a class of superflat bands in general twisted bilayer systems beyond the low-energy physics of magic-angle twisted counterparts. By considering continuous lattice dislocation, we obtain intrinsic localized states, which are spectrally isolated at lowest and highest energies and spatially centered around the AA stacked region, governed by the macroscopic effective energy potential well. Such localized states exhibit negligible inter-cell coupling and support the formation of superflat bands in a wide and continuous parameter space, which can be mimicked using a twisted bilayer nanophotonic system. Our finding suggests that general twisted bilayer systems can realize continuously tunable superflat bands and the corresponding localized states for various photonic, phononic, and mechanical waves.

关键词

Keywords

references

K. S. Novoselov , 等 . Electric field effect in atomically thin carbon films . Science , 2004 . 306 666 -669 . DOI:10.1126/science.1102896http://doi.org/10.1126/science.1102896 .

F. Zhang , A. H. MacDonald , E. J. Mele . Valley Chern numbers and boundary modes in gapped bilayer graphene . Proc. Natl Acad. Sci. USA , 2013 . 110 10546 -10551 . DOI:10.1073/pnas.1308853110http://doi.org/10.1073/pnas.1308853110 .

K. Liu , 等 . Evolution of interlayer coupling in twisted molybdenum disulfide bilayers . Nat. Commun. , 2014 . 5 4966 DOI:10.1038/ncomms5966http://doi.org/10.1038/ncomms5966 .

M. H. Naik , M. Jain . Ultraflatbands and shear solitons in moiré patterns of twisted bilayer transition metal dichalcogenides . Phys. Rev. Lett. , 2018 . 121 266401 DOI:10.1103/PhysRevLett.121.266401http://doi.org/10.1103/PhysRevLett.121.266401 .

Y. Cao , 等 . Superlattice-induced insulating states and valley-protected orbits in twisted bilayer graphene . Phys. Rev. Lett. , 2016 . 117 116804 DOI:10.1103/PhysRevLett.117.116804http://doi.org/10.1103/PhysRevLett.117.116804 .

X. Lu , 等 . Superconductors, orbital magnets and correlated states in magic-angle bilayer graphene . Nature , 2019 . 574 653 -657 . DOI:10.1038/s41586-019-1695-0http://doi.org/10.1038/s41586-019-1695-0 .

J. Y. Lee , 等 . Theory of correlated insulating behaviour and spin-triplet superconductivity in twisted double bilayer graphene . Nat. Commun. , 2019 . 10 5333 DOI:10.1038/s41467-019-12981-1http://doi.org/10.1038/s41467-019-12981-1 .

Y. Cao , 等 . Tunable correlated states and spin-polarized phases in twisted bilayer-bilayer graphene . Nature , 2020 . 583 215 -220 . DOI:10.1038/s41586-020-2260-6http://doi.org/10.1038/s41586-020-2260-6 .

Y. Cao , 等 . Unconventional superconductivity in magic-angle graphene superlattices . Nature , 2018 . 556 43 -50 . DOI:10.1038/nature26160http://doi.org/10.1038/nature26160 .

Y. Cao , 等 . Correlated insulator behaviour at half-filling in magic-angle graphene superlattices . Nature , 2018 . 556 80 -84 . DOI:10.1038/nature26154http://doi.org/10.1038/nature26154 .

M. Yankowitz , 等 . Tuning superconductivity in twisted bilayer graphene . Science , 2019 . 363 1059 -1064 . DOI:10.1126/science.aav1910http://doi.org/10.1126/science.aav1910 .

J. Jung , A. Raoux , Z. Qiao , A. H. MacDonald . Ab initio theory of moiré superlattice bands in layered two-dimensional materials . Phys. Rev. B , 2014 . 89 205414 DOI:10.1103/PhysRevB.89.205414http://doi.org/10.1103/PhysRevB.89.205414 .

M. Yankowitz , 等 . Dynamic band-structure tuning of graphene moiré superlattices with pressure . Nature , 2018 . 557 404 -408 . DOI:10.1038/s41586-018-0107-1http://doi.org/10.1038/s41586-018-0107-1 .

C. Jin , 等 . Observation of moiré excitons in WSe2/WS2 heterostructure superlattices . Nature , 2019 . 567 76 -80 . DOI:10.1038/s41586-019-0976-yhttp://doi.org/10.1038/s41586-019-0976-y .

A. K. Geim , I. V. Grigorieva . Van der Waals heterostructures . Nature , 2013 . 499 419 -425 . DOI:10.1038/nature12385http://doi.org/10.1038/nature12385 .

A. Mishchenko , 等 . Twist-controlled resonant tunnelling in graphene/boron nitride/graphene heterostructures . Nat. Nanotech. , 2014 . 9 808 -813 . DOI:10.1038/nnano.2014.187http://doi.org/10.1038/nnano.2014.187 .

Y. Liu , 等 . Van der Waals heterostructures and devices . Nat. Rev. Mater. , 2016 . 1 16042 DOI:10.1038/natrevmats.2016.42http://doi.org/10.1038/natrevmats.2016.42 .

K. Tran , 等 . Evidence for moiré excitons in van der Waals heterostructures . Nature , 2019 . 567 71 -75 . DOI:10.1038/s41586-019-0975-zhttp://doi.org/10.1038/s41586-019-0975-z .

H. C. Po , L. Zou , A. Vishwanath , T. Senthil . Origin of Mott insulating behavior and superconductivity in twisted bilayer graphene . Phys. Rev. X , 2018 . 8 031089 .

K. Seo , V. N. Kotov , B. Uchoa . Ferromagnetic Mott state in twisted graphene bilayers at the magic angle . Phys. Rev. Lett. , 2019 . 122 246402 DOI:10.1103/PhysRevLett.122.246402http://doi.org/10.1103/PhysRevLett.122.246402 .

G. Chen , 等 . Evidence of a gate-tunable Mott insulator in a trilayer graphene moiré superlattice . Nat. Phys. , 2019 . 15 237 -241 . DOI:10.1038/s41567-018-0387-2http://doi.org/10.1038/s41567-018-0387-2 .

E. C. Regan , 等 . Mott and generalized Wigner crystal states in WSe2/WS2 moiré superlattices . Nature , 2020 . 579 359 -363 . DOI:10.1038/s41586-020-2092-4http://doi.org/10.1038/s41586-020-2092-4 .

C. Xu , L. Balents . Topological superconductivity in twisted multilayer graphene . Phys. Rev. Lett. , 2018 . 121 087001 DOI:10.1103/PhysRevLett.121.087001http://doi.org/10.1103/PhysRevLett.121.087001 .

E. Codecido , 等 . Correlated insulating and superconducting states in twisted bilayer graphene below the magic angle . Sci. Adv. , 2019 . 5 eaaw9770 DOI:10.1126/sciadv.aaw9770http://doi.org/10.1126/sciadv.aaw9770 .

D. V. Chichinadze , L. Classen , A. V. Chubukov . Nematic superconductivity in twisted bilayer graphene . Phys. Rev. B , 2020 . 101 224513 DOI:10.1103/PhysRevB.101.224513http://doi.org/10.1103/PhysRevB.101.224513 .

G. Tarnopolsky , A. J. Kruchkov , A. Vishwanath . Origin of magic angles in twisted bilayer graphene . Phys. Rev. Lett. , 2019 . 122 106405 DOI:10.1103/PhysRevLett.122.106405http://doi.org/10.1103/PhysRevLett.122.106405 .

A. Kerelsky , 等 . Maximized electron interactions at the magic angle in twisted bilayer graphene . Nature , 2019 . 572 95 -100 . DOI:10.1038/s41586-019-1431-9http://doi.org/10.1038/s41586-019-1431-9 .

Y. Jiang , 等 . Charge order and broken rotational symmetry in magic-angle twisted bilayer graphene . Nature , 2019 . 573 91 -95 . DOI:10.1038/s41586-019-1460-4http://doi.org/10.1038/s41586-019-1460-4 .

R. Bistritzer , A. H. MacDonald . Moiré bands in twisted double-layer graphene . Proc. Natl Acad. Sci. USA , 2011 . 108 12233 -12237 . DOI:10.1073/pnas.1108174108http://doi.org/10.1073/pnas.1108174108 .

K. Kim , 等 . Tunable moiré bands and strong correlations in small-twist-angle bilayer graphene . Proc. Natl Acad. Sci. USA , 2017 . 114 3364 -3369 . DOI:10.1073/pnas.1620140114http://doi.org/10.1073/pnas.1620140114 .

S. Wu , Z. Zhang , K. Watanabe , T. Taniguchi , E. Y. Andrei . Chern insulators, van Hove singularities and topological flat bands in magic-angle twisted bilayer graphene . Nat. Mat. , 2021 . 20 488 -494 . DOI:10.1038/s41563-020-00911-2http://doi.org/10.1038/s41563-020-00911-2 .

Z. Song , 等 . All magic angles in twisted bilayer graphene are topological . Phys. Rev. Lett. , 2019 . 123 036401 DOI:10.1103/PhysRevLett.123.036401http://doi.org/10.1103/PhysRevLett.123.036401 .

Z.-D. Song , L. Elcoro , B. A. Bernevig . Twisted bulk-boundary correspondence of fragile topology . Science , 2020 . 367 794 -797 . DOI:10.1126/science.aaz7650http://doi.org/10.1126/science.aaz7650 .

S. Longhi . Photonic flat-band laser . Opt. Lett. , 2019 . 44 287 -290 . DOI:10.1364/OL.44.000287http://doi.org/10.1364/OL.44.000287 .

S. Kim , J. Lee , H. Jeon , H. J. Kim . Fiber-coupled surface-emitting photonic crystal band edge laser for biochemical sensor applications . Appl. Phys. Lett. , 2009 . 94 133503 DOI:10.1063/1.3114405http://doi.org/10.1063/1.3114405 .

C. Elias , 等 . Flat bands and giant light-matter interaction in hexagonal boron nitride . Phys. Rev. Lett. , 2021 . 127 137401 DOI:10.1103/PhysRevLett.127.137401http://doi.org/10.1103/PhysRevLett.127.137401 .

P. Moon , M. Koshino . Optical absorption in twisted bilayer graphene . Phys. Rev. B , 2013 . 87 205404 DOI:10.1103/PhysRevB.87.205404http://doi.org/10.1103/PhysRevB.87.205404 .

T. M. R. Wolf , J. L. Lado , G. Blatter , O. Zilberberg . Electrically tunable flat bands and magnetism in twisted bilayer graphene . Phys. Rev. Lett. , 2019 . 123 096802 DOI:10.1103/PhysRevLett.123.096802http://doi.org/10.1103/PhysRevLett.123.096802 .

K. H. Su , 等 . Interparticle coupling effects on plasmon resonances of nanogold particles . Nano Lett. , 2003 . 3 1087 -1090 . DOI:10.1021/nl034197fhttp://doi.org/10.1021/nl034197f .

Z. Guo , H. Jiang , Y. Li , H. Chen , G. S. Agarwal . Enhancement of electromagnetically induced transparency in metamaterials using long range coupling mediated by a hyperbolic material . Opt. Express , 2018 . 26 627 -641 . DOI:10.1364/OE.26.000627http://doi.org/10.1364/OE.26.000627 .

Y. Zhang , 等 . Direct observation of a widely tunable bandgap in bilayer graphene . Nature , 2009 . 459 820 -823 . DOI:10.1038/nature08105http://doi.org/10.1038/nature08105 .

E. McCann , M. Koshino . The electronic properties of bilayer graphene . Rep. Prog. Phys. , 2013 . 76 056503 DOI:10.1088/0034-4885/76/5/056503http://doi.org/10.1088/0034-4885/76/5/056503 .

P. San-Jose , J. González , F. Guinea . Non-Abelian gauge potentials in graphene bilayers . Phys. Rev. Lett. , 2012 . 108 216802 DOI:10.1103/PhysRevLett.108.216802http://doi.org/10.1103/PhysRevLett.108.216802 .

B.-Y. Xie , 等 . Visualization of higher-order topological insulating phases in two-dimensional dielectric photonic crystals . Phys. Rev. Lett. , 2019 . 122 233903 DOI:10.1103/PhysRevLett.122.233903http://doi.org/10.1103/PhysRevLett.122.233903 .

S. Huang , 等 . Topologically protected helical states in minimally twisted bilayer graphene . Phys. Rev. Lett. , 2018 . 121 037702 DOI:10.1103/PhysRevLett.121.037702http://doi.org/10.1103/PhysRevLett.121.037702 .

H. Yoo , 等 . Atomic and electronic reconstruction at the van der Waals interface in twisted bilayer graphene . Nat. Mater. , 2019 . 18 448 -453 . DOI:10.1038/s41563-019-0346-zhttp://doi.org/10.1038/s41563-019-0346-z .

H. F. Wang , 等 . Bound states in the continuum in a bilayer photonic crystal with TE-TM cross coupling . Phys. Rev. B , 2018 . 98 214101 DOI:10.1103/PhysRevB.98.214101http://doi.org/10.1103/PhysRevB.98.214101 .

H. Wang , 等 . Exceptional concentric rings in a non-Hermitian bilayer photonic system . Phys. Rev. B , 2019 . 100 165134 DOI:10.1103/PhysRevB.100.165134http://doi.org/10.1103/PhysRevB.100.165134 .

G. Hu , 等 . Topological polaritons and photonic magic angles in twisted α-MoO3 bilayers . Nature , 2020 . 582 209 -213 . DOI:10.1038/s41586-020-2359-9http://doi.org/10.1038/s41586-020-2359-9 .

Views

Downloads

CSCD

Alert me when the article has been cited

Submit

Tools

Publicity Resources

No data

Related Author

No data

Related Institution

No data

⁰