Abstract
AbstractProperties of atomic van der Waals heterostructures are profoundly influenced by interlayer coupling, which critically depends on stacking of the proximal layers. Rotational misalignment or lattice mismatch of the layers gives rise to a periodic modulation of the stacking, the moiré superlattice. Provided the superlattice period extends over many unit cells, the coupled layers undergo lattice relaxation, leading to the concentration of strain at line defects – solitons - separating large area commensurate domains. We visualize such long-range periodic superstructures in thin crystals of hexagonal boron nitride using atomic-force microscopy and nano-infrared spectroscopy. The solitons form sub-surface hexagonal networks with periods of a few hundred nanometers. We analyze the topography and infrared contrast of these networks to obtain spatial distribution of local strain and its effect on the infrared-active phonons of hBN.
Authors
11
- G. X. Ni (first)
- H. Wang (additional)
- B.-Y. Jiang (additional)
- L. X. Chen (additional)
- Y. Du (additional)
- Z. Y. Sun (additional)
- M. D. Goldflam (additional)
- A. J. Frenzel (additional)
- X. M. Xie (additional)
- M. M. Fogler (additional)
- D. N. Basov (additional)
References
46
Referenced
78
-
Bistritzer, R. & MacDonald, A. H. Moiré bands in twisted double-layer graphene. Proc. Natl Acad. Sci. USA 108, 12233–12237 (2011).
(
10.1073/pnas.1108174108
) / Proc. Natl Acad. Sci. USA by R Bistritzer (2011) -
Cao, Y. et al. Unconventional superconductivity in magic-angle graphene superlattices. Nature 556, 43–50 (2018).
(
10.1038/nature26160
) / Nature by Y Cao (2018) -
Geim, A. K. & Grigorieva, I. V. Van der Waals heterostructures. Nature 499, 419–425 (2013).
(
10.1038/nature12385
) / Nature by AK Geim (2013) -
Basov, D. N., Fogler, M. M. & Garcia de Abajo, F. J. Polaritons in van der Waals materials. Science 354, aag1992 (2016).
(
10.1126/science.aag1992
) / Science by DN Basov (2016) -
Low, T. et al. Polaritons in layered two-dimensional materials. Nat. Matters 16, 182–194 (2017).
(
10.1038/nmat4792
) / Nat. Matters by T Low (2017) - Yoo, H. et al. Atomic reconstruction at van der Waals interface in twisted bilayer graphene. arXiv:1804.03806 (2018).
-
Fang, H. et al. Strong interlayer coupling in van der Waals heterostructures built from single-layer chalcogenides. Proc. Natl Acad. Sci. USA 111, 6198–6202 (2014).
(
10.1073/pnas.1405435111
) / Proc. Natl Acad. Sci. USA by H Fang (2014) -
Yu, H., Liu, G. B., Tang, J., Xu, X. & Yao, W. Moiré excitons: from programmable quantum emitter arrays to spin–orbit-coupled artificial lattices. Sci. Adv. 3, e1701696 (2017).
(
10.1126/sciadv.1701696
) / Sci. Adv. by H Yu (2017) -
Wu, F., Lovorn, T. & MacDonald, A. H. Topological exciton bands in moiré heterojunctions. Phys. Rev. Lett. 118, 147401 (2017).
(
10.1103/PhysRevLett.118.147401
) / Phys. Rev. Lett. by F Wu (2017) -
Song, J. C. W., Shytov, A. V. & Levitov, L. S. Electron interactions and gap opening in graphene superlattices. Phys. Rev. Lett. 111, 266801 (2013).
(
10.1103/PhysRevLett.111.266801
) / Phys. Rev. Lett. by JCW Song (2013) -
Alden, S. J. et al. Strain solitons and topological defects in bilayer graphene. Proc. Natl Acad. Sci. USA 110, 11256–11260 (2013).
(
10.1073/pnas.1309394110
) / Proc. Natl Acad. Sci. USA by SJ Alden (2013) -
Woods, C. R. et al. Commensurate–incommensurate transition for graphene on hexagonal boron nitride. Nat. Phys. 9, 329–340 (2013).
(
10.1038/nphys2615
) / Nat. Phys. by CR Woods (2013) -
San-Jose, P. & Prada, E. Helical networks in twisted bilayer graphene under interlayer bias. Phys. Rev. B 88, 121408(R) (2013).
(
10.1103/PhysRevB.88.121408
) / Phys. Rev. B by P San-Jose (2013) -
Sunku, S. S. et al. Photonic crystals for nano-light in moiré graphene superlattices. Science 362, 1153–1156 (2018).
(
10.1126/science.aau5144
) / Science by SS Sunku (2018) -
Ni, G. X. et al. Plasmons in graphene moiré superlattices. Nat. Matters 14, 1217–1222 (2015).
(
10.1038/nmat4425
) / Nat. Matters by GX Ni (2015) -
Shi, Z. et al. Gate-dependent pseudospin mixing in graphene/Boron nitride moiré superlattices. Nat. Phys. 10, 743–747 (2014).
(
10.1038/nphys3075
) / Nat. Phys. by Z Shi (2014) -
Yankowitz, M., Ma, Q., Jarillo-Herrero, P. & LeRoy, B. J. van der Waals heterostructures combining graphene and hexagonal boron nitride. Nat. Rev. Phys. 1, 112–125 (2019).
(
10.1038/s42254-018-0016-0
) / Nat. Rev. Phys. by M Yankowitz (2019) -
Tomadin, A., Polini, M. & Jung, J. Plasmons in realistic graphene/hexagonal boron nitride moiré patterns. Phys. Rev. B 99, 035432 (2019).
(
10.1103/PhysRevB.99.035432
) / Phys. Rev. B by A Tomadin (2019) -
Schaibley, J. R. et al. Valleytronics in 2D materials. Nat. Rev. Mater. 1, 16055 (2016).
(
10.1038/natrevmats.2016.55
) / Nat. Rev. Mater. by JR Schaibley (2016) -
Yankowitz, M. et al. Tuning superconductivity in twisted bilayer graphene. Science https://doi.org/10.1126/science.aav1910 (2019).
(
10.1126/science.aav1910
) / Science by Matthew Yankowitz (2019) -
Huang, S. et al. Topologically protected helical states in minimally twisted bilayer graphene. Phys. Rev. Lett. 121, 037702 (2018).
(
10.1103/PhysRevLett.121.037702
) / Phys. Rev. Lett. by S Huang (2018) -
Kim, K. et al. Tunable moiré bands and strong correlations in small-twist-angle bilayer graphene. Proc. Natl Acad. Sci. USA 114, 3364–3369 (2017).
(
10.1073/pnas.1620140114
) / Proc. Natl Acad. Sci. USA by K Kim (2017) -
Jiang, B.-Y. et al. Plasmon reflections by topological electronic boundaries in bilayer graphene. Nano. Lett. 17, 7080 (2017).
(
10.1021/acs.nanolett.7b03816
) / Nano. Lett. by B-Y Jiang (2017) -
Ju, L. et al. Topological valley transport at bilayer graphene domain walls. Nature 520, 650 (2015).
(
10.1038/nature14364
) / Nature by L Ju (2015) -
Jiang, L. et al. Soliton-dependent plasmon reflection at bilayer graphene domain walls. Nat. Mater. 15, 840–844 (2016).
(
10.1038/nmat4653
) / Nat. Mater. by L Jiang (2016) -
Lyu, B. et al. Phonon polariton-assisted infrared nanoimaging of local strain in hexagonal boron nitride. Nano Lett. 19, 1982–1989 (2019).
(
10.1021/acs.nanolett.8b05166
) / Nano Lett. by B Lyu (2019) -
Atkin, J. M., Berweger, S., Jones, A. C. & Raschke, M. B. Nano-optical imaging and spectroscopy of order, phases, and domains in complex solids. Adv. Phys. 61, 745–842 (2012).
(
10.1080/00018732.2012.737982
) / Adv. Phys. by JM Atkin (2012) -
Caldwell, J. D. et al. Atomic-scale photonic hybrids for mid-infrared and terahertz nanophotonics. Nat. Nano 11, 9–15 (2016).
(
10.1038/nnano.2015.305
) / Nat. Nano by JD Caldwell (2016) -
Dai, S. et al. Tunable phonon polaritons in atomically thin van der Waals crystals of boron nitride. Science 343, 1125 (2014).
(
10.1126/science.1246833
) / Science by S Dai (2014) -
Caldwell, J. D. et al. Photonics with hexagonal boron nitride. Nat. Rev. Mater. 4, 552–567 (2019).
(
10.1038/s41578-019-0124-1
) / Nat. Rev. Mater. by JD Caldwell (2019) -
Ambrosio, A. et al. Selective excitation and imaging of ultraslow phonon polaritons in thin hexagonal boron nitride crystals. Light.: Sci. Appl. 7, 27 (2018).
(
10.1038/s41377-018-0039-4
) / Light.: Sci. Appl. by A Ambrosio (2018) -
Li, P. et al. Hyperbolic phonon-polaritons in boron nitride for near-field optical imaging and focusing. Nature Comm. 6, 7507 (2015).
(
10.1038/ncomms8507
) -
Fei, Z. et al. Gate-tuning of graphene plasmons revealed by infrared nano-imaging. Nano Lett. 11, 4701–4705 (2011).
(
10.1021/nl202362d
) / Nano Lett. by Z Fei (2011) -
Ni, G. X. et al. Ultrafast optical switching of infrared plasmon polaritons in high-mobility graphene. Nat. Photon. 10, 244–247 (2016).
(
10.1038/nphoton.2016.45
) / Nat. Photon. by GX Ni (2016) -
Ni, G. X. et al. Fundamental limits to graphene plasmonics. Nature 557, 530–533 (2018).
(
10.1038/s41586-018-0136-9
) / Nature by GX Ni (2018) -
Huber, A. J., Ziegler, A., Köck, T. & Hillenbrand, R. Infrared nanoscopy of strained semiconductors. Nat. Nano 4, 153–157 (2009).
(
10.1038/nnano.2008.399
) / Nat. Nano by AJ Huber (2009) -
Ma, W. et al. In-plane anisotropic and ultra-low-loss polaritons in a natural van der Waals crystal. Nature 562, 557–562 (2018).
(
10.1038/s41586-018-0618-9
) / Nature by W Ma (2018) - Zheng, Z. et al. A mid-infrared biaxial hyperbolic van der Waals crystal. Sci. Adv. 5, 5 (2019). / Sci. Adv. by Z Zheng (2019)
-
Kim, C.-J. et al. Stacking order dependent second harmonic generation and topological defects in h-BN bilayers. Nano Lett. 13, 5660–5665 (2013).
(
10.1021/nl403328s
) / Nano Lett. by C-J Kim (2013) -
Yoon, D., Son, Y. W. & Cheong, H. Negative thermal expansion coefficient of graphene measured by Raman spectroscopy. Nano Lett. 11, 3227 (2011).
(
10.1021/nl201488g
) / Nano Lett. by D Yoon (2011) -
Paszkowicz, W., Pelka, J. B., Knapp, M., Szyszko, T. & Podsiadlo, S. Lattice parameters and anistropic thermal expansion of the hexagonal boron nitride in the 10–297.5 K temperature range. Appl. Phys. A 75, 431 (2002).
(
10.1007/s003390100999
) / Appl. Phys. A by W Paszkowicz (2002) -
Lebedeva, I. V., Lebedev, A. V., Popov, A. M. & Knizhnik, A. A. Dislocations in stacking and commensurate-incommensurate phase transition in bilayer graphene and hexagonal boron nitride. Phys. Rev. B 93, 235414 (2016).
(
10.1103/PhysRevB.93.235414
) / Phys. Rev. B by IV Lebedeva (2016) - Xian, L., Kennes, D. M., Tancogne-Dejean, N., Altarelli, M. & Rubio, A. Multi-flat bands and strong correlations in twisted bilayer boron nitride. arXiv: 1812.08097 (2018).
-
Ribeiro-Palau, R. et al. Twistable electronics with dynamically rotable heterostructures. Science 361, 690–693 (2018).
(
10.1126/science.aat6981
) / Science by R Ribeiro-Palau (2018) -
Yankowitz, M., Xue, J. & LeRoy, B. J. Graphene on hexagonal boron nitride. J. Phys. Condens. Matter 26, 303201 (2014).
(
10.1088/0953-8984/26/30/303201
) / J. Phys. Condens. Matter by M Yankowitz (2014) - Weaire, D. & Hutzler, S. The Physics of Foams. (Oxford University Press, Oxford, 1999). / The Physics of Foams by D Weaire (1999)
Dates
Type | When |
---|---|
Created | 5 years, 10 months ago (Sept. 25, 2019, 6:03 a.m.) |
Deposited | 2 years, 8 months ago (Dec. 16, 2022, 8:27 p.m.) |
Indexed | 2 days, 2 hours ago (Aug. 23, 2025, 1:19 a.m.) |
Issued | 5 years, 11 months ago (Sept. 25, 2019) |
Published | 5 years, 11 months ago (Sept. 25, 2019) |
Published Online | 5 years, 11 months ago (Sept. 25, 2019) |
@article{Ni_2019, title={Soliton superlattices in twisted hexagonal boron nitride}, volume={10}, ISSN={2041-1723}, url={http://dx.doi.org/10.1038/s41467-019-12327-x}, DOI={10.1038/s41467-019-12327-x}, number={1}, journal={Nature Communications}, publisher={Springer Science and Business Media LLC}, author={Ni, G. X. and Wang, H. and Jiang, B.-Y. and Chen, L. X. and Du, Y. and Sun, Z. Y. and Goldflam, M. D. and Frenzel, A. J. and Xie, X. M. and Fogler, M. M. and Basov, D. N.}, year={2019}, month=sep }