In recent decades, scientists have developed the means to engineer synthetic periodic arrays with feature sizes below the wavelength of light. When such features are appropriately structured, electromagnetic radiation can be manipulated in unusual ways, resulting in optical metamaterials whose function is directly controlled through nanoscale structure. Nature, too, has adopted such techniques—for example in the unique colouring of butterfly wings—to manipulate photons as they propagate through nanoscale periodic assemblies. In this Perspective, we highlight the intriguing potential of designer structuring of electronic matter at scales at and below the electron wavelength, which affords a new range of synthetic quantum metamaterials with unconventional responses. Driven by experimental developments in stacking atomically layered heterostructures—such as mechanical pick-up/transfer assembly—atomic-scale registrations and structures can be readily tuned over distances smaller than characteristic electronic length scales (such as the electron wavelength, screening length and electron mean free path). Yet electronic metamaterials promise far richer categories of behaviour than those found in conventional optical metamaterial technologies. This is because, unlike photons, which scarcely interact with each other, electrons in subwavelength-structured metamaterials are charged and strongly interact. As a result, an enormous variety of emergent phenomena can be expected and radically new classes of interacting quantum metamaterials designed.
This is a preview of subscription content, access via your institution
Open Access articles citing this article.
Nature Communications Open Access 10 July 2023
Light: Science & Applications Open Access 16 June 2023
Nature Communications Open Access 14 May 2021
Access Nature and 54 other Nature Portfolio journals
Get Nature+, our best-value online-access subscription
$29.99 / 30 days
cancel any time
Subscribe to this journal
Receive 12 print issues and online access
$259.00 per year
only $21.58 per issue
Rent or buy this article
Prices vary by article type
Prices may be subject to local taxes which are calculated during checkout
Geim, A. K. & Grigorieva, I. V. Van der Waals heterostructures. Nature 499, 419 (2013).
Novoselov, K. S. et al. Two-dimensional atomic crystals. Proc. Natl Acad. Sci. USA 102, 10451–10453 (2005).
Zhou, J. et al. A library of atomically thin metal chalcogenides. Nature 556, 355–359 (2018).
Dean, C. R. et al. Boron nitride substrates for high-quality graphene electronics. Nature Nanotech. 5, 722–726 (2010).
Wang, L. et al. One-dimensional electrical contact to a two-dimensional material. Science 342, 614–617 (2013).
Novoselov, K. S., Mishchenko, A., Carvalho, A. & Castro Neto, A. H. 2D materials and van der Waals heterostructures. Science 353, aac9439 (2016).
Santos, D., Lopes, J. M., Peres, N. M. R. & Castro Neto, A. H. Graphene bilayer with a twist: electronic structure. Phys. Rev. Lett. 99, 256802 (2007).
Giovannetti, G., Khomyakov, P. A., Brocks, G., Kelly, P. J. & van den Brink, J. Substrate-induced band gap in graphene on hexagonal boron nitride: ab initio density functional calculations. Phys. Rev. B 76, 073103 (2007).
Mele, E. J. Commensuration and interlayer coherence in twisted bilayer graphene. Phys. Rev. B 81, 161405 (2010).
Bistritzer, R. & MacDonald, A. H. Transport between twisted graphene layers. Phys. Rev. B 81, 245412 (2010).
Bistritzer, R. & MacDonald, A. H. Moiré bands in twisted double-layer graphene. Proc. Natl Acad. Sci. USA 108, 12233–12237 (2011).
Woods, C. R. et al. Commensurate–incommensurate transition in graphene on hexagonal boron nitride. Nat. Phys. 10, 451–456 (2014).
Xue, J. et al. Scanning tunnelling microscopy and spectroscopy of ultra-flat graphene on hexagonal boron nitride. Nat. Mater. 10, 282–285 (2011).
Kindermann, M., Uchoa, B. & Miller, D. L. Zero-energy modes and gate-tunable gap in graphene on hexagonal boron nitride. Phys. Rev. B 86, 115415 (2012).
Yankowitz, M. et al. Emergence of superlattice Dirac points in graphene on hexagonal boron nitride. Nat. Phys. 8, 382–386 (2012).
Wallbank, J. R., Patel, A. A., Mucha-Kruczyński, M., Geim, A. K. & Fal'ko, V. I. Generic miniband structure of graphene on a hexagonal substrate. Phys. Rev. B 87, 245408 (2013).
Ponomarenko, L. A. et al. Cloning of Dirac fermions in graphene superlattices. Nature 497, 594–597 (2013).
Dean, C. R. et al. Hofstadter’s butterfly and the fractal quantum Hall effect in moiré superlattices. Nature 497, 598–602 (2013).
Hunt, B. et al. Massive Dirac fermions and Hofstadter butterfly in a van der Waals heterostructure. Science 340, 1427–1430 (2013).
Gorbachev, R. V. et al. Detecting topological currents in graphene superlattices. Science 346, 448–451 (2014).
Li, G. et al. Observation of Van Hove singularities in twisted graphene layers. Nat. Phys. 6, 109 (2010).
Kumar, R. K. et al. High-temperature quantum oscillations caused by recurring Bloch states in graphene superlattices. Science 357, 181–184 (2017).
Xiao, D., Chang, M. C. & Niu, Q. Berry phase effects on electronic properties. Rev. Mod. Phys. 82, 1959 (2010).
Sodemann, I. & Fu, L. Quantum nonlinear Hall effect induced by Berry curvature dipole in time-reversal invariant materials. Phys. Rev. Lett. 115, 216806 (2015).
Morimoto, T. & Naoto, N. Topological nature of nonlinear optical effects in solids. Sci. Adv. 2, e1501524 (2016).
Guinea, F., Castro Neto, A. H. & Peres, N. M. R. Electronic states and Landau levels in graphene stacks. Phys. Rev. B 73, 245426 (2006).
Xiao, D., Yao, W. & Niu, Q. Valley-contrasting physics in graphene: magnetic moment and topological transport. Phys. Rev. Lett. 99, 236809 (2007).
Mak, K. F., McGill, K., Park, J. & McEuen, P. L. The valley Hall effect in MoS2 transistors. Science 344, 1489–1492 (2014).
Sui, M. et al. Gate-tunable topological valley transport in bilayer graphene. Nat. Phys. 11, 1027 (2015).
Shimazaki, Y. et al. Generation and detection of pure valley current by electrically induced Berry curvature in bilayer graphene. Nat. Phys. 11, 1032–1036 (2015).
Lee, J., Mak, K. F. & Shan, J. Electrical control of the valley Hall effect in bilayer MoS2 transistors. Nat. Nanotech. 11, 421–425 (2016).
Lee, J., Wang, Z., Xie, H., Mak, K. F. & Shan, J. Valley magnetoelectricity in single-layer MoS2. Nat. Mater. 16, 887–891 (2017).
Castro, E. V. et al. Biased bilayer graphene: semiconductor with a gap tunable by the electric field effect. Phys. Rev. Lett. 99, 216802 (2007).
Zhang, Y. et al. Direct observation of a widely tunable bandgap in bilayer graphene. Nature 459, 820–823 (2009).
Weitz, R. T., Allen, M. T., Feldman, B. E., Martin, J. & Yacoby, A. Broken-symmetry states in doubly gated suspended bilayer graphene. Science 330, 812–816 (2010).
Velasco, J. Jr et al. Transport spectroscopy of symmetry-broken insulating states in bilayer graphene. Nat. Nanotech. 7, 156–160 (2012).
Nandkishore, R. & Levitov, L. S. Spontaneously ordered states in bilayer graphene. Phys. Scr. T146, 014011 (2012).
Gong, Z. et al. Magnetoelectric effects and valley-controlled spin quantum gates in transition metal dichalcogenide bilayers. Nat. Commun. 4, 2053 (2013).
Bernevig, B. A. & Hughes T. L. Topological Insulators and Topological Superconductors (Princeton Univ. Press, Princeton, 2013).
Zhang, F., MacDonald, A. H. & Mele, E. J. Valley Chern numbers and boundary modes in gapped bilayer graphene. Proc. Natl Acad. Sci. USA 110, 10546–10551 (2013).
Vaezi, A. et al. Topological edge states at a tilt boundary in gated multilayer graphene. Phys. Rev. X 3, 021018 (2013).
Ju, L. et al. Topological valley transport at bilayer graphene domain walls. Nature 520, 650–655 (2015).
Martin, I., Blanter, Y. M. & Morpurgo, A. F. Topological confinement in bilayer graphene. Phys. Rev. Lett. 100, 036804 (2008).
Li, J. et al. Gate-controlled topological conducting channels in bilayer graphene. Nat. Nanotech. 11, 1060–1065 (2016).
Song, J. C. W., Samutpraphoot, P. & Levitov, L. S. Topological Bloch bands in graphene superlattices. Proc. Natl Acad. Sci. 112, 10879–10883 (2015).
Tong, Q. et al. Topological mosaics in moiré superlattices of van der Waals heterobilayers. Nat. Phys. 13, 356–362 (2017).
Qian, X., Liu, J. W., Fu, L. & Li, J. Quantum spin Hall effect in two-dimensional transition metal dichalcogenides. Science 346, 1344–1347 (2014).
Tang, S. J. et al. Quantum spin Hall state in monolayer 1Tʹ-WTe2. Nat. Phys. 13, 683–687 (2017).
Fei, Z. Y. et al. Edge conduction in monolayer WTe2. Nat. Phys. 13, 677–682 (2017).
Wu, S. F. et al. Observation of the quantum spin Hall effect up to 100 kelvin in a monolayer crystal. Science 359, 76–79 (2018).
Sanchez-Yamagishi, J. D. et al. Helical edge states and fractional quantum Hall effect in a graphene electron–hole bilayer. Nat. Nanotech. 12, 118–122 (2017).
Srivastava, A. & Imamoğlu, A. Signatures of Bloch-band geometry on excitons: nonhydrogenic spectra in transition-metal dichalcogenides. Phys. Rev. Lett. 115, 166802 (2015).
Zhou, J., Shan, W.-Y., Yao, W. & Xiao, D. Berry phase modification to the energy spectrum of excitons. Phys. Rev. Lett. 115, 166803 (2015).
Song, J. C. W. & Rudner, M. S. Chiral plasmons without magnetic field. Proc. Natl Acad. Sci. USA 113, 4658–4663 (2016).
Kumar, A. et al. Chiral plasmon in gapped Dirac systems. Phys. Rev. B 93, 041413 (2016).
Haldane, F. D. M. Berry curvature on the Fermi surface: anomalous Hall effect as a topological Fermi-liquid property. Phys. Rev. Lett. 93, 206602 (2004).
Kim, C.-J. et al. Chiral atomically thin films. Nat. Nanotech. 11, 520–524 (2016).
Ma, W. et al. A chiral nanoassemblies-enabled strategy for simultaneously profiling surface glycoprotein and microRNA in living cells. Adv. Mater. 29, 1703410 (2017).
Yamamoto, Y. et al. Photoconductive coaxial nanotubes of molecularly connected electron donor and acceptor layers. Science 314, 1761–1764 (2006).
Novoselov, K. S. et al. Electric field effect in atomically thin carbon films. Science 306, 666–669 (2004).
Tielrooij, K.-J. et al. Out-of-plane heat transfer in van der Waals stacks through electron–hyperbolic phonon coupling. Nat. Nanotech. 13, 41–46 (2018).
Yang, W. et al. A graphene Zener–Klein transistor cooled by a hyperbolic substrate. Nat. Nanotech. 13, 47–52 (2018).
Barati, F. et al. Hot carrier-enhanced interlayer electron–hole pair multiplication in 2D semiconductor heterostructure photocells. Nat. Nanotech. 12, 1134–1139 (2017).
Ross, J. S. et al. Interlayer exciton optoelectronics in a 2D heterostructure p–n junction. Nano Lett. 17, 638–643 (2017).
Kunstmann, J. et al. Momentum-space indirect interlayer excitons in transition-metal dichalcogenide van der Waals heterostructures. Nat. Phys. https://doi.org/10.1038/s41567-018-0123-y (2018).
Fuller, F. D. et al. Vibronic coherence in oxygenic photosynthesis. Nat. Chem. 6, 706–711 (2014).
Dai, S. et al. Graphene on hexagonal boron nitride as a tunable hyperbolic metamaterial. Nat. Nanotech. 10, 682–686 (2015).
Narozhny, B. N. & Levchenko, A. Coulomb drag. Rev. Mod. Phys. 88, 025003 (2016).
Liu, X., Watanabe, K., Taniguchi, T., Halperin, B. I. & Kim, P. Quantum Hall drag of exciton condensate in graphene. Nat. Phys. 13, 746–750 (2017).
Li, J. I. A., Taniguchi, T., Watanabe, K., Hone, J. & Dean, C. R. Excitonic superfluid phase in double bilayer graphene. Nat. Phys. 13, 751–755 (2017).
Chernikov, A. et al. Exciton binding energy and nonhydrogenic Rydberg series in monolayer WS2. Phys. Rev. Lett. 113, 076802 (2014).
Raja, A. et al. Coulomb engineering of the bandgap and excitons in two-dimensional materials. Nat. Commun. 8, 15251 (2017).
Ponomarenko, L. A. et al. Tunable metal–insulator transition in double-layer graphene heterostructures. Nat. Phys. 7, 958–961 (2011).
Alonso-González, P. et al. Acoustic terahertz graphene plasmons revealed by photocurrent nanoscopy. Nat. Nanotech. 12, 31–35 (2017).
Lundeberg, M. B. et al. Tuning quantum nonlocal effects in graphene plasmonics. Science 357, 187–191 (2017).
Alcaraz Iranzo, D. et al. Probing the ultimate plasmon confinement limits with a van der Waals heterostructure. Science 360, 291–295 (2018).
Little, W. A. Possibility of synthesizing an organic superconductor. Phys. Rev. 134, A1416 (1964).
Hamo, A. et al. Electron attraction mediated by Coulomb repulsion. Nature 535, 395–400 (2016).
Roesner, M. et al. Plasmonic superconductivity in layered materials. Preprint at https://arXiv.org/abs/1803.04576 (2018).
Fatemi, V. & Ruhman J. Synthesizing Coulombic superconductivity in van der Waals bilayers. Preprint at https://arxiv.org/abs/1804.04148 (2018).
Ye, J. T. et al. Superconducting dome in a gate-tuned band insulator. Science 338, 1193–1196 (2012).
Gong, C. et al. Discovery of intrinsic ferromagnetism in two-dimensional van der Waals crystals. Nature 546, 265–269 (2017).
Huang, B. et al. Layer-dependent ferromagnetism in a van der Waals crystal down to the monolayer limit. Nature 546, 270–273 (2017).
Yu, Y. et al. Gate-tunable phase transitions in thin flakes of 1T-TaS2. Nat. Nanotech. 10, 270–276 (2015).
Li, L. J. et al. Controlling many-body states by the electric-field effect in a two-dimensional material. Nature 529, 185–189 (2016).
Xi, X., Berger, H., Forró, L., Shan, J. & Mak, K. F. Gate tuning of electronic phase transitions in two-dimensional NbSe2. Phys. Rev. Lett. 117, 106801 (2016).
Jiang, S., Shan, J. & Mak, K. F. Electric-field switching of two-dimensional van der Waals magnets. Nat. Mater. 17, 406–410 (2018).
Huang, B. et al. Electrical control of 2D magnetism in bilayer CrI3. Nat. Nanotech. 13, 544–568 (2018).
Avsar, A. et al. Spin–orbit proximity effect in graphene. Nat. Commun. 5, 4875 (2014).
Wang, Z. et al. Strong interface-induced spin–orbit interaction in graphene on WS2. Nat. Commun. 6, 8339 (2015).
Wang, Z., Tang, C., Sachs, R., Barlas, Y. & Shi, J. Proximity-induced ferromagnetism in graphene revealed by the anomalous Hall effect. Phys. Rev. Lett. 114, 016603 (2015).
Mishchenko, A. et al. Twist-controlled resonant tunnelling in graphene/boron nitride/graphene heterostructures. Nat. Nanotech. 9, 808–818 (2014).
Wallbank, J. R. et al. Tuning the valley and chiral quantum state of Dirac electrons in van der Waals heterostructures. Science 353, 575–579 (2016).
Song, T. et al. Giant tunneling magnetoresistance in spin-filter van der Waals heterostructures. Science eaar4851 (2018)..
Klein, D. R. et al. Probing magnetism in 2D van der Waals crystalline insulators via electron tunneling. Science https://doi.org/10.1126/science.aar3617 (2018).
Wang, Z. et al. Very large tunneling magnetoresistance in layered magnetic semiconductor CrI3. Preprint at https://arxiv.org/abs/1801.08188 (2018).
Kim, H. H. et al. One million percent tunnel magnetoresistance in a magnetic van der Waals heterostructure. Preprint at https://arxiv.org/abs/1804.00028 (2018).
Ribeiro-Palau, R. et al. Twistable electronics with dynamically rotatable heterostructures. Preprint at https://arxiv.org/abs/1804.02038 (2018).
Carr, S. et al. Twistronics: manipulating the electronic properties of two-dimensional layered structures through their twist angle. Phys. Rev. B 95, 075420 (2017).
Park, C. H., Yang, L., Son, Y. W., Cohen, M. L. & Louie, S. G. Anisotropic behaviours of massless Dirac fermions in graphene under periodic potentials. Nat. Phys. 4, 213–217 (2008).
Forsythe, C. et al. Band structure engineering of 2D materials using patterned dielectric superlattices. Nat. Nanotech. 13, 566–571 (2018).
Guinea, F., Katsnelson, M. I. & Geim, A. K. Energy gaps and a zero-field quantum Hall effect in graphene by strain engineering. Nat. Phys. 6, 30–33 (2010).
Xu, S.-Y. et al. Electrically switchable Berry curvature dipole in the monolayer topological insulator WTe2. Nat. Phys. https://doi.org/10.1038/s41567-018-0189–6 (2018).
Zhang, Y., Brink, J. V. D., Felser, C. & Yan, B. (2018). Electrically tuneable nonlinear anomalous Hall effect in two-dimensional transition-metal dichalcogenides WTe2 and MoTe2. Preprint at https://arxiv.org/abs/1804.11069.
Shi, L.-k. & Song, J. C. W. Berry curvature switch and magneto-electric effect in WTe2 monolayer. Preprint at https://arxiv.org/abs/1805.00939 (2018).
You, J. S., Fang, S., Xu, S. Y., Kaxiras, E. & Low, T. The Berry curvature dipole current in transition metal dichalcogenides family. Preprint at https://arxiv.org/abs/1805.02157 (2018).
Song, J. C. W., Shytov, A. V. & Levitov, L. S. Electron interactions and gap opening in graphene superlattices. Phys. Rev. Lett. 111, 266801 (2013).
Cao, Y. et al. Correlated insulator behaviour at half-filling in magic-angle graphene superlattices. Nature 556, 80–84 (2018).
Cao, Y. et al. Unconventional superconductivity in magic-angle graphene superlattices. Nature 556, 43–50 (2018).
Morell, E. S., Correa, J. D., Vargas, P., Pacheco, M. & Barticevic, Z. Flat bands in slightly twisted bilayer graphene: tight-binding calculations. Phys. Rev. B 82, 121407 (2010).
Chen, G. et al. Gate-tunable Mott insulator in trilayer graphene–boron nitride moiré superlattice. Preprint at https://arxiv.org/abs/1803.01985 (2018).
We thank V. Fatemi, F. Koppens, P. McEuen, J. Sanchez-Yamigishi and A. Young for discussions, as well as M. Grossnickle from QMO Labs for graphics assistance. J.C.W.S. acknowledges support from the Singapore National Research Foundation (NRF) under NRF fellowship award NRF-NRFF2016-05 and a Nanyang Technological University (NTU) start-up grant (NTU-SUG). N.M.G. is supported by the Air Force Office of Scientific Research Young Investigator Program (YIP) award no. FA9550-16-1-0216 and by the National Science Foundation Division of Materials Research CAREER award no. 1651247. N.M.G. also acknowledges support through a Cottrell Scholar Award, and through the Canadian Institute for Advanced Research (CIFAR) Azrieli Global Scholar Award.
The authors declare no competing interests.
Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
About this article
Cite this article
Song, J.C.W., Gabor, N.M. Electron quantum metamaterials in van der Waals heterostructures. Nature Nanotech 13, 986–993 (2018). https://doi.org/10.1038/s41565-018-0294-9
This article is cited by
Light: Science & Applications (2023)
Nature Communications (2023)
Nature Nanotechnology (2022)
Nature Reviews Physics (2021)
Nature Communications (2021)