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Polaritons in layered two-dimensional materials

Nature Materials volume 16, pages 182–194 (2017)Cite this article

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Abstract

In recent years, enhanced light–matter interactions through a plethora of dipole-type polaritonic excitations have been observed in two-dimensional (2D) layered materials. In graphene, electrically tunable and highly confined plasmon-polaritons were predicted and observed, opening up opportunities for optoelectronics, bio-sensing and other mid-infrared applications. In hexagonal boron nitride, low-loss infrared-active phonon-polaritons exhibit hyperbolic behaviour for some frequencies, allowing for ray-like propagation exhibiting high quality factors and hyperlensing effects. In transition metal dichalcogenides, reduced screening in the 2D limit leads to optically prominent excitons with large binding energy, with these polaritonic modes having been recently observed with scanning near-field optical microscopy. Here, we review recent progress in state-of-the-art experiments, and survey the vast library of polaritonic modes in 2D materials, their optical spectral properties, figures of merit and application space. Taken together, the emerging field of 2D material polaritonics and their hybrids provide enticing avenues for manipulating light–matter interactions across the visible, infrared to terahertz spectral ranges, with new optical control beyond what can be achieved using traditional bulk materials.

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Figure 1: State-of-the-art graphene plasmonics.
Figure 2: Hyperbolic phonon-polaritons in hBN.
Figure 3: Hyperbolic polaritons beyond hBN.
Figure 4: Excitons in TMDs and beyond.
Figure 5: Hybrid polaritonic and application space of polaritons.

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References

  1. Ritchie, R. Plasma losses by fast electrons in thin films. Phys. Rev. 106, 874–881 (1957).

    Article  CAS  Google Scholar 

  2. Pekar, S. The theory of electromagnetic waves in a crystal in which excitons are produced. Sov. Phys. JETP 6, 785 (1958).

    Google Scholar 

  3. Maier, S. A. Plasmonics: Fundamentals and Applications (Springer Science & Business Media, 2007).

    Google Scholar 

  4. Fei, Z. et al. Gate-tuning of graphene plasmons revealed by infrared nano-imaging. Nature 487, 82–85 (2012).

    CAS  Google Scholar 

  5. Chen, J. et al. Optical nano-imaging of gate-tunable graphene plasmons. Nature 487, 77–81 (2012).

    CAS  Google Scholar 

  6. Song, J. C. & Rudner, M. S. Chiral plasmons without magnetic field. Proc. Natl Acad. Sci. USA 113, 4658–4663 (2016).

    CAS  Google Scholar 

  7. Kumar, A. et al. Chiral plasmon in gapped Dirac systems. Phys. Rev. B 93, 041413 (2016).

    Google Scholar 

  8. Low, T. et al. Plasmons and screening in monolayer and multilayer black phosphorus. Phys. Rev. Lett. 113, 106802 (2014).

    Google Scholar 

  9. Nemilentsau, A., Low, T. & Hanson, G. Anisotropic 2D materials for tunable hyperbolic plasmonics. Phys. Rev. Lett. 116, 066804 (2016).

    Google Scholar 

  10. Dai, S. et al. Tunable phonon polaritons in atomically thin van der Waals crystals of boron nitride. Science 343, 1125–1129 (2014).

    CAS  Google Scholar 

  11. Caldwell, J. D. et al. Sub-diffractional volume-confined polaritons in the natural hyperbolic material hexagonal boron nitride. Nat. Commun. 5, 5221 (2014).

    CAS  Google Scholar 

  12. Caldwell, J. D. et al. Low-loss, infrared and terahertz nanophotonics using surface phonon polaritons. Nanophotonics 4, 44–68 (2015).

    CAS  Google Scholar 

  13. Yoxall, E. et al. Direct observation of ultraslow hyperbolic polariton propagation with negative phase velocity. Nat. Photon. 9, 674–678 (2015).

    CAS  Google Scholar 

  14. Caldwell, J. D., Vurgaftman, I. & Tischler, J. G. Mid-infrared nanophotonics: probing hyperbolic polaritons. Nat. Photon. 9, 638–640 (2015).

    CAS  Google Scholar 

  15. Li, P. et al. Hyperbolic phonon-polaritons in boron nitride for near-field optical imaging and focusing. Nat. Commun. 6, 7507 (2015).

    CAS  Google Scholar 

  16. Dai, S. et al. Subdiffractional focusing and guiding of polaritonic rays in a natural hyperbolic material. Nat. Commun. 6, 6963 (2015).

    CAS  Google Scholar 

  17. Splendiani, A. et al. Emerging photoluminescence in monolayer MoS2 . Nano Lett. 10, 1271–1275 (2010).

    CAS  Google Scholar 

  18. Mak, K. F., Lee, C., Hone, J., Shan, J. & Heinz, T. F. Atomically thin MoS2: a new direct-gap semiconductor. Phys. Rev. Lett. 105, 136805 (2010).

    Article  Google Scholar 

  19. Conley, H. J. et al. Bandgap engineering of strained monolayer and bilayer MoS2 . Nano Lett. 13, 3626–3630 (2013).

    CAS  Google Scholar 

  20. Ross, J. S. et al. Electrical control of neutral and charged excitons in a monolayer semiconductor. Nat. Commun. 4, 1474 (2013).

    Google Scholar 

  21. Ugeda, M. M. et al. Giant bandgap renormalization and excitonic effects in a monolayer transition metal dichalcogenide semiconductor. Nat. Mater. 13, 1091–1095 (2014).

    CAS  Google Scholar 

  22. Mak, K. F. et al. Tightly bound trions in monolayer MoS2 . Nat. Mater. 12, 207–211 (2013).

    CAS  Google Scholar 

  23. Jones, A. M. et al. Optical generation of excitonic valley coherence in monolayer WSe2 . Nat. Nanotech. 8, 634–638 (2013).

    CAS  Google Scholar 

  24. You, Y. et al. Observation of biexcitons in monolayer WSe2 . Nat. Phys. 11, 477–481 (2015).

    CAS  Google Scholar 

  25. Zhang, S. et al. Extraordinary photoluminescence and strong temperature/angle-dependent Raman responses in few-layer phosphorene. ACS Nano 8, 9590–9596 (2014).

    CAS  Google Scholar 

  26. Castellanos-Gomez, A. et al. Isolation and characterization of few-layer black phosphorus. 2D Mater. 1, 025001 (2014).

    Google Scholar 

  27. Yang, J. et al. Optical tuning of exciton and trion emissions in monolayer phosphorene. Light: Sci. Appl. 4, e312 (2015).

    CAS  Google Scholar 

  28. Wang, X. et al. Highly anisotropic and robust excitons in monolayer black phosphorus. Nat. Nanotech. 10, 517–521 (2015).

    CAS  Google Scholar 

  29. Ebbesen, T. W., Lezec, H. J., Ghaemi, H., Thio, T. & Wolff, P. Extraordinary optical transmission through sub-wavelength hole arrays. Nature 391, 667–669 (1998).

    CAS  Google Scholar 

  30. Nie, S. & Emory, S. R. Probing single molecules and single nanoparticles by surface-enhanced Raman scattering. Science 275, 1102–1106 (1997).

    CAS  Google Scholar 

  31. Ozbay, E. Plasmonics: merging photonics and electronics at nanoscale dimensions. Science 311, 189–193 (2006).

    CAS  Google Scholar 

  32. Shalaev, V. M. Optical negative-index metamaterials. Nat. Photon. 1, 41–48 (2007).

    CAS  Google Scholar 

  33. Yu, N. & Capasso, F. Flat optics with designer metasurfaces. Nat. Mater. 13, 139–150 (2014).

    CAS  Google Scholar 

  34. Khurgin, J. B. How to deal with the loss in plasmonics and metamaterials. Nat. Nanotech. 10, 2–6 (2015).

    CAS  Google Scholar 

  35. Falkovsky, L. & Pershoguba, S. Optical far-infrared properties of a graphene monolayer and multilayer. Phys. Rev. B 76, 153410 (2007).

    Google Scholar 

  36. Jablan, M., Buljan, H. & Soljačić, M. Plasmonics in graphene at infrared frequencies. Phys. Rev. B 80, 245435 (2009).

    Google Scholar 

  37. Koppens, F. H., Chang, D. E. & Garcia de Abajo, F. J. Graphene plasmonics: a platform for strong light–matter interactions. Nano Lett. 11, 3370–3377 (2011).

    CAS  Google Scholar 

  38. Nikitin, A. Y., Guinea, F., Garcia-Vidal, F. & Martin-Moreno, L. Fields radiated by a nanoemitter in a graphene sheet. Phys. Rev. B 84, 195446 (2011).

    Google Scholar 

  39. Low, T. & Avouris, P. Graphene plasmonics for terahertz to mid-infrared applications. ACS Nano 8, 1086–1101 (2014).

    CAS  Google Scholar 

  40. Ju, L. et al. Graphene plasmonics for tunable terahertz metamaterials. Nat. Nanotech. 6, 630–634 (2011).

    CAS  Google Scholar 

  41. Yan, H. et al. Damping pathways of mid-infrared plasmons in graphene nanostructures. Nat. Photon. 7, 394–399 (2013).

    CAS  Google Scholar 

  42. Ni, G. et al. Ultrafast optical switching of infrared plasmon polaritons in high-mobility graphene. Nat. Photon. 10, 244–247 (2016).

    CAS  Google Scholar 

  43. Tielrooij, K. et al. Electrical control of optical emitter relaxation pathways enabled by graphene. Nat. Phys. 11, 281–287 (2015).

    CAS  Google Scholar 

  44. Wang, L. et al. One-dimensional electrical contact to a two-dimensional material. Science 342, 614–617 (2013).

    CAS  Google Scholar 

  45. Woessner, A. et al. Highly confined low-loss plasmons in graphene–boron nitride heterostructures. Nat. Mater. 14, 421–425 (2015).

    CAS  Google Scholar 

  46. Principi, A. et al. Plasmon losses due to electron-phonon scattering: The case of graphene encapsulated in hexagonal boron nitride. Phys. Rev. B 90, 165408 (2014).

    Google Scholar 

  47. Alonso-González, P. et al. Controlling graphene plasmons with resonant metal antennas and spatial conductivity patterns. Science 344, 1369–1373 (2014).

    Google Scholar 

  48. Novoselov, K. et al. Two-dimensional gas of massless Dirac fermions in graphene. Nature 438, 197–200 (2005).

    CAS  Google Scholar 

  49. Low, T., Guinea, F., Yan, H., Xia, F. & Avouris, P. Novel midinfrared plasmonic properties of bilayer graphene. Phys. Rev. Lett. 112, 116801 (2014).

    Google Scholar 

  50. Fei, Z. et al. Tunneling plasmonics in bilayer graphene. Nano Lett. 15, 4973–4978 (2015).

    CAS  Google Scholar 

  51. Yan, H., Low, T., Guinea, F., Xia, F. & Avouris, P. Tunable phonon-induced transparency in bilayer graphene nanoribbons. Nano Lett. 14, 4581–4586 (2014).

    CAS  Google Scholar 

  52. Oostinga, J. B., Heersche, H. B., Liu, X., Morpurgo, A. F. & Vandersypen, L. M. Gate-induced insulating state in bilayer graphene devices. Nat. Mater. 7, 151–157 (2008).

    CAS  Google Scholar 

  53. Kuzmenko, A. et al. Gate tunable infrared phonon anomalies in bilayer graphene. Phys. Rev. Lett. 103, 116804 (2009).

    CAS  Google Scholar 

  54. Mak, K. F., He, K., Shan, J. & Heinz, T. F. Control of valley polarization in monolayer MoS2 by optical helicity. Nat. Nanotech. 7, 494–498 (2012).

    CAS  Google Scholar 

  55. Xu, X., Yao, W., Xiao, D. & Heinz, T. F. Spin and pseudospins in layered transition metal dichalcogenides. Nat. Phys. 10, 343–350 (2014).

    CAS  Google Scholar 

  56. Li, L. et al. Black phosphorus field-effect transistors. Nat. Nanotech. 9, 372–377 (2014).

    CAS  Google Scholar 

  57. Johnson, P. B. & Christy, R.-W. Optical constants of the noble metals. Phys. Rev. B 6, 4370–4379 (1972).

    CAS  Google Scholar 

  58. Li, L. et al. Quantum oscillations in a two-dimensional electron gas in black phosphorus thin films. Nat. Nanotech. 10, 608–613 (2015).

    CAS  Google Scholar 

  59. Cui, X. et al. Multi-terminal transport measurements of MoS2 using a van der Waals heterostructure device platform. Nat. Nanotech. 10, 534–540 (2015).

    CAS  Google Scholar 

  60. Kaasbjerg, K., Thygesen, K. S. & Jacobsen, K. W. Phonon-limited mobility in n-type single-layer MoS2 from first principles. Phys. Rev. B 85, 115317 (2012).

    Google Scholar 

  61. Qiao, J., Kong, X., Hu, Z.-X., Yang, F. & Ji, W. High-mobility transport anisotropy and linear dichroism in few-layer black phosphorus. Nat. Commun. 5, 4475 (2014).

    CAS  Google Scholar 

  62. Wunsch, B., Stauber, T., Sols, F. & Guinea, F. Dynamical polarization of graphene at finite doping. New J. Phys. 8, 318 (2006).

    Google Scholar 

  63. Zhu, W. et al. Electronic transport and device prospects of monolayer molybdenum disulphide grown by chemical vapour deposition. Nat. Commun. 5, 3087 (2014).

    Google Scholar 

  64. Tongay, S. et al. Monolayer behaviour in bulk ReS2 due to electronic and vibrational decoupling. Nat. Commun. 5, 3252 (2014).

    Google Scholar 

  65. Island, J. O. et al. Ultrahigh photoresponse of few-layer TiS3 nanoribbon transistors. Adv. Opt. Mater. 2, 641–645 (2014).

    CAS  Google Scholar 

  66. Poddubny, A., Iorsh, I., Belov, P. & Kivshar, Y. Hyperbolic metamaterials. Nat. Photon. 7, 948–957 (2013).

    CAS  Google Scholar 

  67. Jacob, Z., Alekseyev, L. V. & Narimanov, E. Optical hyperlens: far-field imaging beyond the diffraction limit. Opt. Exp. 14, 8247–8256 (2006).

    Google Scholar 

  68. Liu, Z., Lee, H., Xiong, Y., Sun, C. & Zhang, X. Far-field optical hyperlens magnifying sub-diffraction-limited objects. Science 315, 1686–1686 (2007).

    CAS  Google Scholar 

  69. Giles, A. J. et al. Imaging of anomalous internal reflections of hyperbolic phonon-polaritons in hexagonal boron nitride. Nano Lett. 16, 3858–3865 (2016).

    CAS  Google Scholar 

  70. Sun, J., Litchinitser, N. M. & Zhou, J. Indefinite by nature: from ultraviolet to terahertz. ACS Photon. 1, 293–303 (2014).

    CAS  Google Scholar 

  71. Korzeb, K., Gajc, M. & Pawlak, D. A. Compendium of natural hyperbolic materials. Opt. Exp. 23, 25406–25424 (2015).

    CAS  Google Scholar 

  72. Narimanov, E. E. & Kildishev, A. V. Metamaterials: naturally hyperbolic. Nat. Photon. 9, 214–216 (2015).

    CAS  Google Scholar 

  73. Sun, J., Zhou, J., Li, B. & Kang, F. Indefinite permittivity and negative refraction in natural material: graphite. Appl. Phys. Lett. 98, 101901 (2011).

    Google Scholar 

  74. Wieting, T. & Verble, J. Infrared and Raman studies of long-wavelength optical phonons in hexagonal MoS2 . Phys. Rev. B 3, 4286–4292 (1971).

    Google Scholar 

  75. Wu, J.-S. et al. Topological insulators are tunable waveguides for hyperbolic polaritons. Phys. Rev. B 92, 205430 (2015).

    Google Scholar 

  76. Esslinger, M. et al. Tetradymites as natural hyperbolic materials for the near-infrared to visible. ACS Photon. 1, 1285–1289 (2014).

    CAS  Google Scholar 

  77. Aslan, O. B., Chenet, D. A., van der Zande, A. M., Hone, J. C. & Heinz, T. F. Linearly polarized excitons in single-and few-layer ReS2 crystals. ACS Photon. 3, 96–101 (2015).

    Google Scholar 

  78. Yaffe, O. et al. Excitons in ultrathin organic-inorganic perovskite crystals. Phys. Rev. B 92, 045414 (2015).

    Google Scholar 

  79. Chaves, A., Mayers, M., Peeters, F. & Reichman, D. Theoretical investigation of electron-hole complexes in anisotropic two-dimensional materials. Phys. Rev. B 93, 115314 (2016).

    Google Scholar 

  80. Berkelbach, T. C., Hybertsen, M. S. & Reichman, D. R. Theory of neutral and charged excitons in monolayer transition metal dichalcogenides. Phys. Rev. B 88, 045318 (2013).

    Google Scholar 

  81. Chernikov, A. et al. Exciton binding energy and nonhydrogenic Rydberg series in monolayer WS2 . Phys. Rev. Lett. 113, 076802 (2014).

    Google Scholar 

  82. He, K. et al. Tightly bound excitons in monolayer WSe2 . Phys. Rev. Lett. 113, 026803 (2014).

    Google Scholar 

  83. Ye, Z. et al. Probing excitonic dark states in single-layer tungsten disulphide. Nature 513, 214–218 (2014).

    CAS  Google Scholar 

  84. Zhu, B., Chen, X. & Cui, X. Exciton binding energy of monolayer WS2 . Sci. Rep. 5, 9218 (2015).

    Google Scholar 

  85. Koch, S. W., Kira, M., Khitrova, G. & Gibbs, H. Semiconductor excitons in new light. Nat. Mater. 5, 523–531 (2006).

    CAS  Google Scholar 

  86. Wang, F., Dukovic, G., Brus, L. E. & Heinz, T. F. The optical resonances in carbon nanotubes arise from excitons. Science 308, 838–841 (2005).

    CAS  Google Scholar 

  87. Sebastian, L. & Weiser, G. One-dimensional wide energy bands in a polydiacetylene revealed by electroreflectance. Phys. Rev. Lett. 46, 1156–1159 (1981).

    CAS  Google Scholar 

  88. Mai, C. et al. Many-body effects in valleytronics: Direct measurement of valley lifetimes in single-layer MoS2 . Nano Lett. 14, 202–206 (2013).

    Google Scholar 

  89. Plechinger, G. et al. Identification of excitons, trions and biexcitons in single-layer WS2 . Phys. Status Solidi (RRL)-Rapid Res. Lett. 9, 457–461 (2015).

    CAS  Google Scholar 

  90. Zhang, Y. et al. On valence-band splitting in layered MoS2 . ACS Nano 9, 8514–8519 (2015).

    CAS  Google Scholar 

  91. Xu, R. et al. Extraordinarily bound quasi-one-dimensional trions in two-dimensional phosphorene atomic semiconductors. ACS Nano 10, 2046–2053 (2016).

    CAS  Google Scholar 

  92. Chaves, A., Low, T., Avouris, P., Çakır, D. & Peeters, F. Anisotropic exciton Stark shift in black phosphorus. Phys. Rev. B 91, 155311 (2015).

    Google Scholar 

  93. Haug, H. & Koch, S. W. Quantum Theory of the Optical and Electronic Properties of Semiconductors Vol. V (World Scientific, 1990).

    Google Scholar 

  94. Klingshirn, C. F. Semiconductor Optics (Springer Science Business Media, 2012).

    Google Scholar 

  95. Masselink, W. et al. Absorption coefficients and exciton oscillator strengths in AlGaAs-GaAs superlattices. Phys. Rev. B 32, 8027–8034 (1985).

    CAS  Google Scholar 

  96. Gan, X. et al. Controlling the spontaneous emission rate of monolayer MoS2 in a photonic crystal nanocavity. Appl. Phys. Lett. 103, 181119 (2013).

    Google Scholar 

  97. Liu, X. et al. Strong light–matter coupling in two-dimensional atomic crystals. Nat. Photon. 9, 30–34 (2015).

    CAS  Google Scholar 

  98. Fei, Z. et al. Nano-optical imaging of WSe2 waveguide modes revealing light-exciton interactions. Phys. Rev. B 94, 081402(R) (2016).

    Google Scholar 

  99. Geim, A. K. & Grigorieva, I. V. Van der Waals heterostructures. Nature 499, 419–425 (2013).

    CAS  Google Scholar 

  100. 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).

    CAS  Google Scholar 

  101. Fogler, M. M., Butov, L. V. & Novoselov, K. S. High-temperature superfluidity with indirect excitons in van der Waals heterostructures. Nat. Commun. 5, 4555 (2014).

    CAS  Google Scholar 

  102. Rivera, P. et al. Observation of long-lived interlayer excitons in monolayer MoSe2–WSe2 heterostructures. Nat. Commun. 6, 6242 (2015).

    CAS  Google Scholar 

  103. Caldwell, J. D. et al. Atomic-scale photonic hybrids for mid-infrared and terahertz nanophotonics. Nat. Nanotech. 11, 9–15 (2016).

    CAS  Google Scholar 

  104. Dai, S. et al. Graphene on hexagonal boron nitride as a tunable hyperbolic metamaterial. Nat. Nanotech. 10, 682–686 (2015).

    CAS  Google Scholar 

  105. Özçelik, V. O., Azadani, J. G., Yang, C., Koester, S. J. & Low, T. Band alignment of 2D semiconductors for designing heterostructures with momentum space matching. Phys. Rev. B 94, 035125 (2006).

    Google Scholar 

  106. Freitag, M. et al. Photocurrent in graphene harnessed by tunable intrinsic plasmons. Nat. Commun. 4, 1951 (2013).

    Google Scholar 

  107. Rodrigo, D. et al. Mid-infrared plasmonic biosensing with graphene. Science 349, 165–168 (2015).

    CAS  Google Scholar 

  108. Hu, H. et al. Far-field nanoscale infrared spectroscopy of vibrational fingerprints of molecules with graphene plasmons. Nat. Commun. 7, 12334 (2016).

    CAS  Google Scholar 

  109. Carrasco, E., Tamagnone, M., Mosig, J. R., Low, T. & Perruisseau-Carrier, J. Gate-controlled mid-infrared light bending with aperiodic graphene nanoribbons array. Nanotechnology 26, 134002 (2015).

    Google Scholar 

  110. Vakil, A. & Engheta, N. Transformation optics using graphene. Science 332, 1291–1294 (2011).

    CAS  Google Scholar 

  111. Page, A. F., Ballout, F., Hess, O. & Hamm, J. M. Nonequilibrium plasmons with gain in graphene. Phys. Rev. B 91, 075404 (2015).

    Google Scholar 

  112. Khrapach, I. et al. Novel highly conductive and transparent graphene-based conductors. Adv. Mater. 24, 2844–2849 (2012).

    CAS  Google Scholar 

  113. Guo, Y., Cortes, C. L., Molesky, S. & Jacob, Z. Broadband super-Planckian thermal emission from hyperbolic metamaterials. Appl. Phys. Lett. 101, 131106 (2012).

    Google Scholar 

  114. Cortes, C. L. & Jacob, Z. Photonic analog of a van Hove singularity in metamaterials. Phys. Rev. B 88, 045407 (2013).

    Google Scholar 

  115. Lee, C.-H. et al. Atomically thin p–n junctions with van der Waals heterointerfaces. Nat. Nanotech. 9, 676–681 (2014).

    CAS  Google Scholar 

  116. Srivastava, A. & Imamoğlu, A. Signatures of Bloch-band geometry on excitons: nonhydrogenic spectra in transition-metal dichalcogenides. Phys. Rev. Lett. 115, 166802 (2015).

    Google Scholar 

  117. Zhang, L. & Niu, Q. Chiral phonons at high-symmetry points in monolayer hexagonal lattices. Phys. Rev. Lett. 115, 115502 (2015).

    Google Scholar 

  118. Yang, S. et al. Tuning the optical, magnetic, and electrical properties of ReSe2 by nanoscale strain engineering. Nano Lett. 15, 1660–1666 (2015).

    CAS  Google Scholar 

  119. Zhang, Z. et al. Manifestation of unexpected semiconducting properties in few-layer orthorhombic arsenene. Appl. Phys. Exp. 8, 055201 (2015).

    Google Scholar 

  120. Li, Y. et al. Measurement of the optical dielectric function of monolayer transition-metal dichalcogenides: MoS2, MoSe2, WS2, and WSe2 . Phys. Rev. B 90, 205422 (2014).

    Google Scholar 

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Acknowledgements

T.L. acknowledges financial support by DARPA grant award FA8650-16-2-7640. A.C. acknowledges support by CNPq, through the PRONEX/FUNCAP and Science Without Borders programs. J.D.C. acknowledges financial support from the Office of Naval Research that was administered by the NRL Nanoscience Institute. A.K. and N.X.F. acknowledge the financial support by AFOSR MURI (Award No. FA9550-12-1-0488). L.M.M. acknowledges the Spanish Ministry of Economy and Competitiveness under project MAT2014-53432-C5-1-R. F.K. acknowledges financial support from the Spanish Ministry of Economy and Competitiveness, through the ‘Severo Ochoa’ Programme for Centres of Excellence in R&D (SEV-2015-0522), support by Fundacio Cellex Barcelona, the European Union H2020 Programme under grant agreement no 604391 Graphene Flagship’, the ERC starting grant (307806, CarbonLight), and project GRASP (FP7-ICT-2013-613024-GRASP). We also acknowledge useful discussion with A. Chernikov.

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Authors and Affiliations

  1. Department of Electrical & Computer Engineering, University of Minnesota, Minneapolis, Minnesota 55455, USA

    Tony Low & Anshuman Kumar

  2. Departamento de Física, Universidade Federal do Ceará, Caixa Postal 6030, 60455-760 Fortaleza, Ceará, Brazil

    Andrey Chaves

  3. Department of Chemistry, Columbia University, New York, New York 10027, USA

    Andrey Chaves

  4. US Naval Research Laboratory, 4555 Overlook Avenue SW, Washington DC 20375, USA

    Joshua D. Caldwell

  5. Mechanical Engineering Department, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA

    Anshuman Kumar & Nicholas X. Fang

  6. IBM T.J. Watson Research Center, 1101 Kitchawan Road, Yorktown Heights, New York 10598, USA

    Phaedon Avouris

  7. Department of Applied Physics, Stanford University, Stanford, California 94305, USA

    Tony F. Heinz

  8. IMDEA Nanociencia, Calle de Faraday 9, E-28049 Madrid, Spain

    Francisco Guinea

  9. Department of Physics and Astronomy, University of Manchester, Oxford Road, Manchester M13 9PL, UK

    Francisco Guinea

  10. Instituto de Ciencia de Materiales de Aragon and Departamento de Fisica de la Materia Condensada, CSIC-Universidad de Zaragoza, E-50012 Zaragoza, Spain

    Luis Martin-Moreno

  11. ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain

    Frank Koppens

  12. ICREA Institució Catalana de Recerça i Estudis Avancats, 08010 Barcelona, Spain

    Frank Koppens

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Low, T., Chaves, A., Caldwell, J. et al. Polaritons in layered two-dimensional materials. Nature Mater 16, 182–194 (2017). https://doi.org/10.1038/nmat4792

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