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# Fundamental limits to graphene plasmonics

## Abstract

Plasmon polaritons are hybrid excitations of light and mobile electrons that can confine the energy of long-wavelength radiation at the nanoscale. Plasmon polaritons may enable many enigmatic quantum effects, including lasing1, topological protection2,3 and dipole-forbidden absorption4. A necessary condition for realizing such phenomena is a long plasmonic lifetime, which is notoriously difficult to achieve for highly confined modes5. Plasmon polaritons in graphene—hybrids of Dirac quasiparticles and infrared photons—provide a platform for exploring light–matter interaction at the nanoscale6,7. However, plasmonic dissipation in graphene is substantial8 and its fundamental limits remain undetermined. Here we use nanometre-scale infrared imaging to investigate propagating plasmon polaritons in high-mobility encapsulated graphene at cryogenic temperatures. In this regime, the propagation of plasmon polaritons is primarily restricted by the dielectric losses of the encapsulated layers, with a minor contribution from electron–phonon interactions. At liquid-nitrogen temperatures, the intrinsic plasmonic propagation length can exceed 10 micrometres, or 50 plasmonic wavelengths, thus setting a record for highly confined and tunable polariton modes. Our nanoscale imaging results reveal the physics of plasmonic dissipation and will be instrumental in mitigating such losses in heterostructure engineering applications.

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## References

1. 1.

Lu, Y. J. et al. Plasmonic nanolaser using epitaxially grown silver film. Science 337, 450–453 (2012).

2. 2.

Jin, D. et al. Infrared topological plasmons in graphene. Phys. Rev. Lett. 118, 245301 (2017); erratum 119, 019901 (2017).

3. 3.

Karzig, T., Bardyn, C. E., Lindner, N. H. & Refael, G. Topological polaritons. Phys. Rev. X 5, 031001 (2015).

4. 4.

Rivera, N., Kaminer, I., Zhen, B., Joannopoulos, J. D. & Soljacic, M. Shrinking light to allow forbidden transitions on the atomic scale. Science 353, 263–269 (2016).

5. 5.

Boltasseva, A. & Atwater, H. A. Low-loss plasmonics metamaterials. Science 331, 290–291 (2011).

6. 6.

Basov, D. N., Fogler, M. M. & Garcia de Abajo, F. J. Polaritons in van der Waals materials. Science 354, aag1992 (2016).

7. 7.

Low, T. et al. Polaritons in layered two-dimensional materials. Nat. Mater. 16, 182–194 (2017).

8. 8.

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

9. 9.

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

10. 10.

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

11. 11.

McLeod, A. S. et al. Nanotextured phase coexistence in the correlated insulator V2O3. Nat. Phys. 13, 80–86 (2017).

12. 12.

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

13. 13.

Novotny, L. & Hecht, B. Principles of Nano-Optics (Cambridge Univ. Press, Cambridge, 2006).

14. 14.

Atkin, J. H., 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).

15. 15.

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

16. 16.

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

17. 17.

Ni, G. X. et al. Plasmons in graphene moiré superlattices. Nat. Mater. 14, 1217–1222 (2015).

18. 18.

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).

19. 19.

Hwang, E. & Das Sarma, S. Acoustic phonon scattering limited carrier mobility in two-dimensional extrinsic graphene. Phys. Rev. B 77, 115449 (2008).

20. 20.

Park, C. H. et al. Electron-phonon interactions and the intrinsic electrical resistivity of graphene. Nano Lett. 14, 1113–1119 (2014).

21. 21.

Sohier, T., Calandra, M. & Mauri, F. Density-functional calculation of static screening in two-dimensional materials: the long-wavelength dielectric function of graphene. Phys. Rev. B 91, 165428 (2015).

22. 22.

Sun, Z., Basov, D. N. & Fogler, M. M. Universal linear and nonlinear electrodynamics of a Dirac fluid. Proc. Natl Acad. Sci. USA 115, 3285–3289 (2018).

23. 23.

Bandurin, D. A. et al. Negative local resistance caused by viscous electron backflow in graphene. Science 351, 1055–1058 (2016).

24. 24.

Kumar, R. K. et al. Superballistic flow of viscous electron fluid through graphene constrictions. Nat. Phys. 13, 1182 (2017).

25. 25.

Phan, T. V., Song, J. C. W. & Levitov, L. S. Ballistic heat transfer and energy waves in an electron system. Preprint at https://arxiv.org/abs/1306.4972 (2013).

26. 26.

Lundeberg, M. et al. Tuning quantum non-local effects in graphene plasmonics. Science 357, 187–191 (2017).

27. 27.

Halbertal, D. et al. Imaging resonant dissipation from individual atomic defects in graphene. Science 358, 1303–1306 (2017).

28. 28.

Cao, Y. et al. Unconventional superconductivity in magic-angle graphene superlattices. Nature 556, 43–50 (2018).

29. 29.

Caldwell, J. D. et al. Low-loss, infrared and terahertz nanophotonics using surface phonon polaritons. Nanophotonics 4, 44–68 (2014).

30. 30.

Sun, L. et al. Enhancement of plamonic performance in epitaxial silver at low temperature. Sci. Rep. 7, 8917 (2017).

31. 31.

Chochol, J. et al. Plasmonic behavior of III–V semiconductor in far-infrared and terahertz range. J. Eur. Opt. Soc.-Rapid 13, 13 (2017).

32. 32.

Fei, Z. et al. Infrared nanoscopy of Dirac plasmons at the graphene–SiO2 interface. Nano Lett. 11, 4701–4705 (2011).

33. 33.

Kuzmenko, A. B. RefFIT: software to fit optical spectra, v1.2.95.

34. 34.

Waxenegger, J., Trügler, A. & Hohenester, U. Plasmonics simulations with the MNPBEM toolbox: consideration of substrates and layer structures. Comput. Phys. Commun. 193, 138–150 (2015).

35. 35.

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

36. 36.

Amorim, B. et al. Novel effects of strains in graphene and other two-dimensional materials. Phys. Rep. 617, 1–54 (2016).

37. 37.

Pietronero, L., Strässler, S., Zeller, H. R. & Rice, M. J. Electrical conductivity of a graphite layer. Phys. Rev. B 22, 904–910 (1980).

38. 38.

Woods, L. M. & Mahan, G. D. Electron-phonon effects in graphene and armchair (10,10) single-wall carbon nanotubes. Phys. Rev. B 61, 10651 (2000).

39. 39.

von Oppen, F., Guinea, F. & Mariani, E. Synthetic electric fields and phonon damping in carbon nanotubes and graphene. Phys. Rev. B 80, 075420 (2009).

40. 40.

Mariani, E. & von Oppen, F. Temperature-dependent resistivity of suspended graphene. Phys. Rev. B 82, 195403 (2010).

41. 41.

Sohier, T. et al. Phonon-limited resistivity of graphene by first-principles calculations: electron–phonon interactions, strain-induced gauge field, and Boltzmann equation. Phys. Rev. B 90, 125414 (2014).

42. 42.

Piscanec, S., Lazzeri, M., Mauri, F., Ferrari, A. C. & Robertson, J. Kohn anomalies and electron–phonon interactions in graphite. Phys. Rev. Lett. 93, 185503 (2004).

43. 43.

Basko, D. M. & Aleiner, I. L. Interplay of Coulomb and electron–phonon interactions in graphene. Phys. Rev. B 77, 041409 (2008).

44. 44.

Giuliani, G. & Vignale, G. Quantum Theory of the Electron Liquid (Cambridge Univ. Press, Cambridge, 2005).

45. 45.

Maslov, D. L. & Chubukov, A. V. Optical response of correleted electron systems. Rep. Prog. Phys. 80, 026503 (2017).

46. 46.

Sun, Z., Basov, D. N. & Fogler, M. M. Adiabatic amplification of plasmons and demons in 2D systems. Phys. Rev. Lett. 117, 076805 (2016).

## Acknowledgements

We thank A. Charnukha, A. Frenzel, R. Ribeiro-Palau and A. Sternbach for discussions. Research on Dirac quasiparticle dissipation in graphene was supported by DOE-BES DE-SC0018426. Plasmonic nanoscale imaging at cryogenic temperatures was supported by DOE-BES DE-SC0018218. Work on infrared nanoscale antennas and metasurfaces was supported by AFOSR FA9550-15-1-0478. The development of scanning plasmon interferometry was supported by ONR N00014-15-1-2671. Upgrades of the ultrahigh vacuum scanning probe system were supported by ARO grant W911nf-17-1-0543. D.N.B was supported by the Gordon and Betty Moore Foundation’s EPiQS Initiative through Grant GBMF4533. J.H. acknowledges support from ONR N00014-13-1-0662.

### Reviewer information

Nature thanks J. Song, A. Zayats and the other anonymous reviewer(s) for their contribution to the peer review of this work.

## Author information

### Author notes

1. These authors contributed equally: G. X. Ni, A. S. McLeod.

### Affiliations

1. #### Department of Physics, Columbia University, New York, NY, USA

• G. X. Ni
• , A. S. McLeod
• , L. Xiong
• , S. S. Sunku
• , C. R. Dean
•  & D. N. Basov
2. #### Department of Physics, University of California, San Diego, La Jolla, CA, USA

• G. X. Ni
• , A. S. McLeod
• , Z. Sun
• , L. Xiong
• , K. W. Post
• , B.-Y. Jiang
• , M. M. Fogler
•  & D. N. Basov

• L. Wang
•  & J. Hone
4. #### Department of Applied Physics and Applied Mathematics, Columbia University, New York, NY, USA

• S. S. Sunku

### Contributions

G.X.N. and A.S.M. performed the nanoscale infrared measurements and characterizations. Z.S., L.X., B.-Y.J. and M.M.F. provided theoretical calculations. L.W., J.H. and C.R.D. designed and created the device structures. G.X.N., L.X., K.W.P. and S.S.S. performed far-field optical spectroscopy measurements and characterizations. D.N.B. supervised the project. G.X.N., Z.S., M.M.F. and D.N.B. co-wrote the manuscript with input from all co-authors.

### Competing interests

The authors declare no competing interests.

### Corresponding author

Correspondence to D. N. Basov.

## Extended data figures and tables

1. ### Extended Data Fig. 1 AFM topography and s(ω) image of the hBN/graphene/hBN encapsulated device.

a, AFM topography image. The black dashed line marks the physical edge of graphene. b, c, Room-temperature s(ω) images obtained at Vg = 0 V and Vg = 50 V, respectively. G, graphene.

2. ### Extended Data Fig. 2 Plasmonic fringes near a graphene edge at different temperatures.

a, Maps of the near-field amplitude s measured at several temperatures for fixed Vg = 75 V and ω = 886 cm−1. b, Line profiles obtained by averaging over the vertical coordinates in each map. The solid lines are the data and the dash-dotted lines are the simulations.

3. ### Extended Data Fig. 3 Gate dependence of plasmon propagation at cryogenic temperature.

a, Near-field amplitude s as a function of the gate voltage and the distance L from the Au launcher at a fixed frequency of ω = 886 cm−1. b, Illustration of the gate sweeping sequence. c, Line profiles (averaged over ~200 nm perpendicular to the propagation direction) of plasmonic interference fringes at different gate voltages.

4. ### Extended Data Fig. 4 Optical image of an hBN sample on a SiO2/Si substrate.

The dashed red square marks the approximate location of the region used in the reflectance measurements. The hBN thickness is 17 nm.

5. ### Extended Data Fig. 5 Reflectance spectra of the hBN/SiO2/Si structure at T=60–300 K.

af, The black points are the experimental data and the red dashed lines are the fits. The sharp resonance at 1,370 cm−1 is due to the in-plane optical phonon of hBN, and the broad peak at around 1,070 cm−1 is due to the optical phonon of SiO2.

6. ### Extended Data Fig. 6 The hBN in-plane phonon parameters versus the temperature.

a, The fitted phonon linewidth γ x . The squares are the data and the dashed line is a guide for the eye. b, The fitted frequency ωtx.

7. ### Extended Data Fig. 7 Plasmonic oscillations in the vicinity of the Au launching pads.

a, Illustration of the Au pad (gold, with the triangular mesh used in the simulation) on graphene (honeycomb lattice). The red arrow depicts the direction of the external field. The blue arrow symbolizes launched plasmons. Scale bar, 200 nm. b, An example of the simulated electric field distribution (Ez, imaginary part) just above the graphene layer. The grey rectangle represents the right half of the Au pad. The simulation parameters are λp = 170 nm and Q = 130. c, Comparison of the theoretical fit (blue) and the experimental data (red) for Vg = 75 V and T = 60 K. Both the theoretical and experimental traces are obtained by averaging multiple line cuts inside the 600-nm-wide strip indicated by the white dashed lines in b. The phase shift θ = 112° (see text) was used to align the oscillations.

8. ### Extended Data Fig. 8 Device structure and dielectric losses.

a, Schematic of the device, showing the notations for the permittivities and thicknesses of the layers. b, Nano-FTIR spectrum s(ω) obtained with the hBN crystal taken away from the sample edges. c, The contribution γenv of the dielectric environment to the plasmon linewidth as a function of temperature at a frequency of ω = 886 cm−1. The hBN c-axis damping constant is γ z (300 K) = 3.4 cm−1, which is consistent with previous results35.

9. ### Extended Data Fig. 9 Electron–phonon scattering processes.

Diagrams of the scattering processes included in equation (12). The wavy, straight and dashed lines represent photons, electrons and phonons, respectively.

10. ### Extended Data Fig. 10 Electron–phonon scattering rate as a function of temperature.

ac, Temperature dependence of the plasmonic scattering rate and of the d.c. scattering rate. Solid lines in a and b display the results of parameter-free modelling for electron–phonon scattering contributions (a) and electron–electron scattering contributions (b). Solid lines in c display the results of the sum in a and b, as discussed in the main text.

11. ### Extended Data Fig. 11 Plasmon damping rate due to electron–electron scattering as a function of temperature.

The blue solid curve is the plasmon damping rate γee due to electron–electron interactions, computed from equations (17) and (18) for a Fermi energy of $${\varepsilon }_{{\rm{F}}}\equiv \mu (T=0)=0.27\,{\rm{eV}}$$. The red solid curve is the electron collision rate Γee from equation (16). The squares and circles are Γee values extracted from recent d.c. transport studies23,24 at a different carrier density, n ≈ 1012 cm−2.

### DOI

https://doi.org/10.1038/s41586-018-0136-9

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