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.
Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
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.
Extended data figures and tables
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.
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.
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.
The dashed red square marks the approximate location of the region used in the reflectance measurements. The hBN thickness is 17 nm.
a–f, 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.
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.
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.
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.
Diagrams of the scattering processes included in equation (12). The wavy, straight and dashed lines represent photons, electrons and phonons, respectively.
a–c, 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.
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 . 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.