hBN / hBN-graphene phonon polariton

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NMater2020_Direct observation of highly confined phonon polaritons in suspended monolayer hexagonal boron nitride

excite hyperbolic phonon polariton in 2d material

  • momentum compensation above 10^6 cm^-1
    • s-SNOM widely used for 2d polariton probing
      • high resolution imaging
      • momentum compensation typically reaches ~10^5 cm^-1
      • determined by tip size
    • need narrow frequency window

fast electrons can transfer much larger momentum than photons

  • EELS
    • high spatial and energy resolution
      • lattice vibrations
      • interband transitions
      • interactions mediated by large-momenta exchanges
        • polariton-induced shift of resonance peak
    • limited by energy resolution for narrow phonon polariton dispersion

hBN flakes STEM-EELS spectra:

  • aloof configuration
    • in vacuum
    • 10 nm away from hBN edge
    • one peak at 173 meV
      • consistent with previous work
  • bulk geometry
    • inside the flake
    • 20 nm away from hBN edge
    • three peaks, 173 182 196 meV

FEM reproduce EELS spectra of hBN flakes (e beam move from edge to inside)

  • 196 meV, right peak
    • between
      • surface optical phonon SO 195 meV
      • LO phonon 200 meV
    • considering zero-loss peak ?
      • gaussian convolution FWHM 7.5 meV
    • 200 meV redshift to 196 meV, LO phonon
    • evenly distributed
      • characteristic of LO phonon
    • SO phonon localized at edge
      • not observed in exp
      • strong localization at boundary
      • imperfection in edge
  • 182 meV, central peak
    • shift from 195 meV to 183 meV
    • characteristic of phonon polariton
    • excited polaritons propagete to edge, then are reflected by edge
      • then interfere with the excited polariton
      • interference max:
        • $2q\vert d \vert + \phi_{refl} = 2\pi$
          • $ \phi_{refl} $ is phase change by reflection
          • use $ \phi_{refl} = \frac{\pi}{2} $ here
      • by this relation, extract energy loss spectrum in momentum space by spectrum in distance space by changing $d$
    • FEM assigned to symmetric surface phonon polariton SM0-S mode
    • originates in the constructive interference of HPhPs reflected by the edge, followed the $2q \vert d \vert + \phi_{refl} = 2\pi$ law
      • frequency (energy loss) more stable when far enough away from the edge (large d)
  • 173 meV, left peak
    • close to TO phonon but not TO
      • TO cannot be electrically exicted
    • FEM assigned to SM0-S mode, same to central peak
      • frequency difference due to wave vectors
      • much lower and unchangeable q with position
      • arises due to the excitation of HPhPs propagating along the direction perpendicular to the e beam line scan
      • convolution of several peaks
        • blue shift

FEM reproduce EELS spectra of monolayer hBN

  • thickness pick 0.34 nm
  • LO TO are degenerated into one point
  • only one peak with increasing scanning distance to the edge
    • HPhP modes
    • actually the combination of two peaks, low-q and high-q HPhPs
      • can see two peaks but very close to each other in simulation without zero-loss peak (Gaussian smearing)
      • after smearing they get too close so cant regonize
    • low-q HPhP
      • similar to left peak in flakes
      • doesnt change with scanning distance
      • SM0 mode
    • high-q HPhP
      • similar to central peak in flakes
      • constructive interference, incident and edge-reflected HPhP
        • change with d
        • approach to steady value with increasing d, reflection is ignored with large d