Research ArticlePHYSICS

Ultrafast nonlocal collective dynamics of Kane plasmon-polaritons in a narrow-gap semiconductor

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Science Advances  09 Aug 2019:
Vol. 5, no. 8, eaau9956
DOI: 10.1126/sciadv.aau9956
  • Fig. 1 Plasmonic pumping experiment and photoinduced near-field optical response in Hg0.81Cd0.19Te.

    (A) Nano-optical spectroscopy was carried out by means of apertureless scattering-type near-field optical microscope based on a metallic tip of an atomic-force microscope illuminated with broadband IR light and photoexcited with a femtosecond fiber laser operating in the conventional telecommunications window of the Er-doped optical fiber (1530 to 1565 nm) (23); high-fluence data in Fig. 3C were obtained using a free-space amplified laser system (see Materials and Methods). Strong field enhancement and gradient in the sample-tip nanocavity enable large light-matter momentum transfer (on the order of inverse tip radius) and, thus, the excitation and nanospectroscopy of large-momentum collective modes (27), overcoming the long-wavelength restriction of conventional IR optics. (B and C) Photon-energy dependence of the amplitude (B) and phase (C) of the normalized transient near-field signal demodulated at the second harmonic of the tip tapping frequency (O2: O, optical; 2, second harmonic). The spectra are plotted for various pump-probe delays from 0 to 12.2 ps and a pump pulse energy of 1 nJ. The dashed and dotted lines indicate the location of the primary and secondary plasmon-polaritonic feature, respectively. Solid black vertical lines indicate the time delays at which data were obtained.

  • Fig. 2 Ultrafast dynamics of coupled surface plasmon-polaritons.

    (A) Schematic of the electronic band structure of Hg0.81Cd0.19Te along several high-symmetry directions in the Brillouin zone without taking into account small intrinsic doping present in our samples. On the basis of the data in (40), C, HH, and LH denote the electron conduction band, heavy-hole, and light-hole valence band, respectively. Quasi-linear ultrarelativistic segments of band structure near Γ result from a large spin-orbit coupling. Vertical arrows show the optical transitions accessible to the optical pump with a photon energy of 0.8 eV. Note that the LH-C transitions have a much lower joint density of states than HH-C. The bandgap in this compound is ≈0.05 to 0.1 eV at 300 K and substantially temperature dependent (1). Effective masses of low-energy charge-carriers are indicated. (B) Imaginary part of the reflection coefficient rp(ω, q) as a function of frequency ω and in-plane momentum transfer q calculated for a 90-nm thin film of Hg0.81Cd0.19Te on top of CdTe substrate, as described in the text. The two surface modes expected in a thin metallic film (one per interface; red and cyan dashed lines) experience mutual repulsion at long wavelengths due to the coupling between the symmetric and antisymmetric charge oscillations in these modes. (C) Near-field amplitude (red) and phase (blue) calculated using the reflection coefficient in (B) in the lightning rod model of near-field sample-tip interaction referenced to those of gold. The black dashed line is a cut of Im[rp(ω, q)] at q0 = 1/100 nm = 105 cm−1 [white dashed line in (B)]. The gray vertical arrows indicate the depression in the near-field amplitude (solid) and Im[rp(ω, q0)] (dashed) between the two branches of the surface plasmon-polariton. (D and E) Photon energy dependence of the amplitude (D) and phase (E) of the normalized transient near-field signal demodulated at the second harmonic of the tip tapping frequency, presented for select pump-probe delays (open symbols). Arrows indicate the location of the secondary plasmon-polaritonic feature. Dashed lines are the result of a fit using the model dielectric function in Eq. 1 incorporated into the multilayer response of the Hg0.81Cd0.19Te thin film on a CdTe substrate. (F) Unscreened plasma frequency ωpl and scattering rate γ of plasmon-polariton quasiparticles as a function of the pump-probe delay (open symbols), extracted from the fit in (D) and (E). Red and blue solid lines in (F) are the result of a biexponential fit of the dependence of the plasma frequency and scattering rate, respectively, on the pump-probe delay. Horizontal red and blue dashed lines indicate the residual plasma frequency and scattering rate due to long-lived quasiparticle response (>30-ps lifetime).

  • Fig. 3 Quasi-relativistic quantum quasiparticle response in Hg0.81Cd0.19Te.

    (A and B) Classical parabolic (A) and quasi-relativistic Kane (B) low-energy electronic band structure in a semiconductor. Quasi-linear ultrarelativistic segments of the Kane band structure result from a large spin-orbit coupling. The strong itinerant response is dominated by charge-carriers photoexcited predominantly from the HH band to the C band, as indicated by a blue arrow. (C) Dependence of the unscreened plasma frequency (blue symbols) on the number of photons per pump pulse (photon energy is 1.38 eV in this case). The latter is proportional to the number of photoexcited charge-carriers well below the saturated-absorption regime. Solid black as well as dashed green and red lines indicate the best fit to the experimental data obtained using the power-law dependence with exponent p of the plasma frequency on itinerant electron density in the case of classical parabolic (dashed red; p = 1/2) as well as 3D (dashed green; p = 1/3) and 2D (solid black; p = 1/4) quasi-linear Kane dispersion of the C band (see text). The latter two dependencies are purely quantum and have no classical analog (13).

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/5/8/eaau9956/DC1

    Section S1. Sample characterization

    Section S2. Photoinduced near-field optical response

    Section S3. Reflection coefficient rp(ω, q)

    Section S4. Simulated far-field optical response

    Fig. S1. Sample characterization.

    Fig. S2. Photoinduced near-field optical response.

    Fig. S3. Reference measurements and unnormalized spectra.

    Fig. S4. Large-momentum plasmonic modes in Hg0.81Cd0.19Te/CdTe.

    Fig. S5. Skin depth in bulk Hg0.81Cd0.19Te.

    Fig. S6. Calculated far-field IR response.

  • Supplementary Materials

    This PDF file includes:

    • Section S1. Sample characterization
    • Section S2. Photoinduced near-field optical response
    • Section S3. Reflection coefficient rp(ω, q)
    • Section S4. Simulated far-field optical response
    • Fig. S1. Sample characterization.
    • Fig. S2. Photoinduced near-field optical response.
    • Fig. S3. Reference measurements and unnormalized spectra.
    • Fig. S4. Large-momentum plasmonic modes in Hg0.81Cd0.19Te/CdTe.
    • Fig. S5. Skin depth in bulk Hg0.81Cd0.19Te.
    • Fig. S6. Calculated far-field IR response.

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