Research ArticlePHYSICS

Observation of new plasmons in the fractional quantum Hall effect: Interplay of topological and nematic orders

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Science Advances  22 Mar 2019:
Vol. 5, no. 3, eaav3407
DOI: 10.1126/sciadv.aav3407
  • Fig. 1 Observation of new plasmons in the SLL.

    (A) Schematic description of the light scattering geometry at a tilt angle θ. Incident and scattered light have photon energy ωL and ωS and wave vector kL and kS. The total magnetic field BT, the perpendicular component B, and in-plane magnetic field B// are also shown. k = 5.3 × 104 cm−1 for θ = 20° and ωL = 1526 meV. (B) Color plot of RILS spectra of the plasmon measured at θ = 20° in the QELC phase at v = 2.33 as a function of ωL. The mode intensity is resonantly enhanced at the plasmon energy (1.43 meV) marked by an arrow. (C) RILS spectra of plasmons at filling factors in the range 2 < v < 3. Intensities of the spectra in (B) and (C) are normalized to the incident light intensity. (D) Spin-wave (SW) modes in the range of 2 < v ≤ 3. Red arrows mark the position of the spin-wave modes, and black arrows indicate the Zeeman energy. a.u., arbitrary units.

  • Fig. 2 Square-root dependence of plasmon energy on particle density.

    (A) Plasmon energy as a function of particle density in the filling factor range of the spin-up SLL. The blue squares are for electrons, and the red dots are for holes. The blue dashed line is a fit with a square-root dependence on electron density, and the red dashed line is a fit with a square-root dependence on hole density. (B) Data points in (A) as a function of particle density n*. The square-root dependence is described by Eq. 1, where m* = 0.07 m0, q = 5.3 × 104 cm−1, ε = (εGaAs + εAlGaAs)/2 = 12.5, εGaAs is the dielectric constant of GaAs, εAlGaAs is the dielectric constant of AlGaAs, α = 0.09 for electrons, and α = 0.14 for holes. (C) Cartoon showing charge stripes in the SLL under an in-plane magnetic field. For the wave vector q // B// (see Fig. 1A), the plasmon wavelength λ// = 2π/q is much larger than a typical spacing between stripes (a few magnetic lengths).

  • Fig. 3 Dependence of plasmon intensity on filling factor.

    (A) Normalized integrated intensity of the plasmon peaks as a function of filling factor. The integrated intensity is normalized by particle density in the SLL. The black dashed line marks a background value of electronic liquid crystal phases in the SLL. Three red dashed lines mark filling factors of v = 7/3, 5/2, and 8/3 respectively. (B) Characteristic plasmon coherence length L as a function of filling factor. L is determined from the FWHM of the plasmon lines.

  • Fig. 4 Plasmon modes near v = 5/2.

    (A) Color plots of RILS spectra measured at filling factors around v = 2.50 as function of incoming photon energy ωL. Resonance of the plasmon modes appears at close ωL for filling factors around v = 5/2. (B) Normalized integrated intensity of the plasmon peaks around v = 2.50. The green area indicates the appearance of the gapped (incompressible) FQH state, while the gray area indicates gapless (compressible) FQH states (20).

Supplementary Materials

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    • Fig. S1. The plasmon energy versus particle density n* on a log-log plot.

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