Research ArticleCONDENSED MATTER PHYSICS

Detection of thermodynamic “valley noise” in monolayer semiconductors: Access to intrinsic valley relaxation time scales

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Science Advances  01 Mar 2019:
Vol. 5, no. 3, eaau4899
DOI: 10.1126/sciadv.aau4899
  • Fig. 1 Sample, experimental setup, and valley noise spectrum of resident holes in monolayer WSe2.

    (A) Sample: A single WSe2 monolayer is sandwiched between hBN layers and electrically gated. (B) Band structure and σ± optical transitions of hole-doped monolayer WSe2. Even in thermal equilibrium, resident holes spontaneously scatter between K and K′ valleys, giving a randomly fluctuating valley polarization noise. (C) To detect valley noise, a CW probe laser is linearly polarized and focused through the sample. Thermodynamic valley fluctuations impart FR fluctuations δθF(t) on the probe laser, which are detected using balanced photodiodes. LP, linear polarizer; PBS, polarizing beam splitter; FFT, fast Fourier transform. (D) The valley noise power spectrum (squares) of resident holes in monolayer WSe2. Its Lorentzian line shape (solid line) with full width Γ indicates an exponentially decaying valley correlation with relaxation time scale τv = 1/πΓ = 430 ± 20 ns. Inset: Valley relaxation measured separately in a perturbative pump-probe experiment.

  • Fig. 2 Comparing the valley noise measurements with perturbative pump-probe experiments.

    (A) Valley noise spectra of hole-doped WSe2 at different temperatures (solid lines are Lorentzian fits). arb.u., arbitrary units. (B) Hole valley relaxation measured separately by TRFR. (C) Temperature dependence of valley relaxation rate extracted from the valley noise (1/τv = πΓ; red) and relaxation rate measured by TRFR (blue) showing very close agreement. (D) Valley noise spectra acquired using two different background subtraction methods: on/off the WSe2 (red) and absence/presence of in-plane magnetic field Bx (blue). See also fig. S3 for a more detailed field and temperature dependence.

  • Fig. 3 Dependence of the measured noise on probe parameters.

    (A) The total (frequency-integrated) valley noise power scales as the inverse of the cross-sectional area A of the probe laser spot on the sample, as expected for optically detected noise measurements. (B) The total valley noise scales quadratically with the power P of the probe laser, again as expected for noise studies.

  • Fig. 4 Dependence of the hole valley noise on the probe photon energy.

    (A) Optical transmission spectrum of the lightly hole-doped WSe2 monolayer (Vg = +2 V) showing neutral (X0) and positively charged exciton (X+) resonances. (B) Energy-dependent FR spectrum θF(E) induced by an intentional (optically pumped) valley polarization of the resident holes (see text). θF(E) is antisymmetric and centered on X+, as expected. (C) Spectral dependence of the total valley noise power, Embedded Image (blue points). The red points show the square of θF(E) from (B), showing close agreement.

  • Fig. 5 The valley noise spectrum of electron-doped monolayer WSe2.

    The spectrum shows Lorentzian line shape and much larger width Γ (indicating shorter valley relaxation time τv) as compared to the hole-doped regime (cf. Fig. 1D). The spectrum was measured at Vg = −2 V and T = 15 K using the off-WSe2 background subtraction method. Inset: Electron valley relaxation measured independently by conventional (perturbative) TRFR, which corroborates the shorter τv.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/5/3/eaau4899/DC1

    Fig. S1. An example of the raw noise data.

    Fig. S2. Valley noise spectra of resident holes at Bx = 0 and 0.35 T.

    Fig. S3. Temperature and magnetic field dependence of the hole valley relaxation rate.

    Fig. S4. Normalized transmission spectra of the WSe2 monolayer in the hole- and electron-doped regime.

  • Supplementary Materials

    This PDF file includes:

    • Fig. S1. An example of the raw noise data.
    • Fig. S2. Valley noise spectra of resident holes at Bx = 0 and 0.35 T.
    • Fig. S3. Temperature and magnetic field dependence of the hole valley relaxation rate.
    • Fig. S4. Normalized transmission spectra of the WSe2 monolayer in the hole- and electron-doped regime.

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