Research ArticleCONDENSED MATTER PHYSICS

The ultrafast dynamics and conductivity of photoexcited graphene at different Fermi energies

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Science Advances  11 May 2018:
Vol. 4, no. 5, eaar5313
DOI: 10.1126/sciadv.aar5313
  • Fig. 1 Experimental technique and interband-to-intraband heating transition.

    (A) Illustration of the optical pump–THz probe measurement technique and the gate-tunable graphene device design, as explained in the main text and Methods. By applying a gate voltage Vg to the polymer electrolyte, we change the Fermi energy of graphene and thereby its DC conductivity σ0. By applying a source-drain voltage VSD between the two contacts and measuring the current ISD, we extract σ0 (after correcting for contact resistance). (B) The measured THz photoconductivity ΔσTHz as a function of simultaneously measured DC conductivity σ0, following a pump pulse with a wavelength of 800 nm that creates a photoexcited carrier density nexc = 0.5 × 1012/cm2. (C) Theoretical calculation (see Methods) of the THz photoconductivity versus DC conductivity (bottom horizontal axis) or Fermi energy (top horizontal axis) for the same parameters as in the experiment, at time t = 300 fs after photoexcitation. The theoretical results (which are free of adjustable parameters) reproduce the magnitude of the signal within a factor ≲ 2 and the positive-to-negative transition. (D) The calculated carrier density in the conduction band (left vertical axis) and hot-carrier density (right vertical axis) with respect to equilibrium, for the same parameters as in the experiment. The dashed horizontal line indicates nexc, which is the same for all equilibrium DC conductivities. Interband heating occurs when nCBnCB,0 > 0, whereas intraband heating occurs when nHCnHC,0 >0.

  • Fig. 2 Interband versus intraband heating.

    The panels show the calculated electron distribution f(ε) as a function of energy ε, at time t = 0 before photoexcitation (black lines and gray areas) and at a time t = 300 fs (cyan and orange lines and areas). The state occupation in the Dirac cones is also depicted alongside the electron distribution. The wavy lines represent the photoexcitation of electrons (holes) in conduction (valence) band at energy Eph/2 (− Eph/2). The pump photons have energy Eph = 1.5 eV. (A) At the equilibrium Fermi energy EF ≃ 0.05 eV, the broadening of the electron distribution involves electronic transitions from valence to conduction band, represented by cyan arrows, that is, interband heating. (B) At EF ≃ 0.4 eV, the broadening is mostly due to electronic transitions from below to above the chemical potential, represented by orange arrows, that is, intraband heating.

  • Fig. 3 Photon energy scaling for intraband heating.

    (A) The THz photoconductivity ΔσTHz as a function of pump pulse fluence, parametrized by the photoexcited carrier density nexc, for two pump photon energies Eph = 1.0 eV (purple circles) and 2.5 eV (green circles). The solid lines serve as guides to the eye based on saturation curves. These measurements are done at Vg = 0 V, where we measure a DC conductivity of σ0 ≈ 8 e2/h. Using the mobility of ~1000 cm2/Vs, we extract an equilibrium Fermi energy of |EF| ≃ 0.25 eV, corresponding to graphene gated away from the charge neutrality point. The THz photoconductivity saturates for nctexc ≳ 0.05 × 1012/cm2, corresponding to a relatively low-incident fluence < 1 μJ/cm2, as observed earlier (27, 30). The signal (and therefore the hot-carrier density) is larger for the larger photon energy. Thus, larger photon energies are responsible for larger hot-carrier densities. This is a key signature of efficient intraband heating (25). (B) The THz photoconductivity at nexc = 0.2 × 1012/cm2 [vertical dashed line in (A)], as a function of the pump photon energy. The solid circles are experimental data (right vertical axis) and the solid line the result of the theoretical calculation (left vertical axis) for EF = 0.25 eV. Experiment and theory show good qualitative agreement, with a larger absolute value of the THz photoconductivity for larger photon energy. (C) The calculated hot-CM factor HCM, defined in the main text, as a function of the pump photon energy. The HCM-factor increases with photon energy. (D) The electron distributions and the state occupation in the Dirac cone, compare with Fig. 2, before and after photoexcitation with pump photon energy Eph = 2.5 eV (left, green wavy line) and 1.0 eV (right, purple wavy line). The broadening of the electron distribution is larger in the Eph = 2.5 eV case, indicating more intraband heating for larger photon energy.

  • Fig. 4 Photon energy scaling for interband heating.

    This figure is analogous to Fig. 3, with the difference that the measurements are done at Vg = 0.5 V, the point of lowest DC conductivity (σ0 ≈ 2 e2/h), corresponding to graphene close to the charge neutrality point. The calculations are done for EF = 0.05 eV, although because of puddles, the effective Fermi energy in the experiment could be significantly larger. We observe that the value of the THz photoconductivity is positive, whereas in Fig. 3, it is negative. (A and B) The THz photoconductivity for three pump photon energies Eph = 0.5, 1.0, and 2.5 eV. (C) The calculated CM factor, defined in the main text. Interband heating contributes to the broadening of the electron distribution, shown in (D). The broadening of the electron distribution is larger in the Eph = 2.5 eV case, indicating more interband heating for larger photon energy. To understand the magnitude of the photoconductivity, we note that the added carrier density in the conduction band corresponds to Δn = CM⋅ nexc. Using CM = 3 (for a photon energy of 2 eV), nexc = 0.2⋅ 1012/cm2, and a mobility of μ = 1000 cm2/Vs, we obtain an increased conductivity of Δσ = Δneμ = 4 e2/h. This agrees with the calculated increase in conductivity (see Fig. 4B for a photon energy of 2 eV). The measured value is significantly lower, most likely due to electron-hole puddles.

  • Fig. 5 Thermodynamic picture and heating efficiency.

    (A) The electron temperature as a function of equilibrium Fermi energy at time t = 100 fs after photoexcitation, for photoexcited carrier densities nexc = 0.5 × 1012/cm2 (black, solid line) and nexc = 0.17 × 1012/cm2 (gray, dashed line). (B) The energy transfer efficiency as a function of equilibrium Fermi energy at time t = 100 fs after photoexcitation, for photoexcited carrier densities nexc = 0.5 × 1012/cm2 (black, solid line) and nexc = 0.17 × 1012/cm2 (gray, dashed line). The energy transfer efficiency is defined as the ratio between the electron energy density at time t and the photon energy density of the pump pulse and is a highly relevant parameter for photodetectors based on carrier heat, among others. The equilibrium Fermi energy intervals where interband heating or intraband heating are dominant are shaded along the horizontal axes of the panels. These results show that, regardless of the occurrence of interband or intraband heating, photoexcitation leads to an increase of the electron temperature that is larger for the larger photoexcited density. The energy transfer efficiency is 60 to 70% for the higher fluence and 70 to 80% for the lower fluence. This shows that the energy of the absorbed pump photons is efficiently retained by the electron system rather than dissipated into phonons. We also show the temporal evolution of energy dissipation in the system for low fluence (C) and higher fluence (D). The dynamics indicate that, for several hundred femtoseconds, the energy that is deposited by photons into the electronic system is still mainly present as energy in the electrons (electron heat).

Supplementary Materials

  • Supplementary Materials

    This PDF file includes:

    • fig. S1. Sample characterization.
    • fig. S2. Intrinsically undoped graphene.
    • References (61–64)

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