Electrical tunability of terahertz nonlinearity in graphene

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Science Advances  07 Apr 2021:
Vol. 7, no. 15, eabf9809
DOI: 10.1126/sciadv.abf9809
  • Fig. 1 Thermodynamic model calculations for the Fermi energy dependence of the terahertz nonlinearity of graphene.

    (A and B) Driving single-cycle and multicycle terahertz fields, respectively. (C and D) and (E and F) The associated terahertz field–induced heat and SA, respectively, for two-doping levels corresponding to Fermi energies of 80 and 180 meV. The terahertz-induced heat (or equivalently the rise in the electron temperature) leads to a reduction and a temporal modulation of both the intraband conductivity, σ(t) and the power absorption coefficient α(t), as shown in (C) and (D). This results in a nonlinear terahertz field–induced current J(t) = σ(t, ETHz)ETHz(t) in the graphene layer, yielding terahertz field–induced transparency (SA) and electromagnetic reemission at higher odd-order harmonics. Both the terahertz-induced heat and SA become more pronounced when the doping concentration (the Fermi energy, EF) increases, scaling nearly with EF2. (G and H) The spectral amplitudes of the terahertz fields transmitted through graphene relative to the pump field (gray background), for the tested Fermi energies of 80 and 180 meV. a.u., arbitrary units.

  • Fig. 2 Schematics of the terahertz experiments and the gated graphene sample.

    (A) TPTP experiment with gated graphene. The electric field of the terahertz pump is vertically polarized and has a peak field strength up to 80 kV/cm, while the electric field of the terahertz probe is horizontally polarized with a peak field strength of less than 1 kV/cm. (B) Nonlinear terahertz-TDS, using multicycle quasi-monochromatic terahertz pulses oscillating at a fundamental central frequency of 0.3 THz and having a peak electric field up to 80 kV/cm. The transmitted field through the graphene sample consists of higher odd-order harmonics in addition to the fundamental frequency. Note that EF refers to the Fermi energy of the graphene sample, while Ef refers to the peak electric field of the driving THz signal oscillating at the fundamental frequency f. (C) The gated graphene sample device in which the graphene film acts as a channel between source and drain electrodes subjected to a constant potential difference of 0.2 mV. The graphene film is covered on top by an electrolyte subjected to a varying gating voltage to tune the Fermi level of the graphene layer. (D) Experimentally determined gating response of the graphene sample given by the sheet resistance of the graphene film as a function of the gating voltage relative to the voltage V0 corresponding to the minimum Fermi energy in the vicinity of the Dirac point, exhibiting a maximum resistance. Positive VV0 leaves electrons in the graphene layer with the Fermi level elevated in the conduction band, while hole doping with the Fermi level pinning the valence band is induced by negative VV0.

  • Fig. 3 Dependence of terahertz field–induced SA on the gating voltage revealed by TPTP spectroscopy.

    (A and B) The terahertz probe fields before (black) and after (red) intense terahertz pump excitation, normalized to the peak field after excitation with pump peak electric field (80 kV/cm), and their difference (blue) multiplied by four for clarity, for gating voltages of 1 and 0.3 V, respectively. (C) The as-measured peak field transmission of the probe pulses at various gating voltages when the graphene is pumped at 80 kV/cm. T0 is the background probe transmission of the graphene sample before the pump, which increases by decreasing the doping (gating) level. (D) The terahertz probe differential transmission ΔT/T0 = (TT0)/T0, where T is the probe transmission after the pump, as a function of the pump-probe delay time, obtained by analysis of the experimental data of (C). The dots represent the experimental results, while the solid lines are guides for the eye. (E) The peak of the probe differential signal ΔT/T0 as a function of the terahertz pump field at various doping levels and (F) the peak of ΔT/T0, extracted from (E), as a function of the gating voltage at some selected pump peak electric fields. The pink arrows indicate that the data in (D) and (F) are obtained by analysis of data from (C) and (E), respectively, while the violet arrows in (E) and (F) indicate increase in ΔT/T0 with the gate voltage and the driving field, respectively.

  • Fig. 4 Gating dependence of terahertz HHG.

    (A) The terahertz amplitude spectra of the terahertz fields of the incident driving field and the transmitted fields through the graphene sample exhibiting generation of higher odd-order harmonics up to the seventh order for two doping levels, with the driving terahertz signal shown in the inset, and (B) the peak electric field of the generated harmonics as a function of the gating voltage.

  • Fig. 5 The thermodynamic model calculations.

    (A and B) The thermodynamic model calculations (solid lines) and the experimental results (solid circles) of the peak of ΔT/T0 and the electric field of the generated harmonics up to the seventh order, respectively, as functions of the EF and various terahertz pump fields, (C) EF as a function of the gating voltage, and (D) the carrier momentum scattering time as a function of EF.

Supplementary Materials

  • Supplementary Materials

    Electrical tunability of terahertz nonlinearity in graphene

    Sergey Kovalev, Hassan A. Hafez, Klaas-Jan Tielrooij, Jan-Christoph Deinert, Igor Ilyakov, Nilesh Awari, David Alcaraz, Karuppasamy Soundarapandian, David Saleta, Semyon Germanskiy, Min Chen, Mohammed Bawatna, Bertram Green, Frank H. L. Koppens, Martin Mittendorff, Mischa Bonn, Michael Gensch, Dmitry Turchinovich

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    This PDF file includes:

    • Thermodynamic terahertz electronic nonlinearity of graphene
    • Single-band versus two-band calculations
    • Guide to the eye
    • Fitting parameters and supportive Hall effect measurements
    • Figs. S1 to S6
    • References

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