Tuning photoinduced terahertz conductivity in monolayer graphene: Optical-pump terahertz-probe spectroscopy

Optical-pump terahertz-probe differential transmission measurements of as-prepared single layer graphene (AG) (unintentionally hole doped with Fermi energy $E_F$ at $\sim -180\mathrm{meV}$), nitrogen doping compensated graphene (NDG) with $E_F\sim -10$ meV, and thermally annealed doped graphene (TAG) are examined quantitatively to understand the opposite signs of photoinduced dynamic terahertz conductivity $\Delta \sigma$. It is negative for AG and TAG but positive for NDG. We show that the recently proposed mechanism of multiple generations of secondary hot carriers due to Coulomb interaction of photoexcited carriers with the existing carriers together with the intraband scattering can explain the change of photoinduced conductivity sign and its magnitude. We give a quantitative estimate of $\Delta \sigma$ in terms of controlling parameters—the Fermi energy $E_F$ and momentum relaxation time $\tau$. Furthermore, the cooling of photoexcited carriers is analyzed using a supercollision model which involves a defect mediated collision of the hot carriers with the acoustic phonons, thus giving an estimate of the deformation potential.

Figure 1

(a) XPS spectra of AG and NDG showing the C $1s$ line. The main peak at 284.6 eV represents $s{p}^2$ C. Two additional peaks appeared at 285.8 and 288.6 eV corresponding to C–N and C=O bonds. (b) The N 1s XPS spectra of NDG showing two peak at 399.5 and 400.5 eV, which suggest the presence of nongraphitic N–C bonding. (c) Raman spectra of AG, NDG, and TAG.

Figure 2

Terahertz conductivity. (a) Evolution of THz electric field as a function of delay time. (b) Conductivity (in unit of $G_0$) spectra for AG (red solid line), NDG (blue dotted line), and TAG (black dash-dotted line). Inset: FT amplitudes vs frequency.

Figure 3

Transient THz photoconductivity. Evolution of the real part of photoinduced THz conductivity as function of delay time between the 785 nm pump and the THz probe.

Figure 4

Scattering mechanisms. (a) $\Delta {\sigma }_{\text{intra}}$, $\Delta {\sigma }_{\text{el}}$, and $\Delta {\sigma }_{\text{tot}}$ are plotted as a function of Fermi energy $E_F$ at $T_e=700$ K, $\tau =34$ fs, and $b=190$ fs/eV for probe frequency $\omega /2\pi =1$ THz. (b) The contour plot of $\Delta {\sigma }_{\text{tot}}$ as a function of Fermi energy and momentum relaxation time $\tau$ at $T_e=700$ K and $b=190$ fs/eV. The white line represents $\Delta {\sigma }_{\text{tot}}=0$ and indicates the boundary between positive and negative $\Delta {\sigma }_{\text{tot}}$.

Figure 5

The photoinduced change of electron temperature $\Delta T_e\left(0\right)$ at the peak of transient conductivity is plotted as a function of fluence for (a) AG and (b) NDG. The solid lines are the fit to ${\phi }^{1/3}$.

Figure 6

(a) Cooling dynamics of AG. The blue dashed line is fit to normal collision given by Eq. (5) and red solid line is fit to SC given by Eq. (6). (b) Cooling dynamics of NDG. The black dotted curve is fit to normal collision in the nondegenerate limit [Eq. (8)], the blue dashed curve is fit to normal collision in degenerate limit [Eq. (5)], and the red solid curve is fit to SC given by Eq. (6).

Figure 7

Photoinduced conductivity $\Delta \sigma \left(\omega \right)$ as a function of frequency at 2 ps after photoexcitation for (a) AG, (b) NDG, and (c) TAG. The real parts of the data are shown by opened symbols and imaginary parts are shown by closed symbols. The continuous horizontal lines shows the zero reference lines of $\Delta \sigma \left(\omega \right)$. The black and dashed nonlinear black lines are the fit to the Drude-Lorentz model [Eq. (9)].

Figure 8

Fitted parameters for AG. (a) The Drude weight $\mathfrak{D}$ varies as ${\phi }^{1/2}$ (shown by the red solid line). (b) and (c) Oscillator strength $F$ and linewidth $\gamma$ as a function of pump fluence.