Semiconducting-to-Metallic Photoconductivity Crossover and Temperature-Dependent Drude Weight in Graphene

We investigate the transient photoconductivity of graphene at various gate-tuned carrier densities by optical-pump terahertz-probe spectroscopy. We demonstrate that graphene exhibits semiconducting positive photoconductivity near zero carrier density, which crosses over to metallic negative photoconductivity at high carrier density. These observations can be accounted for by the interplay between photoinduced changes of both the Drude weight and carrier scattering rate. Our findings provide a complete picture to explain the opposite photoconductivity behavior reported in (undoped) graphene grown epitaxially and (doped) graphene grown by chemical vapor deposition. Notably, we observe nonmonotonic fluence dependence of the photoconductivity at low carrier density. This behavior reveals the nonmonotonic temperature dependence of the Drude weight in graphene, a unique property of two-dimensional massless Dirac fermions.

Figure 1

(a) Schematic of transparent graphene device geometry and experimental method described in the text. (b) Two-terminal resistance of our device as a function of back-gate voltage $V_g$. The charge neutrality point, corresponding to maximum resistance, is at $V_g=V_{\text{CN}}=3\hspace{0.17em}\hspace{0.17em}\mathrm{V}$. Voltage ranges of positive and negative photoconductivity ($\mathrm{\Delta }{\sigma }_{\tau ,1}$) observed in our experiment are separated by dashed vertical lines.

Figure 2

(a) Measured terahertz electric field waveform transmitted through the sample in equilibrium (black line) and pump-induced change in transmitted terahertz electric field (red line) at $\tau =1.5\mathrm{ps}$. Measurements were performed at room temperature in vacuum with the carrier density set near charge neutrality ($V_g=V_{\text{CN}}+2\mathrm{V}$) and incident pump fluence $\mathcal{F}=10\mu \mathrm{J}/{\mathrm{cm}}^2$. (b) Real ($\mathrm{\Delta }{\sigma }_1$, solid line) and imaginary ($\mathrm{\Delta }{\sigma }_2$, dashed line) parts of the transient terahertz PC extracted from the data in (a). (c) Theoretical simulation of the PC spectra under the same conditions as (a),(b) using the Drude model described in the text. (d)–(f) Experimental data and simulation as in (a)–(c), but at gate $\text{voltage}+52\mathrm{V}$ from the charge neutrality point (electron density $n\approx 3\times {10}^{12}{\mathrm{cm}}^{-2}$).

Figure 3

(a) Measured temporal evolution of the negative change in transmitted field (proportional to the differential conductivity), measured at the peak of the signal in Figs. 2 and 2, at different gate voltages. Measurements were performed at room temperature in vacuum with incident fluence $\mathcal{F}=10\mu \mathrm{J}/{\mathrm{cm}}^2$. (b) Theoretical simulation of the terahertz dynamics in (a), calculated using the model described in the text. Inset shows the estimated temperature profile used to model the data. (c) Mean of $-\mathrm{\Delta }E(t=0{)}_{\tau }/E_0(t=0)$ from $\tau =-1$ to 8 ps, as a function of gate voltage. (d) Simulation of the data in (c).

Figure 4

(a) Temperature-dependent Drude weight [Eq. (2)] at different gate voltages. Saturation at low temperature is due to charge disorder. (b) Estimated temperature dependence of the scattering rate at different gate voltages. (c) Calculated change in conductivity $\mathrm{\Delta }{\sigma }_1(T)$ at $\omega /2\pi =1\mathrm{THz}$, for different carrier densities and temperatures, relative to its value at $T=300\mathrm{K}$. Temperature dependence of both the Drude weight and scattering rate were taken into account. (d) Fluence dependence of PC at fixed pump-probe delay $\tau =3.5\mathrm{ps}$ showing the nonmonotonic behavior expected from our model.