Evolution of hot carrier dynamics in graphene with the Fermi level tuned across the Dirac point

The ultrafast dynamics of photoexcited carriers closely depends on the excitation processes pertaining to the energy band of the materials and the relevant relaxation pathway relies on the interactions between hot carriers and lattice phonons. By using ultrafast optical-pump terahertz (THz)-probe spectroscopy with an ion-gel gate to tune the Fermi energy level $E_F$ in graphene, we are able to reveal the relaxation dynamics of hot carriers at different $E_F$. It is found that the relaxation time increases while the pump-induced differential transmission decreases as $E_F$ approaches the Dirac point. Through self-consistent model calculations, we quantitatively interpret that a temperature-dependent scattering rate is responsible for a negative photoinduced conductivity, and the relaxation transient directly manifests the Dirac spectrum dependence of the optical phonon emission and the carrier scattering rate. More interestingly, the scattering rate of hot carriers also exhibits a strong $E_F$ dependence, which is the most likely to originate from charged impurities inevitably present in graphene. The diminution of photoresponse efficiency across the Dirac point implies that the graphene-based optoelectronic devices may be operable only in the highly doped regime.

Figure 1

Device configuration and characteristics. (a) Schematic diagram of the device, which is coated with a THz transparent solid polymer electrolytes to tune its Fermi level. (b) Resistance as a function of applied gate voltage $V_G$. The dashed line marks the charge neutral point at which the value of the applied gate voltage $V_{CN}$ is approximately 0.24 V and resistance is at a maximum.

Figure 2

(a) Pump-induced differential transmission signal for the bare substrate with an ion gel. (b) Measured transmission of THz electric-field waveforms through the graphene sample (black) and bare substrate with an ion-gels (red) for $V_G-V_{CN}=0.9V$. (c) Complex conductivity of graphene, extracted from the relative transmission. The conductivity is normalized by the quantum conductance of $G_0=2e^2/h$. (d) The differential complex optical conductivity with turning on and off pump excitation in frequency domain, taken at $V_G-V_{CN}=1.5V$ and with 1 ps delay after photoexcitation.

Figure 3

Selected traces of PIDT with different $V_G-V_{CN}$ under low pump fluence $\mathcal{F}\sim 11.3\mu {\mathrm{J}/\mathrm{cm}}^2$ and high $\mathcal{F}\sim 101\mu {\mathrm{J}/\mathrm{cm}}^2$. The graphene sample is driven into (a) an electron-doped regime with low $\mathcal{F}$, (b) a hole-doped regime with low $\mathcal{F}$, (c) an electron-doped regime with high $\mathcal{F}$, and (d) a hole-doped regime with high $\mathcal{F}$. The red lines are analytic fits to the data using an exponential function with a relaxation time constant ${\tau }_d$.

Figure 4

PIDT data analysis and illustration of the relevant relaxation processes. (a) Relaxation time ${\tau }_d$, extracted from the red curves displayed in Fig. 3, as a function of $V_G-V_{CN}$ under different pump fluences $\mathcal{F}$. (b) A schematic diagram to illustrate the relaxation process of photoexcited carriers involving intravalley intraband and intravalley interband phonon scatterings. (c) Representative example to demonstrate that a PIDT signal (black squares) can be fit by our model (blue dashed curve). For comparison, the red curve is fit by monotonic exponential decay. PIDT data were taken at $V_G-V_{CN}=-0.8V$ and $\mathcal{F}=101\mu {\mathrm{J}/\mathrm{cm}}^2$.

Figure 5

The Fermi level dependence of the relaxation dynamics related quantities. (a) Extracted initial carrier temperature $T_e\left(0\right)$ as a function of $E_F$ at $\mathcal{F}=101\mu {\mathrm{J}/\mathrm{cm}}^2$ and $11.3\mu {\mathrm{J}/\mathrm{cm}}^2$. (b) $\beta$ as a function of $E_F$ extracted from $\gamma$. The shaded area indicates the transition regime $\sim \pm 91\mathrm{meV}$. (c) $T_e$ and phonon temperatures at $\Gamma$ and K points as a function of delay time with $V_G-V_{CN}=-0.2V$. The blue curve is fit by an exponential decay. (d) Extracted decay time ${\tau }_T$ of $T_e$ as a function of $E_F$.

Figure 6

Conductivity as a function of $n$. The red dotted line is the theoretical fitting by Eq. (7) for $n>n^{*}$. Here $n^{*}\sim 1.9\times {10}^{12}{\mathrm{cm}}^{-2}$ and $\sigma \sim 0.06(1/k\Omega )$ at CNP.