Ultrafast Carrier Dynamics in Graphene under a High Electric Field

We investigated ultrafast carrier dynamics in graphene with near-infrared transient absorption measurement after intense half-cycle terahertz pulse excitation. The terahertz electric field efficiently drives the carriers, inducing large transparency in the near-infrared region. Theoretical calculations using the Boltzmann transport equation quantitatively reproduce the experimental findings. This good agreement suggests that the intense terahertz field should promote a remarkable impact ionization process and increase the carrier density.

Figure 1

(a) Schematic figure of THz-pump NIR-transient absorption measurement in a Dirac cone. (b) Experimental setup. An 800 nm laser pulse was frequency doubled using $\beta$-barium borate crystal. The relative phase between fundamental and SHG pulses was tuned using an $\alpha$-barium borate crystal and a time plate to maximize the overlap of the two pulses at the focus position. A generated THz pulse was focused on the sample, which was replaced with a thin GaP crystal when measuring the THz electric field. (c) Incident THz electric field and its spectrum. (d) THz induced normalized differential optical density of graphene at 800 nm as a function of delay time.

Figure 2

THz induced normalized differential optical density as a function of time delay with peak electric fields of (a) $170\mathrm{kV}/\mathrm{cm}$ and (b) $300\mathrm{kV}/\mathrm{cm}$: experiment (circle) and simulation (solid line). The relaxation time $\tau$ is obtained by a single exponential fit (dashed line). (c), (d) Calculated carrier density as a function of time delay. Dashed lines represent initial carrier density. (e) THz induced transparency of graphene as a function of a peak electric field: experiment (filled circle) and simulations (solid and dashed lines). Experimental results follow a power law with exponent 2.5 (dotted line).

Figure 3

(a)–(e) Distribution function of holes in $\mathit{k}$ space with various time delays. Dashed circles represent momenta corresponding to the energy of 800 nm transition. (f)–(j) Angle-resolved energy distribution of holes. Fermi-Dirac fitting is represented as a dashed line. Vertical arrows indicate the energy of 800 nm transition. ($\mathit{k}$), (l) Carrier scattering processes included in the calculation: carrier-carrier scattering (CC), optical phonon scattering (op), impact ionization (II) and Auger recombination (AR).