Ultrafast optical modulation of Dirac electrons in gated single-layer graphene

Fermi level dependence of ultrafast optical responses of single-layer graphene has been investigated using sub-10-fs pump-probe spectroscopy under bias voltages. We observe the ultrafast thermalization of photoexcited carriers, whose dynamics can be modulated via bias-induced change of the Fermi level. The relaxation time and the amplitude of the electronic response are maximized when the Fermi level reaches approximately half of the excitation photon energy. From the analysis of the pump-pulse-induced optical conductivity change, we find that the bias-induced blocking of the relaxation pathways and the pump-induced change of the electronic temperature and the Fermi level significantly contribute to the observed ultrafast optical modulation. The results demonstrate the controllability of the ultrafast optical responses in single-layer graphene, which could be useful for future ultrafast electro-optic graphene devices.

Figure 1

(a) Schematic of the sample structure. Ionic liquid was sandwiched by single-layer graphene on $\mathrm{Si}{\mathrm{O}}_2/\mathrm{Si}$ substrate and an indium tin oxide (ITO) coated glass. The resistance of the graphene under applied gate voltage was measured using a digital multimeter. Pump and probe beams were shone on the graphene through the ionic liquid, and the reflectivity change of the probe pulse was measured. (b) Observed resistivity of graphene under the gate voltage. (c) Typical reflectivity change of the graphene without gate voltage. Inset shows the oscillatory coherent phonon signals after subtracting the electronic responses. (d) Fourier transformed spectrum of the oscillatory components in (c). The iTA, D, G, and 2D (or G′) modes of graphene, as well as some vibrational modes of the ionic liquid are observed, as indicated by arrows.

Figure 2

(a) The reflectivity changes of single-layer graphene with different gate voltages. The dashed lines in (a) represent the single exponential fittings to extract the decay times of the fast component. Fourier transformed spectra of the oscillatory components are shown in (b). The dashed line in (b) is the peak position of the G mode when the Fermi level is at the Dirac point. (c) Schematic of the Fermi level at each bias voltage. Red arrows indicate the incident photon energy of the pump laser pulses resonant to the optical transition.

Figure 3

(a) Gate-voltage dependence of the coherent G-mode phonon frequency. The dashed line shows an approximate linear relation between the applied bias voltage and the G-mode frequency. Note that the slope of these lines is different between negative and positive polarities. The inset shows the relation between the applied gate voltage and the Fermi level. (b) Fermi level dependence of the resistance and frequencies of G and 2D modes. (c) Amplitude and relaxation time for the faster component of the transient reflectivity changes observed at $t=10\mathrm{fs}$ as a function of the Fermi level. The hatched area corresponds to the energy region where twice the Fermi level lies in the energy range of the laser spectrum. The dotted lines are the guides for the eyes.

Figure 4

(a) Transient reflectivity changes of single-layer graphene with different probe wavelengths, 700 nm (1.77 eV), 800 nm (1.55 eV), and 900 nm (1.38 eV), without bias voltage. The probe wavelength was separated by a band-pass filter with a bandwidth of 10 nm. The vertical axis is shifted for clarity. (b) Fermi level dependence of the reflectivity change observed at given probe wavelengths at $t=10\mathrm{fs}$. The lower panel shows the calculated result of $\mathrm{\Delta }\sigma \left(T,{\varepsilon }_{\mathrm{F}}\right)$ described in the main text. Dashed lines correspond to the calculated results with the electronic temperature of 300 K, while the solid lines are those of 600 K.

Figure 5

Fermi level dependence of the reflectivity change observed at given probe wavelengths with longer delay times of 10 fs, 100 fs, and 2 ps.