Direct View of Hot Carrier Dynamics in Graphene

The ultrafast dynamics of excited carriers in graphene is closely linked to the Dirac spectrum and plays a central role for many electronic and optoelectronic applications. Harvesting energy from excited electron-hole pairs, for instance, is only possible if these pairs can be separated before they lose energy to vibrations, merely heating the lattice. Until now, the hot carrier dynamics in graphene could only be accessed indirectly. Here, we present a dynamical view on the Dirac cone by time- and angle-resolved photoemission spectroscopy. This allows us to show the quasi-instant thermalization of the electron gas to a temperature of $\approx 2000\mathrm{K}$, to determine the time-resolved carrier density, and to disentangle the subsequent decay into excitations of optical phonons and acoustic phonons (directly and via supercollisions).

Figure 1

(a) Dirac spectrum of graphene with an optical excitation $h{\nu }_{\mathrm{PP}}$ and a probe $h{\nu }_{\mathrm{PB}}$. Following the excitation, electrons (black spheres) thermalize via impact scattering (curved magenta arrows) or Auger recombination (curved black arrows). Decay into holes (orange spheres) in the valence band can be mediated by emission of optical phonons (wiggled red line) with energy $h{\nu }_{\mathrm{OP}}$ or supercollisions involving acoustic phonons (wiggled green line) with energy $h{\nu }_{\mathrm{SC}}$, recoiling on impurities (dashed green line). (b) Photoemission intensity around the Dirac cone for a negative time delay (before the pump pulse). (c) Equilibrium high-resolution spectrum from the same sample taken with synchrotron radiation. Inset: Brillouin zone with measurement direction (dashed red line). (d)–(f) Spectra taken at different time delays. (g)–(i) Corresponding difference spectra, i.e., change with respect to the spectrum before the pump pulse.

Figure 2

(a) Spectrum from Fig. 1d shown as momentum distribution cuts (only a subset is shown) and fits of the individual cuts by Lorentzians to determine intensity and position. (b) Intensity obtained in this way plotted as a function of energy and time delay. (c) Fitted MDC peak positions at two time delays. (d)–(i) Cuts through the data in (b) with fits by Fermi-Dirac distributions convoluted with a Gaussian to account for the energy resolution. (j) Fitted distributions at selected time delays.

Figure 3

(a) Electronic temperature $T_e(t)$ as a function of time delay (markers). Fitting the data to the three temperature model provides an electronic temperature fit with (solid black line) and without (dashed amber line) the supercollision (SC) term. From the fit, we also obtain the temperatures of the optical phonons (solid blue line) and the acoustic phonons (solid red line). (b) Photoinduced carrier density $n_I$ and carrier multiplication calculated from the fitted electronic temperature.