UP1: Ultrafast nanooptics

M. Breusing, C. Ropers

Fig. 1:(a) Idealized electronic bandstructure of graphene showing a linear dispersion. (b) Schematic of temporally evolving electronic occupation probabilities assuming ultrafast thermalization towards zero chemical potential (metal case). (c) The same for persistent carrier densities such as in semiconductors. (d) Solid circles: time dependence of the spectrally integrated transmission change ΔT/T0=(T-T0)/T0 (T, T0: sample transmission with and without excitation). Dash-dotted line: cross correlation of pump and probe pulses. Gray line: numerical fit. Inset: fluence dependence of the transmission change.

The field of carbon-based electronics is of growing interest, due to unique electronic and lattice properties of materials like graphite, graphene and carbon nanotubes. Graphite consists of a stack of quasi-two-dimensional graphene sheets with an electronic bandstructure showing a linear dispersion (see Fig.1a). Up to now, the ultrafast carrier dynamics of this semimetal is not fully understood. Depending on the interband and intraband carrier scattering rates, carrier dynamics in graphite could resemble more that of a metal or that of a semiconductor [Figs. 1 (b) and (c)].
In a recent project, we investigated the dynamics of photoexcited carriers with a density up to 10²⁰ cm^-3 in freestanding 30 nm thin graphite films [BRE]. We applied pump-probe spectroscopy with 7-fs pulses from a mode-locked Ti:sapphire oscillator, offering a bandwidth of 0.7 eV around 1.5 eV. In Fig. 1 (d), the spectrally integrated transmission change ΔT/T₀ is presented, revealing an initial fast decay with a time constant of 13 ± 3 fs and a subsequent slower 100 fs decay. The transmission change is caused by absorption saturation of direct optical transitions with the fast decay due to carrier equilibration and the slower decay due to carrier cooling. Spectrally resolved measurements [BRE] confirm the ultrafast equilibration of electrons and holes.

Fig. 2: Time-dependent carrier temperature (black circles) and chemical potential (grey triangles) derived from transmission spectra

Carrier equilibration establishes Fermi-Dirac statistics of electrons and holes, allowing for an assignment of a chemical potential (µ) and a carrier temperature (T_e) at later delay times. Within the first picoseconds after excitation, only distributions calculated with different quasi-Fermi levels for electrons and holes fit our measurements. Carrier–optical-phonon scattering causes a carrier relaxation with a drop of T_e from above 2500 K to below 1000 K within 100 fs, while the chemical potential rises up to 0.4 eV (see Fig. 2).
To analyse these microscopic scattering processes, we simulated the carrier dynamics by solving the Bloch-Boltzmann-Peierls equations. The simulations confirm our interpretation and indicate that intraband relaxation of electrons and holes is much faster than their interband relaxation/recombination, pointing to a semiconductor-like behaviour with separated quasi-equilibrated distributions of electrons and holes.