Abstract
The transient optical conductivity of freely suspended graphene was examined by femtosecond time-resolved spectroscopy using pump excitation at 400 nm and probe radiation at 800 nm. The optical conductivity (or, equivalently, absorption) changes abruptly upon excitation and subsequently relaxes to its initial value on the time scale of 1 ps. The form of the induced change in the optical conductivity varies strongly with excitation conditions, exhibiting a crossover from enhanced to decreased optical conductivity with increasing pump fluence. We describe the graphene response in terms of transient heating of the electrons, with the characteristic relaxation time of the transient conductivity reflecting the cooling of the electron system and the strongly coupled optical phonons through emission of lower energy phonons. The change in the optical conductivity is attributed to a combination of induced absorption from intra-band transitions of the photo-generated carriers and bleaching of the inter-band transitions by Pauli blocking. The former effect, which corresponds to the high-frequency wing of the Drude response, dominates at low pump fluence. In this regime of a limited rise in the electron temperature, an increase in the optical conductivity is observed. At high pump fluence, elevated electron temperatures are achieved. The decrease in the inter-band bleaching then dominates the transient response, the intra-band contribution being overwhelmed despite an increase in the Drude scattering rate with temperature. The temporal evolution of the optical conductivity in all the regimes can be described within a model including the intra- and inter-band contributions with a time-varying electronic temperature. An increased Drude scattering rate is inferred for high electron temperature and mechanisms for this enhancement are considered. The calculated scattering rate for interactions of the carriers with zone-center and zone-edge optical phonons agrees well with the rates obtained from experiment.
Highlights
To date all ultrafast pump-probe measurements of graphene have observed an induced bleaching of the absorption under optical excitation [7-9]. This behavior arises from Pauli blocking of the strong inter-band optical transitions [7-9] and is expected for electronic temperatures sufficiently high to induced filling of the states
We report observation of a dominant intra-band contribution to the transient optical response, with a corresponding enhanced absorption. We identify this effect through probing freely suspended graphene samples at relatively low pump fluence
The transient optical response exhibits a crossover from enhanced absorption to bleaching as Pauli blocking of inter-band transitions becomes more prominent
Summary
1) Determination of the electronic temperature Here we describe the model employed for the heat capacity of the strongly coupled optical phonons. Eq (E1) by comparison with a previous experiment in which transient phonon temperatures for femtosecond laser excitation of graphite were determined by timeresolved Raman scattering [A5, A6] Fitting these earlier measurements to a polynomial yields the following relation between the absorbed fluence (or energy density) per graphene layer and the temperature:. To model the temporal evolution of the sub-system of the electronic excitations and the strongly coupled phonons, we assume that the energy relaxes as a rate of 1/τph through the anharmonic decay, with Eq (E1) yielding the variation of the temperature This temperature dynamics is insert in Eq (1) from the main text of the paper to fit our pump-probe dynamics experiment. The two first terms are intra-band scattering processes and the last two are inter-band ones
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