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Snapshots of non-equilibrium Dirac carrier distributions in graphene


The optical properties of graphene are made unique by the linear band structure and the vanishing density of states at the Dirac point. It has been proposed that even in the absence of a bandgap, a relaxation bottleneck at the Dirac point may allow for population inversion and lasing at arbitrarily long wavelengths. Furthermore, efficient carrier multiplication by impact ionization has been discussed in the context of light harvesting applications. However, all of these effects are difficult to test quantitatively by measuring the transient optical properties alone, as these only indirectly reflect the energy- and momentum-dependent carrier distributions. Here, we use time- and angle-resolved photoemission spectroscopy with femtosecond extreme-ultraviolet pulses to directly probe the non-equilibrium response of Dirac electrons near the K-point of the Brillouin zone. In lightly hole-doped epitaxial graphene samples, we explore excitation in the mid- and near-infrared, both below and above the minimum photon energy for direct interband transitions. Whereas excitation in the mid-infrared results only in heating of the equilibrium carrier distribution, interband excitations give rise to population inversion, suggesting that terahertz lasing may be possible. However, in neither excitation regime do we find any indication of carrier multiplication, questioning the applicability of graphene for light harvesting.

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Figure 1: Atomic and electronic structure of graphene.
Figure 2: Free-carrier absorption regime versus direct interband transitions.
Figure 3: Metallic response for excitation at ωpump = 300 meV and F = 0.8 mJ cm−2.
Figure 4: Population inversion for excitation at ωpump = 950 meV and F = 4.6 mJ cm−2.
Figure 5: No indication for carrier multiplication.
Figure 6: Competition between impact ionization and Auger heating in graphene.


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We thank M. Eckstein and F. Kärtner for many fruitful discussions and J. Harms for drawing Figs 2a,c and 6. S. Forti, C. Coletti and K. V. Emtsev helped with the static ARPES measurements at the SLS, partially supported by the German Research Foundation (DFG) within the priority programme ‘graphene’ SPP 1459 (Sta 315/8-1). P. Rice, R. Chapman and N. Rodrigues are acknowledged for technical support during the Artemis beam time that was funded by LASERLAB-EUROPE (EC FP7).

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I.G., J.C.P., M.M. and C.C. performed the time-resolved experiments. E.S. managed the laboratory and I.C.E.T. ran the laser system; both I.C.E.T. and E.S. provided technical support during the beam time. A.S., A.K. and U.S. grew and characterized the samples. I.G. analysed the data. I.G. and A.C. interpreted the results and wrote the manuscript.

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Correspondence to Isabella Gierz or Andrea Cavalleri.

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Gierz, I., Petersen, J., Mitrano, M. et al. Snapshots of non-equilibrium Dirac carrier distributions in graphene. Nature Mater 12, 1119–1124 (2013).

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