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Snapshots of non-equilibrium Dirac carrier distributions in graphene

Abstract

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.

References

  1. Li, T. et al. Femtosecond population inversion and stimulated emission of dense Dirac fermions in graphene. Phys. Rev. Lett. 108, 167401 (2012).

    Article  CAS  Google Scholar 

  2. Sun, D. et al. Ultrafast relaxation of excited Dirac fermions in epitaxial graphene using optical differential transmission spectroscopy. Phys. Rev. Lett. 101, 157402 (2008).

    Article  Google Scholar 

  3. Breusing, M., Ropers, C. & Elsaesser, T. Ultrafast carrier dynamics in graphite. Phys. Rev. Lett. 102, 086809 (2009).

    Article  Google Scholar 

  4. Breusing, M. et al. Ultrafast nonequilibrium carrier dynamics in a single graphene layer. Phys. Rev. B 83, 153410 (2011).

    Article  Google Scholar 

  5. Kampfrath, T., Perfetti, L., Schapper, F., Frischkorn, C. & Wolf, M. Strongly coupled optical phonons in the ultrafast dynamics of the electronic energy and current relaxation in graphite. Phys. Rev. Lett. 95, 187403 (2005).

    Article  Google Scholar 

  6. Lui, C. H., Mak, K. F., Shan, J. & Heinz, T. F. Ultrafast photoluminescence from graphene. Phys. Rev. Lett. 105, 127404 (2010).

    Article  Google Scholar 

  7. George, P. A. et al. Ultrafast optical-pump terahertz-probe spectroscopy of the carrier relaxation and recombination dynamics in epitaxial graphene. Nano Lett. 8, 4248–4251 (2008).

    Article  CAS  Google Scholar 

  8. Wang, H. et al. Ultrafast relaxation dynamics of hot optical phonons in graphene. Appl. Phys. Lett. 96, 081917 (2010).

    Article  Google Scholar 

  9. Gilbertson, S. et al. Tracing ultrafast separation and coalescence of carrier distributions in graphene with time-resolved photoemission. J. Phys. Chem. Lett. 3, 64–68 (2012).

    Article  CAS  Google Scholar 

  10. Winzer, T., Knorr, A. & Malić, E. Carrier multiplication in graphene. Nano Lett. 10, 4839–4843 (2010).

    Article  CAS  Google Scholar 

  11. Winzer, T. & Malić, E. Impact of Auger processes on carrier dynamics in graphene. Phys. Rev. B 85, 241404(R) (2012).

    Article  Google Scholar 

  12. Riedl, C., Coletti, C., Iwasaki, T., Zakharov, A. A. & Starke, U. Quasi-free-standing epitaxial graphene on SiC obtained by hydrogen intercalation. Phys. Rev. Lett. 103, 246804 (2009).

    Article  CAS  Google Scholar 

  13. Forti, S. et al. Large-area homogeneous quasifree standing epitaxial graphene on SiC(0001): Electronic and structural characterization. Phys. Rev. B 84, 125449 (2011).

    Article  Google Scholar 

  14. Bostwick, A., Ohta, T., Seyller, T., Horn, K. & Rotenberg, E. Quasiparticle dynamics in graphene. Nature Phys. 3, 36–40 (2007).

    Article  CAS  Google Scholar 

  15. Bostwick, A. et al. Observation of plasmarons in quasi-freestanding doped graphene. Science 328, 999–1002 (2010).

    Article  CAS  Google Scholar 

  16. Nair, R. R. et al. Fine structure constant defines visual transparency of graphene. Science 320, 1308 (2008).

    Article  CAS  Google Scholar 

  17. Bao, Q. et al. Atomic-layer graphene as a saturable absorber for ultrafast pulsed lasers. Adv. Funct. Mater. 19, 3077–3083 (2009).

    Article  CAS  Google Scholar 

  18. Sun, Z. et al. Graphene mode-locked ultrafast laser. ACS Nano 4, 803–810 (2010).

    Article  CAS  Google Scholar 

  19. Ryzhii, V., Ryzhii, M. & Otsuji, T. Negative dynamic conductivity of graphene with optical pumping. J. Appl. Phys. 101, 083114 (2007).

    Article  Google Scholar 

  20. Winzer, T., Malić, E. & Knorr, A. Microscopic mechanism for transient population inversion and optical gain in graphene. Preprint at http://arxiv.org/abs/1209.4833v1 (2012).

  21. Bonaccorso, F., Sun, Z., Hasan, T. & Ferrari, A. C. Graphene photonics and optoelectronics. Nature Photon. 4, 611–622 (2010).

    Article  CAS  Google Scholar 

  22. Gabor, N. M. et al. Hot carrier-assisted intrinsic photoresponse in graphene. Science 334, 648–652 (2011).

    Article  CAS  Google Scholar 

  23. Shirley, E. L., Terminello, L. J., Santoni, A. & Himpsel, F. J. Brillouin-zone-selection effects in graphite photoelectron angular distributions. Phys. Rev. B 51, 13614 (1995).

    Article  CAS  Google Scholar 

  24. Mathias, S. et al. Angle-resolved photoemission spectroscopy with a femtosecond high harmonic light source using a two-dimensional imaging electron analyzer. Rev. Sci. Instrum. 78, 083105 (2007).

    Article  CAS  Google Scholar 

  25. Rohwer, T. et al. Collapse of long-range charge order tracked by time-resolved photoemission at high momenta. Nature 471, 490–493 (2011).

    Article  CAS  Google Scholar 

  26. Petersen, J. C. et al. Clocking the melting transition of charge and lattice order in 1T-TaS2 with ultrafast extreme- ultraviolet angle-resolved photoemission spectroscopy. Phys. Rev. Lett. 107, 177402 (2011).

    Article  CAS  Google Scholar 

  27. Frassetto, F. et al. Single-grating monochromator for extreme-ultraviolet ultrashort pulses. Opt. Express 19, 19169–19181 (2011).

    Article  CAS  Google Scholar 

  28. Ashcroft, N. W. & Mermin, N. D. Solid State Physics (Thomson Learning, 1976).

    Google Scholar 

  29. Butscher, S., Milde, F., Hirtschulz, M., Malić, E. & Knorr, A. Hot electron relaxation and phonon dynamics in graphene. Appl. Phys. Lett. 91, 203103 (2007).

    Article  Google Scholar 

  30. Bonini, N., Lazzeri, M., Marzari, N. & Mauri, F. Phonon anharmonicities in graphite and graphene. Phys. Rev. Lett. 99, 176802 (2007).

    Article  Google Scholar 

  31. Yan, H. et al. Time-resolved Raman spectroscopy of optical phonons in graphite: Phonon anharmonic coupling and anomalous stiffening. Phys. Rev. B 80, 121403(R) (2009).

    Article  Google Scholar 

  32. Kang, K., Abdula, D., Cahill, D. G. & Shim, M. Lifetimes of optical phonons in graphene and graphite by time-resolved incoherent anti-Stokes Raman scattering. Phys. Rev. B 81, 165405 (2010).

    Article  Google Scholar 

  33. Sun, D. et al. Ultrafast relaxation of excited Dirac fermions in epitaxial graphene using optical differential transmission spectroscopy. Phys. Rev. Lett. 104, 136802 (2010).

    Article  Google Scholar 

  34. Song, J. C. W., Reizer, M. Y. & Levitov, L. S. Disorder-assisted electron-phonon scattering and cooling pathways in graphene. Phys. Rev. Lett. 109, 106602 (2012).

    Article  Google Scholar 

  35. Graham, M. W., Shi, S-F., Ralph, D. C., Park, J. & McEuen, P, L. Photocurrent measurements of supercollision cooling in graphene. Nature Phys. 9, 103–108 (2013).

    Article  CAS  Google Scholar 

  36. Cavalieri, A. L. et al. Attosecond spectroscopy in condensed matter. Nature 449, 1029–1032 (2007).

    Article  CAS  Google Scholar 

  37. Johannsen, J. C. et al. Direct view of hot carrier dynamics in graphene. Phys. Rev. Lett. 111, 027403 (2013).

    Article  Google Scholar 

Download references

Acknowledgements

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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The authors declare no competing financial interests.

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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). https://doi.org/10.1038/nmat3757

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