Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Snapshots of non-equilibrium Dirac carrier distributions in graphene

Nature Materials volume 12, pages 1119–1124 (2013)Cite this article

Subjects

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.

This is a preview of subscription content, access via your institution

Relevant articles

Open Access articles citing this article.

Access options

Rent or buy this article

Prices vary by article type

from$1.95

to$39.95

Learn more

Prices may be subject to local taxes which are calculated during checkout

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 ℏωpump = 300 meV and F = 0.8 mJ cm−2.
Figure 4: Population inversion for excitation at ℏωpump = 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).

Author information

Authors and Affiliations

  1. Max Planck Institute for the Structure and Dynamics of Matter, 22761 Hamburg, Germany

    Isabella Gierz, Jesse C. Petersen, Matteo Mitrano & Andrea Cavalleri

  2. Department of Physics, Clarendon Laboratory, University of Oxford, OX1 3PU Oxford, UK

    Jesse C. Petersen & Andrea Cavalleri

  3. Central Laser Facility, STFC Rutherford Appleton Laboratory, OX11 0QX Harwell, UK

    Cephise Cacho, I. C. Edmond Turcu & Emma Springate

  4. Max Planck Institute for Solid State Research, 70569 Stuttgart, Germany

    Alexander Stöhr, Axel Köhler & Ulrich Starke

Authors
  1. Isabella Gierz
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jesse C. Petersen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Matteo Mitrano
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Cephise Cacho
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. I. C. Edmond Turcu
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Emma Springate
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Alexander Stöhr
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. Axel Köhler
    View author publications

    You can also search for this author in PubMed Google Scholar

  9. Ulrich Starke
    View author publications

    You can also search for this author in PubMed Google Scholar

  10. Andrea Cavalleri
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

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.

Corresponding authors

Correspondence to Isabella Gierz or Andrea Cavalleri.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

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

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nmat3757

This article is cited by

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing