# Carrier dynamics in Landau-quantized graphene featuring strong Auger scattering

## Abstract

The energy spectrum of common two-dimensional electron gases consists of a harmonic (that is, equidistant) ladder of Landau levels, thus preventing the possibility of optically addressing individual transitions. In graphene, however, owing to its non-harmonic spectrum, individual levels can be addressed selectively. Here, we report a time-resolved experiment directly pumping discrete Landau levels in graphene. Energetically degenerate Landau-level transitions from n = −1 to n = 0 and from n = 0 to n = 1 are distinguished by applying circularly polarized THz light. An analysis based on a microscopic theory shows that the zeroth Landau level is actually depleted by strong Auger scattering, even though it is optically pumped at the same time. The surprisingly strong electron–electron interaction responsible for this effect is directly evidenced through a sign reversal of the pump–probe signal.

## Access options

Rent or Buy article

from\$8.99

All prices are NET prices.

## References

1. 1

Drexler, C. et al. Magnetic quantum ratchet effect in graphene. Nature Nanotech. 8, 104–107 (2013).

2. 2

Ponomarenko, L. A. et al. Cloning of Dirac fermions in graphene superlattices. Nature 497, 594–597 (2013).

3. 3

Dean, C. R. et al. Hofstadter’s butterfly and the fractal quantum Hall effect in moire superlattices. Nature 497, 598–602 (2013).

4. 4

Hunt, B. et al. Massive Dirac fermions and Hofstadter butterfly in a van der Waals heterostructure. Science 340, 1427–1430 (2013).

5. 5

Bolotin, K. I., Ghahari, F., Shulman, M. D., Stormer, H. L. & Kim, P. Observation of the fractional quantum Hall effect in graphene. Nature 462, 196–199 (2009).

6. 6

Du, X., Skachko, I., Duerr, F., Luican, A. & Andrei, E. Y. Fractional quantum Hall effect and insulating phase of Dirac electrons in graphene. Nature 462, 192–195 (2009).

7. 7

Novoselov, K. S. et al. Two-dimensional gas of massless Dirac fermions in graphene. Nature 438, 197–200 (2005).

8. 8

Zhang, Y., Tan, J. W., Stormer, H. L. & Kim, P. Experimental observation of the quantum Hall effect and Berry’s phase in graphene. Nature 438, 201–204 (2005).

9. 9

Sadowski, M. L., Martinez, G., Potemski, M., Berger, C. & deHeer, W. A. Landau level spectroscopy of ultrathin graphene layers. Phys. Rev. Lett. 97, 266405 (2006).

10. 10

Plochocka, P. et al. High energy limit of massless Dirac fermions in multilayer graphene using magneto-optical transmission spectroscopy. Phys. Rev. Lett. 100, 087401 (2008).

11. 11

Orlita, M. et al. Approaching the Dirac point in high-mobility multilayer epitaxial graphene. Phys. Rev. Lett. 101, 267601 (2008).

12. 12

Neugebauer, P., Orlita, M., Faugeras, C., Barra, A-L. & Potemski, M. How perfect can graphene be? Phys. Rev. Lett. 103, 136403 (2009).

13. 13

Crassee, I. et al. Giant Faraday rotation in single- and multilayer graphene. Nature Phys. 7, 48–51 (2011).

14. 14

Kawano, Y. Wide-band frequency tunable terahertz and infrared detection with graphene. Nanotechnology 24, 21404 (2013).

15. 15

Dawlaty, J. M., Shivaraman, S., Chandrashekhar, M., Rana, F. & Spencer, M. G. Measurement of ultrafast carrier dynamics in epitaxial graphene. Appl. Phys. Lett. 92, 042116 (2008).

16. 16

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

17. 17

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

18. 18

Winnerl, S. et al. Carrier relaxation in epitaxial graphene photoexcited near the Dirac point. Phys. Rev. Lett. 107, 237401 (2011).

19. 19

Brida, D. et al. Ultrafast collinear scattering and carrier multiplication in graphene. Nature Commun. 4, 1987 (2013).

20. 20

Tielrooij, K. J. et al. Photoexcitation cascade and multiple hot-carrier generation in graphene. Nature Phys. 9, 248–252 (2013).

21. 21

Plochocka, P. et al. Slowing hot-carrier relaxation in graphene using a magnetic field. Phys. Rev. B 80, 245415 (2009).

22. 22

Foster, M. S. & Aleiner, I. L. Slow imbalance relaxation and thermoelectric transport in graphene. Quasiclassical cyclotron resonance of Dirac fermions in highly doped graphene. Phys. Rev. B 79, 085415 (2010).

23. 23

Otsuji, T. et al. Graphene-based devices in terahertz science and technology. J. Phys. D 45, 303001 (2012).

24. 24

Rana, F. Electron–hole generation and recombination rates for Coulomb scattering in graphene. Phys. Rev. B 76, 155431 (2007).

25. 25

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

26. 26

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

27. 27

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

28. 28

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

29. 29

Berger, C. et al. Electronic confinement and coherence in patterned epitaxial graphene. Science 312, 1191–1196 (2006).

30. 30

Ferrari, A. C. et al. Raman spectrum of graphene and graphene layers. Phys. Rev. Lett. 97, 187401 (2006).

31. 31

Sun, D. et al. Spectroscopic measurement of interlayer screening in multilayer epitaxial graphene. Phys. Rev. Lett. 104, 136802 (2010).

32. 32

Winnerl, S. et al. Time-resolved spectroscopy on epitaxial graphene in the infrared spectral range: Relaxation dynamics and saturation behaviour. J. Phys. Condens. Matter 25, 054202 (2013).

33. 33

Witowski, A. M. et al. Quasiclassical cyclotron resonance of Dirac fermions in highly doped graphene. Phys. Rev. B 82, 165305 (2010).

34. 34

Orlita, M. et al. Classical to quantum crossover of the cyclotron resonance in graphene: A study of the strength of intraband absorption. New J. Phys. 14, 095008 (2012).

35. 35

Wang, Z-W. et al. The temperature dependence of optical phonon scattering in graphene under strong magnetic field. J. Phys. Soc. Jpn 82, 094606 (2013).

36. 36

Wendler, F., Knorr, A. & Malic, E. Resonant carrier-phonon scattering in graphene under Landau quantization. Appl. Phys. Lett. 103, 253117 (2013).

37. 37

Goerbig, M. O. Electronic properties of graphene in a strong magnetic field. Rev. Mod. Phys. 83, 1193–1243 (2011).

38. 38

Haug, H. & Koch, S. W. Quantum Theory of the Optical and Electronic Properties of Semiconductors (World Scientific, 2009).

39. 39

Malic, E. & Knorr, A. Graphene and Carbon Nanotubes – Ultrafast Relaxation Dynamics and Optics (Wiley-VCH, 2013).

40. 40

Malic, E., Winzer, T., Bobkin, E. & Knorr, A. Microscopic theory of absorption and ultrafast many-particle kinetics in graphene. Phys. Rev. B 84, 205406 (2011).

41. 41

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).

42. 42

Betz, A. C. et al. Supercollision cooling in undoped graphene. Nature Phys. 9, 109–112 (2013).

43. 43

Roldán, R., Goerbig, M. O. & Fuchs, J-N. The magnetic field particle-hole excitation spectrum in doped graphene and in a standard two-dimensional electron gas. Semicond. Sci. Technol. 25, 034005 (2010).

44. 44

Ando, T. & Uemura, Y. Theory of quantum transport in a two-dimensional electron system under magnetic fields. I. Characteristics of level broadening and transport under strong fields. J. Phys. Soc. Jpn 36, 959–967 (1974).

45. 45

Sprinkle, M. et al. First direct observation of a nearly ideal graphene band structure. Phys. Rev. Lett. 103, 226803 (2009).

## Acknowledgements

Support from the German Science Foundation DFG in the framework of the Priority Program 1459 Graphene is acknowledged. E.M. and F.W. are grateful to the Einstein Foundation Berlin. The research at the free-electron laser FELBE was supported by the European Community’s Seventh Framework Programme (FP7/2007–2013) under Grant agreement No. 226716. Part of this work has been supported by the ERC-2012-AdG-320590 MOMB project as well as the EC Graphene Flagship. We are grateful to P. Michel and the FELBE team for their dedicated support. The Grenoble group acknowledges fruitful discussions with D. M. Basko.

## Author information

Authors

### Contributions

S.W., M.M., M.H., M.O. and M.P. conceived the experiments; M.M. performed the experiments, partly together with M.O. and S.W.; M.M., S.W., H.S. and M.H. analysed and interpreted the data; F.W., E.M. and A.K. developed the microscopic theoretical model. M.O. and M.P. originated the considerations for critical level occupation described in the Supplementary Methods. C.B. and W.A.d.H. prepared the samples; S.W. and E.M. wrote the paper with major input and edits from M.H. All authors discussed the results and commented on the manuscript.

### Corresponding authors

Correspondence to Martin Mittendorff or Stephan Winnerl.

## Ethics declarations

### Competing interests

The authors declare no competing financial interests.

## Supplementary information

### Supplementary Information

Supplementary Information (PDF 636 kb)

## Rights and permissions

Reprints and Permissions

Mittendorff, M., Wendler, F., Malic, E. et al. Carrier dynamics in Landau-quantized graphene featuring strong Auger scattering. Nature Phys 11, 75–81 (2015). https://doi.org/10.1038/nphys3164

• Accepted:

• Published:

• Issue Date:

• ### Transient lensing from a photoemitted electron gas imaged by ultrafast electron microscopy

• Omid Zandi
• , Allan E. Sykes
• , Ryan D. Cornelius
• , Francis M. Alcorn
• , Brandon S. Zerbe
• , Phillip M. Duxbury
• , Bryan W. Reed
•  & Renske M. van der Veen

Nature Communications (2020)

• ### Impact Ionization Induced by Terahertz Radiation in HgTe Quantum Wells of Critical Thickness

• S. Hubmann
• , G.V. Budkin
• , M. Urban
• , V.V. Bel’kov
• , A.P. Dmitriev
• , J. Ziegler
• , D.A. Kozlov
• , N.N. Mikhailov
• , S.A. Dvoretsky
• , Z.D. Kvon
• , D. Weiss
•  & S.D. Ganichev

Journal of Infrared, Millimeter, and Terahertz Waves (2020)

• ### Terahertz Nonlinear Optics of Graphene: From Saturable Absorption to High‐Harmonics Generation

• Hassan A. Hafez
• , Sergey Kovalev
• , Klaas‐Jan Tielrooij
• , Mischa Bonn
• , Michael Gensch
•  & Dmitry Turchinovich

Advanced Optical Materials (2020)

• ### Ultrasensitive Photoresponse of Graphene Quantum Dots in the Coulomb Blockade Regime to THz Radiation

• Elisa Riccardi
• , Sylvain Massabeau
• , Federico Valmorra
• , Simon Messelot
• , Michael Rosticher
• , Jérôme Tignon
• , Kenji Watanabe
• , Takashi Taniguchi
• , Matthieu Delbecq
• , Sukhdeep Dhillon
• , Robson Ferreira
• , Sébastien Balibar
• , Takis Kontos
•  & Juliette Mangeney

Nano Letters (2020)

• ### Terahertz Photoconductivity in Graphene in a Magnetic Field

• Yu. B. Vasiliev
• , S. N. Novikov
• , S. N. Danilov
•  & S. D. Ganichev

Semiconductors (2020)