The nature of localization in graphene under quantum Hall conditions

Nature Physics

Volumn 5, Issue 9, 2009, Pages 669-674

  Martin, J ^a,b   Akerman, N ^b   Ulbricht, G ^c   Lohmann, T ^c   Von Klitzing, K ^c   Smet, J H ^c   Yacoby, A ^a,b  

^a HARVARD UNIVERSITY   (United States)

^b WEIZMANN INSTITUTE OF SCIENCE   (Israel)

^c MAX PLANCK INSTITUT FÜR FESTKÖRPERFORSCHUNG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

COULOMB INTERACTIONS; ELECTRONIC DENSITY OF STATES; GALLIUM ARSENIDE; GRAPHENE TRANSISTORS; III-V SEMICONDUCTORS; QUANTUM HALL EFFECT; QUANTUM THEORY; SEMICONDUCTING GALLIUM; SEMICONDUCTING GALLIUM ARSENIDE; SINGLE ELECTRON TRANSISTORS;

HIGH MOBILITY; LOCALIZED STATE; ORDERS OF MAGNITUDE; PARTICLE LOCALIZATIONS; QUANTUM HALL REGIME; SEMICONDUCTOR HETEROSTRUCTURES; STRONG DISORDERS; TWO-DIMENSIONAL ELECTRON SYSTEM;

GRAPHENE;

EID: 70249095897     PISSN: 17452473     EISSN: 17452481     Source Type: Journal    
DOI: 10.1038/nphys1344     Document Type: Article

References (36)

1. Prange, R. E. & Girvin, S. M. (eds) The Quantum Hall Effect (Springer, 1987).
2. Novoselov, K. S. et al. Two-dimensional gas of massless Dirac fermions in graphene. Nature 438, 197-200 (2005).
3. Zhang, Y., Tan, Y.-W., Stormer, H. L. & Kim, P. Experimental observation of the quantum Hall effect and Berry?s phase in graphene. Nature 438, 201-204 (2005).
4. Ostrovsky, P. M., Gornyi, I. V. & Mirlin, A. D. Theory of anomalous quantum Hall effects in graphene. Phys. Rev. B 77, 195430 (2008).
5. Huckestein, B. Scaling theory of the integer quantum Hall effect. Rev. Mod. Phys. 67, 357-396 (1995).
6. Castro Neto, A. H., Guinea, F., Peres, N. M. R., Novoselov, K. S. & Geim, A. K. The electronic properties of graphene. Rev. Mod. Phys. 79, 109-162 (2009).
7. Ilani, S. et al. The macroscopic nature of localization in the quantum Hall effect. Nature 427, 328-332 (2004).
8. Efros, A. L. Non-linear screening and the background density of 2DEG states in magnetic field. Solid State Commun. 67, 1019-1022 (1988).
9. Fogler, M. M., Novikov, D. S. & Shklovskii, B. I. Screening of hypercritical charge in graphene. Phys. Rev. B 76, 233402 (2007).
10. Fogler, M. M. Neutrality point of graphene with coplanar charged impurities. Preprint at
11. Struck, A. & Kramer, B. Electron correlations and single particle physics in the integer quantum Hall effect. Phys. Rev. Lett. 97, 106801 (2006).
12. Jain, J. K. Composite Fermions (Cambridge Univ. Press, 2007).
13. Nomura, K. & MacDonald, A. H. Quantum Hall ferromagnetism in graphene. Phys. Rev. Lett. 96, 256602 (2006).
14. Alicea, J. & Fisher, M. P. Interplay between lattice-scale physics and the quantum Hall effect in graphene. Solid State Commun. 143, 504-509 (2007).
15. Checkelsky, J. G., Li, L. & Ong, N. P. Divergent resistance at the Dirac point in graphene: Evidence for a transition in high magnetic field. Phys. Rev. B 79, 115434 (2009).
16. Sheng, L., Sheng, D. N., Haldane, F. D. M. & Balents, L. Odd-integer quantum Hall effect in graphene: Interaction and disorder effects. Phys. Rev. Lett. 99, 196802 (2007).
17. Pereira, A. L. C. & Schulz, P. A. Valley polarization effects on localization in graphene Landau levels. Phys. Rev. B 77, 075416 (2008).
18. Geim, A. K. & Novoselov, K. S. The rise of graphene. Nature Mater. 6, 183-191 (2007).
19. Tan, Y.-W. et al. Measurement of scattering rate and minimum conductivity in graphene. Phys. Rev. Lett. 99, 246803 (2007).
20. Chen, J.-H. et al. Charged impurity scattering in graphene. Nature Phys. 4, 377-381 (2008).
21. Du, X., Skacho, I., Barker, A. & Andrei, E. Y. Approaching ballistic transport in suspended graphene. Nature Nanotech. 3, 491-495 (2008).
22. Bolotin, K. I. et al. Ultrahigh mobility in suspended graphene. Solid State Commun. 146, 351-355 (2008).
23. Novoselov, K. S. et al. Electric field effect in atomically thin carbon films. Science 306, 666-669 (2004).
24. Novoselov, K. S. et al. Two-dimensional atomic crystals. Proc. Natl Acad. Sci. USA 102, 10451-10453 (2005).
25. Schedin, F. et al. Detection of individual gas molecules adsorbed on graphene. Nature Mater. 6, 652-655 (2007).
26. Yoo, M. J. et al. Scanning single-electron transistor microscopy: Imaging individual charges. Science 276, 579-582 (1997).
27. Yacoby, A., Hess, H. F., Fulton, T. A., Pfeiffer, L. N. & West, K. W. Electrical imaging of the quantum Hall state. Solid State Commun. 111, 1-13 (1999).
28. Zhu, W., Shi, Q. W., Wang, X. R., Chen, J. & Hou, J. G. The shape of disorder broadened Landau subbands in graphene. Phys. Rev. Lett. 102, 056803 (2009).
29. Li, G., Luican, A. & Andrei, E. Y. Scanning tunneling spectroscopy of graphene on graphite. Phys. Rev. Lett. 102, 176804 (2009).
30. Brandt, N. B., Chudinov, S. M. & Ponomarev, Y. G. Semimetals 1, Graphite and its Compounds (North-Holland, 1988).
31. Martin, J. et al. Observation of electron-hole puddles in graphene using a scanning single electron transistor. Nature Phys. 4, 144-148 (2008).
32. Barlas, Y., Pereg-Barnea, T., Polini, M., Asgari, R. & MacDonald, A. H. Chirality and correlations in graphene. Phys. Rev. Lett. 98, 236601-236604 (2007).
33. Hu, B. Y.-K., Hwang, E. H. & Das Sarma, S. Density of states of disordered graphene. Phys. Rev. B 78, 165411 (2008).
34. Adam, S., Hwang,E. H., Galitski,V. M. & Das Sarma, S. Aself-consistent theory for graphene transport. Proc. Natl Acad. Sci. USA 104, 18392-18397 (2007).
35. Zhang, Y., Brar, V. W., Girit, C., Zettl, A. & Crommie, M. F. Origin of spatial charge inhomogeneity in graphene. Preprint at
36. 2 . Phys. Rev. B 79, 205411 (2009).