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Spin and valley quantum Hall ferromagnetism in graphene

Nature Physics volume 8, pages 550–556 (2012)Cite this article

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Abstract

Electronic systems with multiple degenerate degrees of freedom can support a rich variety of broken symmetry states. In a graphene Landau level (LL), strong Coulomb interactions and the fourfold spin–valley degeneracy lead to an approximate SU(4) isospin symmetry. At partial filling, exchange interactions can break this symmetry, manifesting as further Hall plateaus outside the normal integer sequence. Here we report the observation of a number of these quantum Hall isospin ferromagnetic (QHIFM) states, which we classify according to their real spin structure using tilted field magnetotransport. The large activation gaps confirm the Coulomb origin of all the broken symmetry states, but the order depends strongly on LL index. In the high-energy LLs the Zeeman effect is the dominant aligning field, leading to real spin ferromagnets hosting skyrmionic excitations at half filling, whereas in the ‘relativistic’ zero LL lattice scale interactions drive the system to a spin unpolarized state.

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Figure 1: All-integer quantum Hall effect in graphene on hBN.
Figure 2: Activation gaps of half-filled quartet LLs.
Figure 3: Skyrmion transport at ν=−4.
Figure 4: Transport phenomena at quarter filling.
Figure 5: Reentrant QHE in tilted field in the higher LLs.

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References

  1. Geim, A. K. & Novoselov, K. S. The rise of graphene. Nature Mater. 6, 183–191 (2007).

    Article  ADS  Google Scholar 

  2. Ando, T., Fowler, A. B. & Stern, F. Electronic properties of two-dimensional systems. Rev. Mod. Phys. 54, 437–672 (1982).

    Article  ADS  Google Scholar 

  3. Ezawa, Z. F. Quantum Hall Effects: Field Theoretical Approach and Related Topics (World Scientific, 2000).

    Book  Google Scholar 

  4. Shayegan, M. et al. Two-dimensional electrons occupying multiple valleys in alas. Phys. Status Solidi. 243, 3629–3642 (2006).

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

  6. Barlas, Y., Yang, K. & Macdonald, A. Quantum Hall effects in graphene-based two-dimensional electron systems. Nanotechnology 12, 052001 (2012).

    Article  ADS  Google Scholar 

  7. Nomura, K. & MacDonald, A. H. Quantum Hall ferromagnetism in graphene. Phys. Rev. Lett. 96, 256602 (2006).

    Article  ADS  Google Scholar 

  8. Zhang, Y. et al. Landau-level splitting in graphene in high magnetic fields. Phys. Rev. Lett. 96, 136806 (2006).

    Article  ADS  Google Scholar 

  9. Jiang, Z., Zhang, Y., Stormer, H. L. & Kim, P. Quantum Hall states near the charge-neutral Dirac point in graphene. Phys. Rev. Lett. 99, 106802 (2007).

    Article  ADS  Google Scholar 

  10. Checkelsky, J. G., Li, L. & Ong, N. P. Zero-energy state in graphene in a high magnetic field. Phys. Rev. Lett. 100, 206801 (2008).

    Article  ADS  Google Scholar 

  11. 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).

    Article  ADS  Google Scholar 

  12. Dean, C. R. et al. Boron nitride substrates for high-quality graphene electronics. Nature Nanotechnol. 5, 722–726 (2010).

    Article  ADS  Google Scholar 

  13. Dean, C. R. et al. Multicomponent fractional quantum Hall effect in graphene. Nature Phys. 7, 693–696 (2011).

    Article  ADS  Google Scholar 

  14. Yang, K., Das Sarma, S. & MacDonald, A. H. Collective modes and skyrmion excitations in graphene SU(4) quantum Hall ferromagnets. Phys. Rev. B 74, 075423 (2006).

    Article  ADS  Google Scholar 

  15. Alicea, J. & Fisher, M. P. Interplay between lattice-scale physics and the quantum Hall effect in graphene. Solid State Commun. 143, 504–509 (2007).

    Article  ADS  Google Scholar 

  16. Goerbig, M. O., Moessner, R. & Douçot, B. Electron interactions in graphene in a strong magnetic field. Phys. Rev. B 74, 161407 (2006).

    Article  ADS  Google Scholar 

  17. 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).

    Article  ADS  Google Scholar 

  18. Luk’yanchuk, I. A. & Bratkovsky, A. M. Lattice-induced double-valley degeneracy lifting in graphene by a magnetic field. Phys. Rev. Lett. 100, 176404 (2008).

    Article  ADS  Google Scholar 

  19. Abanin, D. A., Parameswaran, S. A., Kivelson, S. A. & Sondhi, S. L. Nematic valley ordering in quantum Hall systems. Phys. Rev. B 82, 035428 (2010).

    Article  ADS  Google Scholar 

  20. Khveshchenko, D. V. Magnetic-field-induced insulating behavior in highly oriented pyrolitic graphite. Phys. Rev. Lett. 87, 206401 (2001).

    Article  ADS  Google Scholar 

  21. Gorbar, E. V., Gusynin, V. P., Miransky, V. A. & Shovkovy, I. A. Magnetic field driven metal-insulator phase transition in planar systems. Phys. Rev. B 66, 045108 (2002).

    Article  ADS  Google Scholar 

  22. Abanin, D. A., Lee, P. A. & Levitov, L. S. Spin-filtered edge states and quantum Hall effect in graphene. Phys. Rev. Lett. 96, 176803 (2006).

    Article  ADS  Google Scholar 

  23. Alicea, J. & Fisher, M. P. A. Graphene integer quantum Hall effect in the ferromagnetic and paramagnetic regimes. Phys. Rev. B 74, 075422 (2006).

    Article  ADS  Google Scholar 

  24. Gusynin, V. P., Miransky, V. A., Sharapov, S. G. & Shovkovy, I. A. Excitonic gap, phase transition, and quantum Hall effect in graphene. Phys. Rev. B 74, 195429 (2006).

    Article  ADS  Google Scholar 

  25. Fertig, H. A. & Brey, L. Luttinger liquid at the edge of undoped graphene in a strong magnetic field. Phys. Rev. Lett. 97, 116805 (2006).

    Article  ADS  Google Scholar 

  26. Fuchs, J-N. & Lederer, P. Spontaneous parity breaking of graphene in the quantum Hall regime. Phys. Rev. Lett. 98, 016803 (2007).

    Article  ADS  Google Scholar 

  27. Herbut, I. F. Theory of integer quantum Hall effect in graphene. Phys. Rev. B 75, 165411 (2007).

    Article  ADS  Google Scholar 

  28. Abanin, D. A. et al. Dissipative quantum Hall effect in graphene near the Dirac point. Phys. Rev. Lett. 98, 196806 (2007).

    Article  ADS  Google Scholar 

  29. Jung, J. & MacDonald, A. H. Theory of the magnetic-field-induced insulator in neutral graphene sheets. Phys. Rev. B 80, 235417 (2009).

    Article  ADS  Google Scholar 

  30. Nomura, K., Ryu, S. & Lee, D-H. Field-induced Kosterlitz–Thouless transition in the N=0 Landau level of graphene. Phys. Rev. Lett. 103, 216801 (2009).

    Article  ADS  Google Scholar 

  31. Shimshoni, E., Fertig, H. A. & Pai, G. V. Onset of an insulating zero-plateau quantum Hall state in graphene. Phys. Rev. Lett. 102, 206408 (2009).

    Article  ADS  Google Scholar 

  32. Das Sarma, S. & Yang, K. The enigma of the ν=0 quantum Hall effect in graphene. Solid State Commun. 149, 1502–1506 (2009).

    Article  ADS  Google Scholar 

  33. Hou, C-Y., Chamon, C. & Mudry, C. Deconfined fractional electric charges in graphene at high magnetic fields. Phys. Rev. B 81, 075427 (2010).

    Article  ADS  Google Scholar 

  34. Kharitonov, M. Phase diagram for the ν=0 quantum Hall state in monolayer graphene. Phys. Rev. B 85, 115439 (2012).

    Article  Google Scholar 

  35. Checkelsky, J. G., Li, L. & Ong, N. P. Divergent resistance at the Dirac point in graphene: Evidence for a transition in a high magnetic field. Phys. Rev. B 79, 115434 (2009).

    Article  ADS  Google Scholar 

  36. Zhang, L. et al. Breakdown of the N=0 quantum Hall state in graphene: Two insulating regimes. Phys. Rev. B 80, 241412 (2009).

    Article  ADS  Google Scholar 

  37. 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).

    Article  ADS  Google Scholar 

  38. Zhang, L., Zhang, Y., Khodas, M., Valla, T. & Zaliznyak, I. A. Metal to insulator transition on the N=0 Landau level in graphene. Phys. Rev. Lett. 105, 046804 (2010).

    Article  ADS  Google Scholar 

  39. Abanin, D. A., Lee, P. A. & Levitov, L. S. Randomness-induced xy ordering in a graphene quantum Hall ferromagnet. Phys. Rev. Lett. 98, 156801 (2007).

    Article  ADS  Google Scholar 

  40. Aleiner, I. L., Kharzeev, D. E. & Tsvelik, A. M. Spontaneous symmetry breaking in graphene subjected to an in-plane magnetic field. Phys. Rev. B 76, 195415 (2007).

    Article  ADS  Google Scholar 

  41. König, M. et al. Quantum spin Hall insulator state in HgTe quantum wells. Science 318, 766–770 (2007).

    Article  ADS  Google Scholar 

  42. Nicholas, R. J., Haug, R. J., Klitzing, K. v. & Weimann, G. Exchange enhancement of the spin splitting in a GaAs–GaxAl1−xAs heterojunction. Phys. Rev. B 37, 1294–1302 (1988).

    Article  ADS  Google Scholar 

  43. Sondhi, S. L., Karlhede, A., Kivelson, S. A. & Rezayi, E. H. Skyrmions and the crossover from the integer to fractional quantum Hall effect at small Zeeman energies. Phys. Rev. B 47, 16419 (1993).

    Article  ADS  Google Scholar 

  44. Fertig, H. A., Brey, L., Cote, R. & MacDonald, A. H. Charged spin-texture excitations and the Hartree–Fock approximation in the quantum Hall effect. Phys. Rev. B 50, 11018–11021 (1994).

    Article  ADS  Google Scholar 

  45. Schmeller, A., Eisenstein, J. P., Pfeiffer, L. N. & West, K. W. Evidence for Skyrmions and single spin flips in the integer quantized Hall effect. Phys. Rev. Lett. 75, 4290–4293 (1995).

    Article  ADS  Google Scholar 

  46. Nederveen, A. J. & Nazarov, Y. V. Skyrmions in disordered heterostructures. Phys. Rev. Lett. 82, 406–409 (1999).

    Article  ADS  Google Scholar 

  47. Xue, J. et al. Scanning tunnelling microscopy and spectroscopy of ultra-flat graphene on hexagonal boron nitride. Nature Mater. 10, 282–285 (2011).

    Article  ADS  Google Scholar 

  48. Papic, Z., Goerbig, M. O. & Regnault, N. Atypical fractional quantum Hall effect in graphene at filling factor 1/3. Phys. Rev. Lett. 105, 176802 (2010).

    Article  ADS  Google Scholar 

  49. Toke, C. & Jain, J. K. Multi-component fractional quantum Hall states in graphene: SU(4) versus SU(2) http://arxiv.org/abs/1105.5270 (2011).

  50. Maude, D. K. et al. Spin excitations of a two-dimensional electron gas in the limit of vanishing Landé; g factor. Phys. Rev. Lett. 77, 4604 (1996).

    Article  ADS  Google Scholar 

  51. Shkolnikov, Y. P., Misra, S., Bishop, N. C., De Poortere, E. P. & Shayegan, M. Observation of quantum Hall valley Skyrmions. Phys. Rev. Lett. 95, 066809 (2005).

    Article  ADS  Google Scholar 

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Acknowledgements

We acknowledge discussions with I. Aleiner, A. Macdonald, Y. Barlas, R. Cote, W. Luo and M. Kharitonov. The measurements were made at NHMFL, which is supported by National Science Foundation Cooperative Agreement DMR-0654118, the State of Florida and the US Department of Energy. We thank S. Hannahs, T. Murphy, J.-H. Park and S. Maier for experimental assistance at NHMFL. This work is supported by the US Defense Advanced Research Projects Agency Carbon Electronics for RF Applications, the Air Force Office of Scientific Research Multidisciplinary University Research Initiative, the Focus Center Research Program through the Center for Circuit and System Solutions and Functional Engineered Nano Architectonics, the Nanoscale Science and Engineering Center (CHE-0117752) and the New York Division of Science, Technology and Innovation. P.K. and A.F.Y. acknowledge support from the US Department of Energy (DE-FG02-05ER46215).

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  1. A. F. Young and C. R. Dean: These authors contributed equally to this work

Authors and Affiliations

  1. Department of Physics, Columbia University, New York, New York 10027, USA

    A. F. Young, H. Ren, P. Cadden-Zimansky & P. Kim

  2. Department of Electrical Engineering, Columbia University, New York, New York 10027, USA

    C. R. Dean & K. L. Shepard

  3. Department of Mechanical Engineering, Columbia University, New York, New York 10027, USA

    C. R. Dean, L. Wang & J. Hone

  4. Advanced Materials Laboratory, National Institute for Materials Science, 1-1 Namiki, Tsukuba, 305-0044, Japan

    K. Watanabe & T. Taniguchi

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Contributions

A.F.Y., C.R.D. and P.K. conceived the experiment and analysed the data. A.F.Y., C.R.D., L.W. and H.R. fabricated the samples. A.F.Y., C.R.D., L.W., H.R. and P.C-Z. made the measurements. A.F.Y., C.R.D. and P.K. wrote the paper. T.T. and K.W. synthesized the hBN crystals. J.H., K.L.S. and P.K. advised on experiments.

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Correspondence to A. F. Young or P. Kim.

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Young, A., Dean, C., Wang, L. et al. Spin and valley quantum Hall ferromagnetism in graphene. Nature Phys 8, 550–556 (2012). https://doi.org/10.1038/nphys2307

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