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.

Even-denominator fractional quantum Hall physics in ZnO

Abstract

The fractional quantum Hall (FQH) effect emerges in high-quality two-dimensional electron systems exposed to a magnetic field when the Landau-level filling factor, νe, takes on a rational value. Although the overwhelming majority of FQH states have odd-denominator fillings, the physical properties of the rare and fragile even-denominator states are most tantalizing in view of their potential relevance for topological quantum computation. For decades, GaAs has been the preferred host for studying these even-denominator states, where they occur at νe = 5/2 and 7/2. Here we report an anomalous series of quantized even-denominator FQH states outside the realm of III–V semiconductors in the MgZnO/ZnO 2DES electron at νe = 3/2 and 7/2, with precursor features at 9/2; all while the 5/2 state is absent. The effect in this material occurs concomitantly with tunability of the orbital character of electrons at the chemical potential, thereby realizing a new experimental means for investigating these exotic ground states.

This is a preview of subscription content

Access options

Buy article

Get time limited or full article access on ReadCube.

$32.00

All prices are NET prices.

Figure 1: Base temperature (T < 20 mK) magnetotransport data recorded on the MgZnO/ZnO heterostructure.
Figure 2: Energy level sequence and magnetotransport map with sample rotation.
Figure 3: Tilt angle dependence of the resistance and activation energy at prominent FQH states.
Figure 4: Base temperature transport mapping with sample rotation around νe = 3/2.

References

  1. Das Sarma, S. & Pinczuk, A. (eds) Perspectives in the Quantum Hall Effects (John Wiley, 1997).

    Google Scholar 

  2. Suen, Y. W., Engel, L. W., Santos, M. B., Shayegan, M. & Tsui, D. C. Observation of a ν = 1/2 fractional quantum Hall state in a double-layer electron system. Phys. Rev. Lett. 68, 1379–1382 (1992).

    ADS  Article  Google Scholar 

  3. Eisenstein, J. P., Boebinger, G. S., Pfeiffer, L. N., West, K. W. & Song, H. New fractional quantum Hall state in double-layer two-dimensional electron systems. Phys. Rev. Lett. 68, 1383–1386 (1992).

    ADS  Article  Google Scholar 

  4. Luhman, D. et al. Observation of a fractional quantum Hall state at ν = 1/4 in a wide GaAs quantum well. Phys. Rev. Lett. 101, 266804 (2008).

    ADS  Article  Google Scholar 

  5. Liu, Y. et al. Fractional quantum Hall effect at ν = 1/2 in hole systems confined to GaAs quantum wells. Phys. Rev. Lett. 112, 046804 (2014).

    ADS  Article  Google Scholar 

  6. Liu, Y. et al. Even-denominator fractional quantum Hall effect at a Landau level crossing. Phys. Rev. B 89, 165313 (2014).

    ADS  Article  Google Scholar 

  7. Wiedmann, S., Gusev, G. M., Bakarov, A. K. & Portal, J. C. Emergent fractional quantum Hall effect at even denominator ν = 3/2 in a triple quantum well in tilted magnetic fields. J. Phys. Conf. Ser. 334, 012026 (2011).

    Article  Google Scholar 

  8. Ki, D-K., Fal’ko, V., Abanin, D. A. & Morpurgo, A. Observation of even-denominator fractional quantum Hall effect in suspended bilayer graphene. Nano Lett. 14, 2135–2139 (2014).

    ADS  Article  Google Scholar 

  9. Willett, R. et al. Observation of an even-denominator quantum number in the fractional quantum Hall effect. Phys. Rev. Lett. 59, 1776–1779 (1987).

    ADS  Article  Google Scholar 

  10. Pan, W. et al. Exact quantization of the even-denominator fractional quantum Hall state at ν = 5/2 Landau level filling factor. Phys. Rev. Lett. 83, 3530–3533 (1999).

    ADS  Article  Google Scholar 

  11. Eisenstein, J. P., Cooper, K. B., Pfeiffer, L. N. & West, K. W. Insulating and fractional quantum Hall states in the first excited Landau level. Phys. Rev. Lett. 88, 076801 (2002).

    ADS  Article  Google Scholar 

  12. Halperin, B. I. Theory of the quantized Hall conductance. Helv. Phys. Acta 56, 75–102 (1983).

    Google Scholar 

  13. Jain, J. K. Composite-fermion approach for the fractional quantum Hall effect. Phys. Rev. Lett. 63, 199–202 (1989).

    ADS  Article  Google Scholar 

  14. Scarola, V. W., Park, K. & Jain, J. K. Cooper instability of composite fermions. Nature 406, 863–865 (2000).

    ADS  Article  Google Scholar 

  15. Moore, G. & Read, N. Nonabelions in the fractional quantum Hall effect. Nucl. Phys. B 360, 362–396 (1991).

    ADS  MathSciNet  Article  Google Scholar 

  16. Nayak, C., Simon, S. H., Stern, A., Freedman, M. & Das Sarma, S. Non-Abelian anyons and topological quantum computation. Rev. Mod. Phys. 80, 1083–1159 (2008).

    ADS  MathSciNet  Article  Google Scholar 

  17. Stern, A. Non-Abelian states of matter. Nature 464, 187–193 (2010).

    ADS  Article  Google Scholar 

  18. Lilly, M. P., Cooper, K. B., Eisenstein, J. P., Pfeiffer, L. N. & West, K. W. Evidence for an anisotropic state of two-dimensional electrons in high Landau levels. Phys. Rev. Lett. 82, 394–397 (1999).

    ADS  Article  Google Scholar 

  19. Fogler, M. M. & Koulakov, A. A. Laughlin liquid to charge-density-wave transition at high Landau levels. Phys. Rev. B 55, 9326–9329 (1997).

    ADS  Article  Google Scholar 

  20. Rezayi, E. H., Haldane, F. D. M. & Yang, K. Charge-density-wave ordering in half-filled high Landau levels. Phys. Rev. Lett. 83, 1219–1222 (1999).

    ADS  Article  Google Scholar 

  21. Tsukazaki, A. et al. Observation of the fractional quantum Hall effect in an oxide. Nature Mater. 9, 889–893 (2010).

    ADS  Article  Google Scholar 

  22. Vakili, K. et al. Spin-dependent resistivity at transitions between integer quantum Hall states. Phys. Rev. Lett. 94, 176402 (2005).

    ADS  Article  Google Scholar 

  23. Gamez, G. & Muraki, K. ν = 5/2 fractional quantum Hall state in low-mobility electron systems: Different roles of disorder. Phys. Rev. B 88, 075308 (2013).

    ADS  Article  Google Scholar 

  24. De Poortere, E. P., Tutuc, E., Papadakis, S. J. & Shayegan, M. Resistance spikes at transitions between quantum Hall ferromagnets. Science 290, 1546–1549 (2000).

    ADS  Article  Google Scholar 

  25. Jungwirth, T. & MacDonald, A. H. Resistance spikes and domain wall loops in Ising quantum ferromagnets. Phys. Rev. Lett. 87, 216801 (2001).

    ADS  Article  Google Scholar 

  26. MacDonald, A. H. & Girvin, S. M. Collective excitations of fractional Hall states and Wigner crystallization in higher Landau levels. Phys. Rev. B 33, 4009–4013 (1986).

    ADS  Article  Google Scholar 

  27. Choi, H. C., Kang, W., Das Sarma, S., Pfeiffer, L. N. & West, K. W. Activation gaps of fractional quantum Hall effect in the second Landau level. Phys. Rev. B 77, 081301 (2008).

    ADS  Article  Google Scholar 

  28. Du, R. R. et al. Fractional quantum Hall effect around ν = 3/2: Composite fermions with a spin. Phys. Rev. Lett. 75, 3926–3929 (1995).

    ADS  Article  Google Scholar 

  29. Pan, W. et al. Strongly anisotropic electronic transport at Landau level filling factor ν = 9/2 and ν = 5/2 under a tilted magnetic field. Phys. Rev. Lett. 83, 820–823 (1999).

    ADS  Article  Google Scholar 

  30. Lilly, M. P., Cooper, K. B., Eisenstein, J. P., Pfeiffer, L. N. & West, K. W. Anisotropic states of two-dimensional electron systems in high Landau levels: Effect of an in-plane magnetic field. Phys. Rev. Lett. 83, 824–827 (1999).

    ADS  Article  Google Scholar 

  31. Sodemann, I. & MacDonald, A. H. Theory of native orientational pinning in quantum Hall nematics. Preprint at http://arXiv.org/abs/1307.5489 (2013).

  32. Papić, Z. & Abanin, D. A. Topological phases in the zeroth Landau level of bilayer graphene. Phys. Rev. Lett. 112, 046602 (2014).

    ADS  Article  Google Scholar 

  33. Falson, J., Maryenko, D., Kozuka, Y., Tsukazaki, A. & Kawasaki, M. Magnesium doping controlled density and mobility of two-dimensional electron gas in MgxZn1−xO/ZnO heterostructures. Appl. Phys. Express 4, 091101 (2011).

    ADS  Article  Google Scholar 

Download references

Acknowledgements

We thank K. v. Klitzing, T. Arima, R. Morf, M. Shayegan, Y. Liu and V. Scarola for discussions. This work was partly supported by Grant-in-Aids for Scientific Research (S) No. 24226002 from MEXT, Japan, ‘Funding Program for World-Leading Innovative R&D on Science and Technology (FIRST)’ Program from the Japan Society for the Promotion of Science (JSPS) initiated by the Council for Science and Technology Policy and the German Ministry of Science and Education (BMBF). J.F. acknowledges the support of the Marubun Research Promotion Foundation.

Author information

Authors and Affiliations

Authors

Contributions

J.F. grew the heterostructure. J.F., B.F. and D.Z. performed the low-temperature measurements. J.F. analysed the data. J.F. and J.H.S. wrote the manuscript with input from all authors. All authors discussed the results and planned the experiments with J.F., D.M., Y.K., A.T. and M.K. initiating the project.

Corresponding authors

Correspondence to J. H. Smet or M. Kawasaki.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary Information

Supplementary Information (PDF 7933 kb)

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Falson, J., Maryenko, D., Friess, B. et al. Even-denominator fractional quantum Hall physics in ZnO. Nature Phys 11, 347–351 (2015). https://doi.org/10.1038/nphys3259

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nphys3259

Further reading

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