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Ultra-high-quality two-dimensional electron systems

Nature Materials volume 20, pages 632–637 (2021)Cite this article

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Abstract

Two-dimensional electrons confined to GaAs quantum wells are hallmark platforms for probing electron–electron interactions. Many key observations have been made in these systems as sample quality has improved over the years. Here, we present a breakthrough in sample quality via source-material purification and innovation in GaAs molecular beam epitaxy vacuum chamber design. Our samples display an ultra-high mobility of 44 × 106 cm2 V–1 s–1 at an electron density of 2.0 × 1011 cm–2. These results imply only 1 residual impurity for every 1010 Ga/As atoms. The impact of such low impurity concentration is manifold. Robust stripe and bubble phases are observed, and several new fractional quantum Hall states emerge. Furthermore, the activation gap (Δ) of the fractional quantum Hall state at the Landau-level filling (ν) = 5/2, which is widely believed to be non-Abelian and of potential use for topological quantum computing, reaches Δ ≈ 820 mK. We expect that our results will stimulate further research on interaction-driven physics in a two-dimensional setting and substantially advance the field.

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Fig. 1: Improving vacuum quality and its assessment in a state-of-the-art MBE chamber.
Fig. 2: Mobility versus 2D electron density for our GaAs 2DESs.
Fig. 3: Low-temperature (T ≈ 30 mK) magnetoresistance data of a GaAs 2DES with density n ≈ 1.0 × 1011 cm–2.
Fig. 4: Low-temperature (T ≈ 30 mK) magnetotransport data of n ≈ 1.0 × 1011 cm–2 samples at higher Landau-level fillings.

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Data supporting the results in this paper and the Supplementary Information are available on request to the corresponding author. Source data are provided with this paper.

References

  1. Tsui, D. C., Stormer, H. L. & Gossard, A. C. Two-dimensional magnetotransport in the extreme quantum limit. Phys. Rev. Lett. 48, 1559–1562 (1982).

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  3. Andrei, E. Y. et al. Observation of a magnetically induced Wigner solid. Phys. Rev. Lett. 60, 2765–2768 (1988).

    Article  CAS  Google Scholar 

  4. Jiang, H. W. et al. Quantum liquid versus electron solid around ν = 1/5 Landau-level filling. Phys. Rev. Lett. 65, 633–636 (1990).

    Article  CAS  Google Scholar 

  5. Goldman, V. J., Santos, M., Shayegan, M. & Cunningham, J. E. Evidence for two-dimensional quantum Wigner crystal. Phys. Rev. Lett. 65, 2189–2192 (1990).

    Article  CAS  Google Scholar 

  6. Deng, H. et al. Commensurability oscillations of composite fermions induced by the periodic potential of a Wigner crystal. Phys. Rev. Lett. 117, 096601 (2016).

    Article  CAS  Google Scholar 

  7. 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).

    Article  CAS  Google Scholar 

  8. Du, R. R. et al. Strongly anisotropic transport in higher two-dimensional Landau levels. Solid State Commun. 109, 389–394 (1999).

    Article  CAS  Google Scholar 

  9. 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).

    Article  CAS  Google Scholar 

  10. Shayegan, M. in High Magnetic Fields: Science and Technology Vol. 3 (eds Herlach, F. & Miura, N.) 31–60 (World Scientific, 2006).

  11. Jain, J. K. Composite Fermions (Cambridge Univ. Press, 2007).

  12. Lay, T. S. et al. High-quality two-dimensional electron system confined in an AlAs quantum well. Appl. Phys. Lett. 62, 3120–3122 (1993).

    Article  CAS  Google Scholar 

  13. de Poortere, E. P. et al. Enhanced electron mobility and high order fractional quantum Hall states in AlAs quantum wells. Appl. Phys. Lett. 80, 1583–1585 (2002).

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  15. Bishop, N. C. et al. Valley polarization and susceptibility of composite fermions around a filling factor ν = 3/2. Phys. Rev. Lett. 98, 266404 (2007).

    Article  CAS  Google Scholar 

  16. Chung, Y. J. et al. Multivalley two-dimensional electron system in an AlAs quantum well with mobility exceeding 2 x 106 cm2V-1s-1. Phys. Rev. Mater. 2, 071001R (2018).

    Article  Google Scholar 

  17. Hossain, M. S. et al. Unconventional anisotropic even-denominator fractional quantum Hall state in a system with mass anisotropy. Phys. Rev. Lett. 121, 256601 (2018).

    Article  CAS  Google Scholar 

  18. Lai, K. et al. Two-flux composite fermion series of the fractional quantum Hall states in strained Si. Phys. Rev. Lett. 93, 156805 (2004).

    Article  CAS  Google Scholar 

  19. Kott, T. M., Hu, B., Brown, S. H. & Kane, B. E. Valley-degenerate two-dimensional electrons in the lowest Landau level. Phys. Rev. B 89, 041107R (2014).

    Article  Google Scholar 

  20. 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  CAS  Google Scholar 

  21. 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  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  23. Zibrov, A. A. et al. Even-denominator fractional quantum Hall states at an isospin transition in monolayer graphene. Nat. Phys. 14, 930–935 (2018).

    Article  CAS  Google Scholar 

  24. Polshyn, H. et al. Quantitative transport measurements of fractional quantum Hall energy gaps in edgeless graphene devices. Phys. Rev. Lett. 121, 226801 (2018).

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  26. Falson, J. et al. Even-denominator fractional quantum Hall physics in ZnO. Nat. Phys. 11, 347–351 (2015).

    Article  CAS  Google Scholar 

  27. Shi, Q., Zudov, M. A., Morrison, C. & Myronov, M. Spinless composite fermions in an ultrahigh-quality strained Ge quantum well. Phys. Rev. B 91, 241303R (2015).

    Article  Google Scholar 

  28. Mironov, O. A. et al. Fractional quantum Hall states in a Ge quantum well. Phys. Rev. Lett. 116, 176802 (2016).

    Article  CAS  Google Scholar 

  29. Shi, Q. et al. Odd- and even-denominator fractional quantum Hall states in monolayer WSe2. Nat. Nanotechnol. 15, 569–573 (2020).

    Article  CAS  Google Scholar 

  30. Friess, B. et al. Negative permittivity in bubble and stripe phases. Nat. Phys. 13, 1124–1129 (2017).

    Article  CAS  Google Scholar 

  31. Hossain, M. S. et al. Bloch ferromagnetism of composite fermions. Nat. Phys. https://doi.org/10.1038/s41567-020-1000-z (2020).

  32. Pfeiffer, L. & West, K. W. The role of MBE in recent quantum Hall effect physics discoveries. Physica E 20, 57–64 (2003).

    Article  CAS  Google Scholar 

  33. Umansky, V. et al. MBE growth of ultra-low disorder 2DEG with mobility exceeding 35x106 cm2 /V s. J. Cryst. Growth 311, 1658–1661 (2009).

    Article  CAS  Google Scholar 

  34. Schlom, D. G. & Pfeiffer, L. N. Upward mobility rocks! Nat. Mater. 9, 881–883 (2010).

    Article  CAS  Google Scholar 

  35. Gardner, G. C., Fallahi, S., Watson, J. D. & Manfra, M. J. Modified MBE hardware and techniques and role of gallium purity for attainment of two dimensional electron gas mobility >35x106 cm2 /V s in GaAs/AlGaAs quantum wells grown by MBE. J. Cryst. Growth 441, 71–77 (2016).

    Article  CAS  Google Scholar 

  36. Hwang, E. H. & das Sarma, S. Limit to two-dimensional mobility in modulation-doped GaAs quantum structures: how to achieve a mobility of 100 million. Phys. Rev. B 77, 235437 (2008).

    Article  Google Scholar 

  37. das Sarma, S., Hwang, E. H., Kodiyalam, S., Pfeiffer, L. N. & West, K. W. Transport in two-dimensional modulation-doped semiconductor structures. Phys. Rev. B 91, 205304 (2015).

    Article  Google Scholar 

  38. Sammon, M., Zudov, M. A. & Shklovskii, B. I. Mobility and quantum mobility of modern GaAs/AlGaAs heterostructures. Phys. Rev. Mater. 2, 064604 (2018).

    Article  CAS  Google Scholar 

  39. Schlapfer, F., Dietsche, W., Reichl, C., Faelt, S. & Wegscheider, W. Photoluminescence and the gallium problem for highest-mobility GaAs/AlGaAs-based 2d electron gases. J. Cryst. Growth 442, 114–120 (2016).

    Article  CAS  Google Scholar 

  40. Chung, Y. J., Baldwin, K. W., West, K. W., Shayegan, M. & Pfeiffer, L. N. Surface segregation and the Al problem in GaAs quantum wells. Phys. Rev. Mater. 2, 034006 (2018).

    Article  CAS  Google Scholar 

  41. Chung, Y. J. et al. Working principles of doping-well structures for high-mobility two-dimensional electron systems. Phys. Rev. Mater. 4, 044003 (2020).

    Article  CAS  Google Scholar 

  42. Pan, W., Baldwin, K. W., West, K. W., Pfeiffer, L. N. & Tsui, D. C. Fractional quantum Hall effect at Landau level filling ν = 4/11. Phys. Rev. B 91, 041301R (2015).

    Article  Google Scholar 

  43. Shayegan, M., Goldman, V. J., Jiang, C., Sajoto, T. & Santos, M. Growth of low-density two-dimensional electron system with very high mobility by molecular beam epitaxy. Appl. Phys. Lett. 52, 1086–1088 (1988).

    Article  CAS  Google Scholar 

  44. Pfeiffer, L., West, K. W., Stormer, H. L. & Baldwin, K. W. Electron mobilities exceeding 107 cm2 /V s in modulation-doped GaAs. Appl. Phys. Lett. 55, 1888–1890 (1989).

    Article  CAS  Google Scholar 

  45. Sajoto, T., Suen, Y. W., Engel, L. W., Santos, M. B. & Shayegan, M. Fractional quantum Hall effect in very-low-density GaAs/AlxGa1-xAs heterostructures. Phys. Rev. B 41, 8449–8460 (1990).

    Article  CAS  Google Scholar 

  46. Gold, A. Temperature dependence of mobility in AlxGa1-x/GaAs heterostructures for impurity scattering. Phys. Rev. B 41, 8537–8540 (1990).

    Article  CAS  Google Scholar 

  47. Watson, J. D., Csáthy, G. A. & Manfra, M. J. Impact of heterostructure design on transport properties in the second Landau level of in situ back-gated two-dimensional electron gases. Phys. Rev. Appl. 3, 064004 (2015).

    Article  Google Scholar 

  48. 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).

    Article  CAS  Google Scholar 

  49. Willett, R. L., Pfeiffer, L. N. & West, K. W. Measurement of filling factor 5/2 quasiparticle interference with observation of charge e/4 and e/2 period oscillations. Proc. Natl Acad. Sci. USA 106, 8853–8858 (2009).

    Article  CAS  Google Scholar 

  50. Ro, D. et al. Electron bubbles and the structure of the orbital wave function. Phys. Rev. B 99, 201111R (2019).

    Article  Google Scholar 

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Acknowledgements

We acknowledge support through the National Science Foundation (grants DMR 1709076 and ECCS 1906253) for measurements and the National Science Foundation (grant MRSEC DMR 1420541), the Gordon and Betty Moore Foundation’s EPiQS programme (grant GBMF9615 to L.N.P.) and the Department of Energy Basic Energy Sciences (grant DE-FG02-00-ER45841) for sample fabrication and characterization.

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Author notes

  1. These authors contributed equally: Yoon Jang Chung, K. A. Villegas Rosales.

Authors and Affiliations

  1. Department of Electrical Engineering, Princeton University, Princeton, NJ, USA

    Yoon Jang Chung, K. A. Villegas Rosales, K. W. Baldwin, P. T. Madathil, K. W. West, M. Shayegan & L. N. Pfeiffer

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Contributions

Y.J.C. and L.N.P. conceived the work. K.W.B., K.W.W. and L.N.P. designed and built the MBE chamber. Y.J.C., K.W.B., K.W.W. and L.N.P. designed, grew and evaluated the quality of all samples at T ≈ 0.3 K. K.A.V.-R. and P.T.M. performed the dilution refrigerator measurements. Y.J.C. and M.S. wrote the manuscript with input from all co-authors.

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Correspondence to Yoon Jang Chung.

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Peer review information Nature Materials thanks Joseph Falson, Minjoo Lee and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Supplementary Information

Supplementary Figs. 1–4, Discussion and Table 1.

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Chung, Y.J., Villegas Rosales, K.A., Baldwin, K.W. et al. Ultra-high-quality two-dimensional electron systems. Nat. Mater. 20, 632–637 (2021). https://doi.org/10.1038/s41563-021-00942-3

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