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Aharonov–Bohm interference of fractional quantum Hall edge modes

Nature Physics volume 15, pages 563–569 (2019)Cite this article

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Abstract

The braiding statistics of certain fractional quantum Hall states can be probed via interferometry of their edge states. Practical difficulties—including loss of phase coherence—make this a challenging task. We demonstrate the operation of a small Fabry–Perot interferometer in which highly coherent Aharonov–Bohm oscillations are observed in the integer and fractional quantum Hall regimes. Careful design of the heterostructure suppresses Coulomb effects and promotes strong phase coherence. We characterize the coherency of edge-mode interference by the energy scale for thermal damping and determine the velocities of the inner and outer edge modes independently via selective backscattering of edge modes originating in the N = 0, 1, 2 Landau levels. We also observe clear Aharonov–Bohm oscillations at fractional filling factors ν = 2/3 and ν = 1/3, which indicates that our device architecture provides a platform for measurement of anyonic braiding statistics.

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Fig. 1: Heterostructure design and device layout.
Fig. 2: Scanning electron micrograph of the interferometer.
Fig. 3: Bulk magnetotransport and Coulomb blockade.
Fig. 4: Interference measurements at ν = 1.
Fig. 5: Edge-mode velocity measurements.
Fig. 6: Interference of fractional quantum Hall states.

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Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.

References

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

    Book  Google Scholar 

  2. Chamon, C. et al. Two point-contact interferometer for quantum Hall systems. Phys. Rev. B 55, 2331–2343 (1997).

    Article  ADS  Google Scholar 

  3. Sarma, S. D., Freedman, M. & Nayak, C. Topologically protected qubits from a possible non-Abelian fractional quantum Hall state. Phys. Rev. Lett. 94, 166802 (2005).

    Article  ADS  Google Scholar 

  4. Stern, A. & Halperin, B. I. Proposed experiments to probe the non-Abelian ν = 5/2 quantum Hall state. Phys. Rev. Lett. 96, 016802 (2006).

    Article  ADS  Google Scholar 

  5. Kim, E. Aharonov–Bohm interference and fractional statistics in a quantum Hall interferometer. Phys. Rev. Lett. 97, 216404 (2006).

    Article  ADS  Google Scholar 

  6. Halperin, B. I. Statistics of quasiparticles and the hierarchy of fractional quantized Hall states. Phys. Rev. Lett. 52, 1583–1586 (1984).

    Article  ADS  Google Scholar 

  7. Zhang, Y. et al. Distinct signatures for Coulomb blockade and interference in electronic Fabry–Perot interferometers. Phys. Rev. B 79, 241304(R) (2009).

    Article  ADS  Google Scholar 

  8. Lin, P. V., Camino, F. E. & Goldman, V. J. Electron interferometry in the quantum Hall regime: Aharonov–Bohm effect of interacting electrons. Phys. Rev. B 80, 125310 (2009).

    Article  ADS  Google Scholar 

  9. Baer, S. et al. Cyclic depopulation of edge states in a large quantum dot. New J. Phys. 15, 023035 (2013).

    Article  ADS  Google Scholar 

  10. Ofek, N. et al. Role of interactions in an electron Fabry–Perot interferometer operating in the quantum Hall effect regime. Proc. Natl Acad. Sci. USA 107, 5276–5281 (2010).

    Article  ADS  Google Scholar 

  11. Halperin, B. I. & Rosenow, B. Influence of interactions on flux and back-gate period of quantum Hall interferometers. Phys. Rev. Lett. 98, 106801 (2007).

    Article  ADS  Google Scholar 

  12. Halperin, B. I., Stern, A., Neder, I. & Rosenow, B. Theory of the Fabry–Perot quantum Hall interferometer. Phys. Rev. B 83, 155440 (2011).

    Article  ADS  Google Scholar 

  13. von Keyserlingk, C. W., Simon, S. H. & Rosenow, B. Enhanced bulk–edge Coulomb coupling in fractional Fabry–Perot interferometers. Phys. Rev. Lett. 115, 126807 (2015).

    Article  ADS  Google Scholar 

  14. Manfra, M. J. Molecular beam epitaxy of ultra-high-quality AlGaAs/GaAs heterostructures: enabling physics in low-dimensional electronic systems. Annu. Rev. Condens. Matter Phys. 5, 347–373 (2014).

    Article  ADS  Google Scholar 

  15. 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 >35 × 106 cm2/Vs in AlGaAs/GaAs quantum wells grown by MBE. J. Cryst. Growth 441, 71–77 (2016).

  16. Sahasrabudhe, H. et al. Optimization of edge state velocity in the integer quantum Hall regime. Phys. Rev. B 97, 085302 (2018).

    Article  ADS  Google Scholar 

  17. Eisenstein, J. P., Pfeiffer, L. N. & West, K. W. Independently contacted two-dimensional electron systems in double quantum wells. Appl. Phys. Lett. 57, 2324–2326 (1990).

    Article  ADS  Google Scholar 

  18. Beenakker, C. W. J. Theory of Coulomb-blockade oscillations in the conductance of a quantum dot. Phys. Rev. B 44, 1646–1656 (1991).

    Article  ADS  Google Scholar 

  19. McClure, D. T. Interferometer based studies of quantum Hall phenomena. PhD thesis, Harvard Univ. (2012).

  20. Roulleau, P. et al. Direct measurement of the coherence length of edge states in the integer quantum Hall regime. Phys. Rev. Lett. 100, 126802 (2008).

    Article  ADS  Google Scholar 

  21. McClure, D. T. et al. Edge-state velocity and coherence in a quantum Hall Fabry–Perot interferometer. Phys. Rev. Lett. 103, 206806 (2009).

    Article  ADS  Google Scholar 

  22. Gurman, I., Sabo, R., Heiblum, M., Umansky, V. & Mahalu, D. Dephasing of an electronic two-path interferometer. Phys. Rev. B 93, 121412 (R) (2016).

    Article  ADS  Google Scholar 

  23. Choi, H. K. et al. Robust electron pairing in the integer quantum Hall effect. Nat. Commun. 6, 7435 (2015).

    Article  Google Scholar 

  24. Sivan, I. et al. Interaction-induced interference in the integer quantum Hall effect. Phys. Rev. B 97, 125405 (2018).

    Article  ADS  Google Scholar 

  25. Frigeri, G. A., Scherer, D. D. & Rosenow, B. Subperiods and apparent pairing in integer quantum Hall interferometers. Preprint at https://arxiv.org/abs/1709.04504 (2017).

  26. Chklovskii, D. B., Shklovskii, B. I. & Glazman, L. I. Electrostatics of edge channels. Phys. Rev. B 46, 4026–4034 (1992).

    Article  ADS  Google Scholar 

  27. Chklovskii, D. B., Matveev, K. A. & Shklovskii, B. I. Ballistic conductance of interacting electrons in the quantum Hall regime. Phys. Rev. B 47, 12605–12617 (1993).

    Article  ADS  Google Scholar 

  28. Montambaux, G. Semiclassical quantization of skipping orbits. Eur. Phys. J. B 79, 215–224 (2011).

    Article  ADS  MathSciNet  Google Scholar 

  29. McClure, D. T., Chang, W., Marcus, C. M., Pfeiffer, L. N. & West, K. W. Fabry–Perot interferometry with fractional charges. Phys. Rev. Lett. 108, 256804 (2012).

    Article  ADS  Google Scholar 

  30. Camino, F. E., Zhou, W. & Goldman, V. J. Aharonov–Bohm superperiod in a Laughlin quasiparticle interferometer. Phys. Rev. Lett. 95, 246802 (2005).

    Article  ADS  Google Scholar 

  31. Camino, F. E., Zhou, W. & Goldman, V. J. e/3 Laughlin quasiparticle primary-filling ν = 1/3 interferometer. Phys. Rev. Lett. 98, 076805 (2007).

    Article  ADS  Google Scholar 

  32. 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  ADS  Google Scholar 

  33. Willett, R. L., Nayak, C., Shtengel, K., Pfeiffer, L. N. & West, K. W. Magnetic-field-tuned Aharonov–Bohm oscillations and evidence for non-Abelian anyons at ν = 5/2. Phys. Rev. Lett. 111, 186401 (2013).

    Article  ADS  Google Scholar 

  34. Laughlin, R. B. Anomalous quantum Hall effect: an incompressible quantum fluid with fractionally charged excitation. Phys. Rev. Lett. 50, 1395–1398 (1983).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  36. de-Picciotto, R. et al. Direct observation of a fractional charge. Nature 389, 162–164 (1997).

    Article  ADS  Google Scholar 

  37. Goldman, V. J. Resonant tunneling in the quantum Hall regime: measurement of fractional charge. Science 267, 1010–1012 (1995).

    Article  ADS  Google Scholar 

  38. Goldman, V. J. Resonant tunneling in the quantum Hall regime: measurement of fractional charge. Surf. Sci. 361/362, 1–6 (1995).

    Article  ADS  Google Scholar 

  39. Girvin, S. M. Particle–hole symmetry in the anomalous quantum Hall effect. Phys. Rev. B 29, 6012–6014 (1984).

    Article  ADS  MathSciNet  Google Scholar 

  40. MacDonald, A. H. Edge states in the fractional-quantum-Hall-effect regime. Phys. Rev. Lett. 64, 220–223 (1990).

    Article  ADS  Google Scholar 

  41. Chang, A. M. A unified transport theory for the integral and fractional quantum Hall effects: phase boundaries, edge currents, and transmission/reflection probabilities. Solid State Commun. 74, 871–876 (1990).

    Article  ADS  Google Scholar 

  42. Beenakker, C. W. J. Edge channels for the fractional quantum Hall effect. Phys. Rev. Lett. 64, 216–219 (1990).

    Article  ADS  Google Scholar 

  43. Meir, Y. Composite edge states in the ν = 2/3 fractional quantum Hall regime. Phys. Rev. Lett. 72, 2624–2627 (1993).

    Article  ADS  Google Scholar 

  44. Kane, C. L., Fisher, M. P. A. & Polchinski, J. Randomness at the edge: theory of quantum Hall transport at filling ν = 2/3. Phys. Rev. Lett. 72, 4129–4132 (1994).

    Article  ADS  Google Scholar 

  45. Bid, A., Ofek, N., Heiblum, M., Umansky, V. & Mahalu, D. Shot noise and charge at the 2/3 composite fractional quantum Hall state. Phys. Rev. Lett. 103, 236802 (2009).

    Article  ADS  Google Scholar 

  46. Sabo, R. et al. Edge reconstruction in fractional quantum Hall states. Nat. Phys. 13, 491–496 (2017).

    Article  Google Scholar 

  47. Hu, Z., Rezayi, E. H., Wan, X. & Yang, K. Edge-mode velocities and thermal coherence of quantum Hall interferometers. Phys. Rev. B 80, 235330 (2009).

    Article  ADS  Google Scholar 

  48. Wan, X., Yang, K. & Rezayi, E. H. Reconstruction of fractional quantum Hall edges. Phys. Rev. Lett. 88, 056802 (2002).

    Article  ADS  Google Scholar 

  49. Joglekar, Y. N., Nguyen, H. K. & Murthy, G. Edge reconstructions in fractional quantum Hall systems. Phys. Rev. B 68, 035332 (2003).

    Article  ADS  Google Scholar 

  50. Goldsten, M. & Gefen, Y. Suppression of interference in quantum Hall Mach–Zehnder geometry by upstream neutral modes. Phys. Rev. Lett. 117, 276804 (2016).

    Article  ADS  Google Scholar 

  51. Park, J., Gefen, Y. & Sim, H. Topological dephasing in the ν = 2/3 fractional quantum Hall regime. Phys. Rev. B 92, 245437 (2015).

    Article  ADS  Google Scholar 

  52. Inoue, H. et al. Proliferation of neutral modes in fractional quantum Hall states. Nat. Commun. 5, 4067 (2014).

    Article  Google Scholar 

  53. Du, R. R., Stormer, H. L., Tsui, D. C., Pfeiffer, L. N. & West, K. W. Experimental evidence for new particles in the fractional quantum Hall effect. Phys. Rev. Lett. 70, 2944–2947 (1993).

    Article  ADS  Google Scholar 

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Acknowledgements

This work was supported by the Department of Energy, Office of Basic Energy Sciences, under award number DE-SC0006671. Additional support for sample growth from the W. M. Keck Foundation and Nokia Bell Labs is gratefully acknowledged. We thank M. Heiblum, R. L. Willett and S. H. Simon for helpful comments that improved our manuscript.

Author information

Authors and Affiliations

  1. Department of Physics and Astronomy, Purdue University, West Lafayette, IN, USA

    J. Nakamura, S. Fallahi, H. Sahasrabudhe, S. Liang & M. J. Manfra

  2. Birck Nanotechnology Center, Purdue University, West Lafayette, IN, USA

    J. Nakamura, S. Fallahi, S. Liang, G. C. Gardner & M. J. Manfra

  3. School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN, USA

    R. Rahman & M. J. Manfra

  4. Microsoft Station Q Purdue, Purdue University, West Lafayette, IN, USA

    G. C. Gardner & M. J. Manfra

  5. School of Materials Engineering, Purdue University, West Lafayette, IN, USA

    M. J. Manfra

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  1. J. Nakamura
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Contributions

J.N. and M.J.M. designed the heterostructures and experiments. S.F., S.L. and G.C.G. conducted molecular beam epitaxy growth. J.N. fabricated the devices, performed the measurements and analysed the data with input from M.J.M. H.S. and R.R. performed numerical simulations. J.N. and M.M. wrote the manuscript with input from all authors.

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Correspondence to M. J. Manfra.

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Journal peer review information: Nature Physics thanks Thomas Ihn and the other anonymous reviewer(s) for their contribution to the peer review of this work.

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Nakamura, J., Fallahi, S., Sahasrabudhe, H. et al. Aharonov–Bohm interference of fractional quantum Hall edge modes. Nat. Phys. 15, 563–569 (2019). https://doi.org/10.1038/s41567-019-0441-8

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