Skip to main content

Thank you for visiting 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.

Anyonic interference and braiding phase in a Mach-Zehnder interferometer


Fractional quantum Hall states have long been predicted to be a testing ground of fractional—anyonic—exchange statistics. These topological states, which can have either an Abelian or non-Abelian character, harbour quasiparticles with fractional charges. The charge of the quasiparticles can be measured by shot noise measurements, whereas their quantum statistics can be revealed by appropriate interference experiments. The multipath Fabry–Pérot electronic interferometer is easier to fabricate, but it is often plagued by Coulomb interactions, area breathing with the magnetic field and fluctuating charges. Yet, recent experiments with an adequately screened Fabry–Pérot interferometer allowed the observation of anyonic interference at a bulk filling factor of ν = 1/3. Here we demonstrate the interference and braiding of anyons in an interaction-free two-path Mach–Zehnder interferometer tuned to bulk filling of ν = 2/5 with an outermost ν = 1/3 edge mode. Interference with this mode reveals a phase dependence that corresponds to the predicted anyonic braiding. This proves that a Mach–Zehnder interferometer is a powerful tool that probes the quantum statistics of complex anyonic states.

This is a preview of subscription content, access via your institution

Relevant articles

Open Access articles citing this article.

Access options

Rent or buy this article

Get just this article for as long as you need it


Prices may be subject to local taxes which are calculated during checkout

Fig. 1: Device structure and conductance quantization.
Fig. 2: Integer and fractional AB interference patterns.
Fig. 3: Charge determination via shot noise measurements and temperature-dependent visibility.
Fig. 4: Visibility in the integer and fractional regimes.

Data availability

Source data are provided with this paper. All other data related to this paper are available from the corresponding author upon reasonable request.


  1. Halperin, B. I. Quantized Hall conductance, current-carrying edge states, and the existence of extended states in a two-dimensional disordered potential. Phys. Rev. B 25, 2185–2190 (1982).

    Article  ADS  Google Scholar 

  2. Wen, X.-G. in Quantum Field Theory of Many-Body Systems: From the Origin of Sound to an Origin of Light and Electrons (Oxford Univ. Press, 2004).

  3. Kane, C. L. & Fisher, M. P. A. in Perspectives in Quantum Hall Effects: Novel Quantum Liquids in Low‐Dimensional Semiconductor Structures (eds Das Sarma, S. & Pinczuk, A.) (John Wiley, 1996).

  4. Stern, A. Anyons and the quantum Hall effect—a pedagogical review. Ann. Phys. 323, 204–249 (2008).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  5. Zheng, H. Z., Wei, H. P., Tsui, D. C. & Weimann, G. Gate-controlled transport in narrow GaAs/AlxGa1–xAs heterostructures. Phys. Rev. B 34, 5635–5638 (1986).

    Article  ADS  Google Scholar 

  6. Heiblum, M. & Feldman, D. E. Edge probes of topological order. Int. J. Mod. Phys. A 35, 18 (2020).

    Article  MathSciNet  Google Scholar 

  7. Chang, A. M. Chiral Luttinger liquids at the fractional quantum Hall edge. Rev. Mod. Phys. 75, 1449–1505 (2003).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  8. Arovas, D., Schrieffer, J. R. & Wilczek, F. Fractional statistics and the quantum Hall effect. Phys. Rev. Lett. 53, 722–723 (1984).

    Article  ADS  Google Scholar 

  9. dePicciotto, R. et al. Direct observation of a fractional charge. Nature 389, 162–164 (1997).

    Article  ADS  Google Scholar 

  10. Saminadayar, L., Glattli, D. C., Jin, Y. & Etienne, B. Observation of the e/3 fractionally charged Laughlin quasiparticle. Phys. Rev. Lett. 79, 2526–2529 (1997).

    Article  ADS  Google Scholar 

  11. Leinaas, J. M. & Myrheim, J. On the theory of identical particles. Nuovo Cim. B 37, 1–23 (1977).

    Article  ADS  Google Scholar 

  12. Wilczek, F. Magnetic flux, angular momentum, and statistics. Phys. Rev. Lett. 48, 1144–1146 (1982).

    Article  ADS  Google Scholar 

  13. 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 

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

    Article  ADS  Google Scholar 

  15. Schuster, R. et al. Phase measurement in a quantum dot via a double-slit interference experiment. Nature 385, 417–420 (1997).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  17. Zhang, Y. M. et al. Distinct signatures for Coulomb blockade and Aharonov-Bohm interference in electronic Fabry-Perot interferometers. Phys. Rev. B 79, 241304 (2009).

    Article  ADS  Google Scholar 

  18. Chamon, C. D. C., Freed, D. E., Kivelson, S. A., Sondhi, S. L. & Wen, X. G. Two point-contact interferometer for quantum Hall systems. Phys. Rev. B 55, 2331–2343 (1997).

    Article  ADS  Google Scholar 

  19. 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 

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

    Article  ADS  Google Scholar 

  21. Nakamura, J. et al. Aharonov–Bohm interference of fractional quantum Hall edge modes. Nat. Phys. 15, 563–569 (2019).

    Article  Google Scholar 

  22. Nakamura, J., Liang, S., Gardner, G. C. & Manfra, M. J. Direct observation of anyonic braiding statistics. Nat. Phys. 16, 931–936 (2020).

    Article  Google Scholar 

  23. Sivan, I. et al. Observation of interaction-induced modulations of a quantum Hall liquid’s area. Nat. Commun. 7, 12184 (2016).

    Article  ADS  Google Scholar 

  24. Rosenow, B. & Simon, S. H. Telegraph noise and the Fabry-Perot quantum Hall interferometer. Phys. Rev. B 85, 201302 (2012).

    Article  ADS  Google Scholar 

  25. Ji, Y. et al. An electronic Mach–Zehnder interferometer. Nature 422, 415–418 (2003).

    Article  ADS  Google Scholar 

  26. Neder, I., Heiblum, M., Levinson, Y., Mahalu, D. & Umansky, V. Unexpected behavior in a two-path electron interferometer. Phys. Rev. Lett. 96, 016804 (2006).

    Article  ADS  Google Scholar 

  27. Neder, I. et al. Interference between two indistinguishable electrons from independent sources. Nature 448, 333–337 (2007).

    Article  ADS  Google Scholar 

  28. Neder, I., Heiblum, M., Mahalu, D. & Umansky, V. Entanglement, dephasing, and phase recovery via cross-correlation measurements of electrons. Phys. Rev. Lett. 98, 036803 (2007).

    Article  ADS  Google Scholar 

  29. Roulleau, P. et al. Finite bias visibility of the electronic Mach-Zehnder interferometer. Phys. Rev. B 76, 161309 (2007).

    Article  ADS  Google Scholar 

  30. Law, K. T., Feldman, D. E. & Gefen, Y. Electronic Mach-Zehnder interferometer as a tool to probe fractional statistics. Phys. Rev. B 74, 045319 (2006).

    Article  ADS  Google Scholar 

  31. Feldman, D. E. & Kitaev, A. Detecting non-Abelian statistics with an electronic Mach-Zehnder interferometer. Phys. Rev. Lett. 97, 186803 (2006).

    Article  ADS  Google Scholar 

  32. Roulleau, P. et al. Noise dephasing in edge states of the integer quantum Hall regime. Phys. Rev. Lett. 101, 186803 (2008).

    Article  ADS  Google Scholar 

  33. 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 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  36. Bhattacharyya, R., Banerjee, M., Heiblum, M., Mahalu, D. & Umansky, V. Melting of interference in the fractional quantum Hall effect: appearance of neutral modes. Phys. Rev. Lett. 122, 246801 (2019).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  38. Goldstein, 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 

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

    Article  ADS  Google Scholar 

  40. Biswas, S. et al. Shot noise does not always provide the quasiparticle charge. Nat. Phys. 18, 1476–1481 (2022).

  41. Khanna, U., Goldstein, M. & Gefen, Y. Fractional edge reconstruction in integer quantum Hall phases. Phys. Rev. B 103, L121302 (2021).

    Article  ADS  Google Scholar 

  42. Khanna, U., Goldstein, M. & Gefen, Y. Emergence of neutral modes in Laughlin-like fractional quantum Hall phases. Phys. Rev. Lett. 129, 146801 (2022).

  43. Ponomarenko, V. V. & Averin, D. V. Mach-Zehnder interferometer in the fractional quantum Hall regime. Phys. Rev. Lett. 99, 066803 (2007).

    Article  ADS  Google Scholar 

  44. Feldman, D. E., Gefen, Y., Kitaev, A., Law, K. T. & Stern, A. Shot noise in an anyonic Mach-Zehnder interferometer. Phys. Rev. B 76, 085333 (2007).

    Article  ADS  Google Scholar 

  45. Campagnano, G. et al. Hanbury Brown-Twiss interference of anyons. Phys. Rev. Lett. 109, 106802 (2012).

    Article  ADS  Google Scholar 

  46. Kane, C. L. Telegraph noise and fractional statistics in the quantum Hall effect. Phys. Rev. Lett. 90, 226802 (2003).

    Article  ADS  Google Scholar 

  47. Thouless, D. & Gefen, Y. Fractional quantum Hall effect and multiple Aharonov-Bohm periods. Phys. Rev. Lett. 66, 806–809 (1991).

    Article  ADS  Google Scholar 

  48. Guyon, R., Devillard, P., Martin, T. & Safi, I. Klein factors in multiple fractional quantum Hall edge tunneling. Phys. Rev. B 65, 153304 (2002).

    Article  ADS  Google Scholar 

  49. Safi, I., Devillard, P. & Martin, T. Partition noise and statistics in the fractional quantum Hall effect. Phys. Rev. Lett. 86, 4628–4631 (2001).

    Article  ADS  Google Scholar 

  50. Ofek, N. Interference Measurements at the Integer and Fractional Quantum Hall Effect. PhD thesis, Weizmann Institute of Science (2010).

Download references


We acknowledge M. Banerjee, A. Das, D. E. Feldman, Y. Gefen, I. Neder and A. Stern for useful discussions, and the continuous support of the Sub-Micron Center staff. M.H. acknowledges support from the European Research Council under the European Community’s Seventh Framework Program (FP7/2007-2013)/ERC under grant agreement no. 713351 and the Minerva foundation under grant no. 713534.

Author information

Authors and Affiliations



H.K.K. and S.B. designed and fabricated the devices. H.K.K. and S.B. performed the measurements and analysed the data with N.O. M.H. supervised the experiment and analysis. V.U. developed and grew the heterostructure supporting the two-dimensional electron gas. All the authors contributed to writing the manuscript.

Corresponding author

Correspondence to Moty Heiblum.

Ethics declarations

Competing interests

The authors declare no competing interests.

Peer review

Peer review information

Nature Physics thanks the anonymous reviewers for their contribution to the peer review of this work.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

Supplementary Sections 1–9 and Figs. 1–9.

Source data

Source Data Fig. 1

Source data for Fig. 1c.

Source Data Fig. 2

Source data for Fig. 2a,c.

Source Data Fig. 3

Source data for Fig. 3a–d.

Source Data Fig. 4

Source data for Fig. 4a–g.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Kundu, H.K., Biswas, S., Ofek, N. et al. Anyonic interference and braiding phase in a Mach-Zehnder interferometer. Nat. Phys. (2023).

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI:

This article is cited by


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