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.

  • Technical Review
  • Published:

Anyons in quantum Hall interferometry

Abstract

The quantum Hall (QH) effect represents a unique playground where quantum coherence of electrons can be exploited for various applications, from metrology to quantum computation. In the fractional regime, it also hosts anyons, emergent quasiparticles that are neither bosons nor fermions and possess fractional statistics. Their detection and manipulation represent key milestones in view of topologically protected quantum computation schemes. Exploiting the high degree of phase coherence, edge states in the QH regime have been investigated by designing and constructing electronic interferometers, able to reveal the coherence and statistical properties of the interfering constituents. Here, we review the two main geometries developed in the QH regime, the Mach–Zehnder and the Fabry–Pérot interferometers. We present their basic working principles, fabrication methods and the main results obtained in both the integer and the fractional QH regimes. We will also show how recent technological advances led to the direct experimental demonstration of fractional statistics for Laughlin quasiparticles in a Fabry–Pérot interferometric setup.

Key points

  • The quantum Hall effect represents the first known example of topological quantum matter, whose intrinsic robustness is pivotal for many applications, from metrological standard to quantum information purposes.

  • Transport is mediated by charge carriers moving along the edge of the system with a high degree of phase coherence, which has been exploited to build electronic analogues of quantum optic experiments.

  • Electronic interferometry in the integer and the fractional quantum Hall regimes has emerged as a unique playground to study and exploit the coherence and correlations of propagating quasiparticles. Two main geometries have been studied and realized, Mach–Zehnder and Fabry–Pérot interferometers.

  • Excitations in the fractional quantum Hall regime are predicted to be anyons, quasiparticles with fractional charges and fractional statistics. The fractional statistics, in particular, has attracted a lot of interest in view of potential applications in topological quantum computation.

  • Recent experimental advances in quantum Hall interferometry have led to the first direct observation of fractional statistics in a Fabry–Pérot setup.

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

Access options

Rent or buy this article

Prices vary by article type

from$1.95

to$39.95

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

Fig. 1: The electronic Mach–Zehnder interferometer.
Fig. 2: Visibility and coherence of Aharonov–Bohm oscillations.
Fig. 3: Impact of neutral modes on the interference signal.
Fig. 4: The electronic Fabry–Pérot interferometer.
Fig. 5: Coulomb-dominated versus Aharonov–Bohm regime.
Fig. 6: Detection of anyonic statistics.

Similar content being viewed by others

References

  1. von Klitzing, K. et al. 40 years of the quantum Hall effect. Nat. Rev. Phys. 2, 397–401 (2020).

    Article  Google Scholar 

  2. Thouless, D. J., Kohmoto, M., Nightingale, M. P. & den Nijs, M. Quantized Hall conductance in a two-dimensional periodic potential. Phys. Rev. Lett. 49, 405–408 (1982).

    Article  ADS  Google Scholar 

  3. Haldane, F. D. M. Nobel lecture: Topological quantum matter. Rev. Mod. Phys. 89, 040502 (2017).

    Article  MathSciNet  ADS  Google Scholar 

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

    Article  MathSciNet  MATH  ADS  Google Scholar 

  5. 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  MathSciNet  MATH  ADS  Google Scholar 

  6. 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  ADS  Google Scholar 

  7. 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 

  8. Bocquillon, E. et al. Electron quantum optics in ballistic chiral conductors. Ann. Phys. 526, 1–30 (2014).

    Article  Google Scholar 

  9. Rosenow, B., Levkivskyi, I. P. & Halperin, B. I. Current correlations from a mesoscopic anyon collider. Phys. Rev. Lett. 116, 156802 (2016).

    Article  ADS  Google Scholar 

  10. Roussel, B., Cabart, C., Fève, G., Thibierge, E. & Degiovanni, P. Electron quantum optics as quantum signal processing. Phys. Status Solidi B 254, 1600621 (2017).

    Article  ADS  Google Scholar 

  11. Glattli, D. C. & Roulleau, P. S. Levitons for electron quantum optics. Phys. Status Solidi B 254, 1600650 (2017).

    Article  ADS  Google Scholar 

  12. Bäuerle, C. et al. Coherent control of single electrons: a review of current progress. Rep. Prog. Phys. 81, 056503 (2018).

    Article  MathSciNet  ADS  Google Scholar 

  13. Ionicioiu, R., Amaratunga, G. & Udrea, F. Quantum computation with ballistic electrons. Int. J. Mod. Phys. B 15, 125–133 (2001).

    Article  MATH  ADS  Google Scholar 

  14. Stace, T. M., Barnes, C. H. W. & Milburn, G. J. Mesoscopic one-way channels for quantum state transfer via the quantum Hall effect. Phys. Rev. Lett. 93, 126804 (2004).

    Article  ADS  Google Scholar 

  15. Fève, G., Degiovanni, P. & Jolicoeur, T. Quantum detection of electronic flying qubits in the integer quantum Hall regime. Phys. Rev. B 77, 035308 (2008).

    Article  ADS  Google Scholar 

  16. Giovannetti, V., Taddei, F., Frustaglia, D. & Fazio, R. Multichannel architecture for electronic quantum Hall interferometry. Phys. Rev. B 77, 155320 (2008).

    Article  ADS  Google Scholar 

  17. Bordone, P., Bellentani, L. & Bertoni, A. Quantum computing with quantum-Hall edge state interferometry. Semicond. Sci. Technol. 34, 103001 (2019).

    Article  ADS  Google Scholar 

  18. Shimizu, T., Nakamura, T., Hashimoto, Y., Endo, A. & Katsumoto, S. Gate-controlled unitary operation on flying spin qubits in quantum Hall edge states. Phys. Rev. B 102, 235302 (2020).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  20. Wilczek, F. Quantum mechanics of fractional-spin particles. Phys. Rev. Lett. 49, 957–959 (1982).

    Article  MathSciNet  ADS  Google Scholar 

  21. Halperin, B. I. & Jain, J. K. (eds) Fractional Quantum Hall Effects (World Scientific, 2020).

  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. Bartolomei, H. et al. Fractional statistics in anyon collisions. Science 368, 173–177 (2020).

    Article  MathSciNet  ADS  Google Scholar 

  24. Wilczek, F. Fractional Statistics and Anyon Superconductivity (World Scientific, 1990).

  25. Berry, M. V. Quantal phase factors accompanying adiabatic changes. Proc. R. Soc. Lond. A Math. Phys. Sci. 392, 45–57 (1984).

    MathSciNet  MATH  ADS  Google Scholar 

  26. Aharonov, Y. & Bohm, D. Significance of electromagnetic potentials in the quantum theory. Phys. Rev. 115, 485–491 (1959).

    Article  MathSciNet  MATH  ADS  Google Scholar 

  27. Wen, X.-G. Topological orders and edge excitations in fractional quantum Hall states. Adv. Phys. 44, 405–473 (1995).

    Article  ADS  Google Scholar 

  28. 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 

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

    Article  ADS  Google Scholar 

  30. 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 

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

    Article  ADS  Google Scholar 

  32. Marquardt, F. & Bruder, C. Influence of dephasing on shot noise in an electronic Mach-Zehnder interferometer. Phys. Rev. Lett. 92, 056805 (2004).

    Article  ADS  Google Scholar 

  33. Chung, V. S.-W., Samuelsson, P. & Büttiker, M. Visibility of current and shot noise in electrical Mach-Zehnder and Hanbury Brown Twiss interferometers. Phys. Rev. B 72, 125320 (2005).

    Article  ADS  Google Scholar 

  34. Förster, H., Pilgram, S. & Büttiker, M. Decoherence and full counting statistics in a Mach-Zehnder interferometer. Phys. Rev. B 72, 075301 (2005).

    Article  ADS  Google Scholar 

  35. 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 

  36. Neder, I., Marquardt, F., Heiblum, M., Mahalu, D. & Umansky, V. Controlled dephasing of electrons by non-Gaussian shot noise. Nat. Phys. 3, 534–537 (2007).

    Article  Google Scholar 

  37. 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 

  38. Litvin, L. V., Tranitz, H. P., Wegscheider, W. & Strunk, C. Decoherence and single electron charging in an electronic Mach-Zehnder interferometer. Phys. Rev. B 75, 033315 (2007).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  40. Litvin, L. V., Helzel, A., Tranitz, H.-P., Wegscheider, W. & Strunk, C. Two beam Aharonov–Bohm interference in the integer quantum Hall regime. Physica E 40, 1706–1708 (2008).

    Article  ADS  Google Scholar 

  41. Litvin, L. V., Helzel, A., Tranitz, H.-P., Wegscheider, W. & Strunk, C. Edge-channel interference controlled by Landau level filling. Phys. Rev. B 78, 075303 (2008).

    Article  ADS  Google Scholar 

  42. 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 

  43. 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 

  44. Roulleau, P. et al. High visibility in an electronic Mach–Zehnder interferometer with random phase fluctuations. Physica E 40, 1048–1050 (2008).

    Article  ADS  Google Scholar 

  45. Roulleau, P. et al. Tuning decoherence with a voltage probe. Phys. Rev. Lett. 102, 236802 (2009).

    Article  ADS  Google Scholar 

  46. Bieri, E. et al. Finite-bias visibility dependence in an electronic Mach-Zehnder interferometer. Phys. Rev. B 79, 245324 (2009).

    Article  ADS  Google Scholar 

  47. Litvin, L. V., Helzel, A., Tranitz, H.-P., Wegscheider, W. & Strunk, C. Phase of the transmission amplitude for a quantum dot embedded in the arm of an electronic Mach-Zehnder interferometer. Phys. Rev. B 81, 205425 (2010).

    Article  ADS  Google Scholar 

  48. Weisz, E. et al. Controlled dephasing of an electron interferometer with a path detector at equilibrium. Phys. Rev. Lett. 109, 250401 (2012).

    Article  ADS  Google Scholar 

  49. Levkivskyi, I. P. & Sukhorukov, E. V. Dephasing in the electronic Mach-Zehnder interferometer at filling factor ν = 2. Phys. Rev. B 78, 045322 (2008).

    Article  ADS  Google Scholar 

  50. Levkivskyi, I. P. & Sukhorukov, E. V. Noise-induced phase transition in the electronic Mach-Zehnder interferometer. Phys. Rev. Lett. 103, 036801 (2009).

    Article  ADS  Google Scholar 

  51. Rosenow, B. & Gefen, Y. Dephasing by a zero-temperature detector and the Friedel sum rule. Phys. Rev. Lett. 108, 256805 (2012).

    Article  ADS  Google Scholar 

  52. Helzel, A. et al. Counting statistics and dephasing transition in an electronic Mach-Zehnder interferometer. Phys. Rev. B 91, 245419 (2015).

    Article  ADS  Google Scholar 

  53. Chalker, J. T., Gefen, Y. & Veillette, M. Y. Decoherence and interactions in an electronic Mach-Zehnder interferometer. Phys. Rev. B 76, 085320 (2007).

    Article  ADS  Google Scholar 

  54. Huynh, P.-A. et al. Quantum coherence engineering in the integer quantum Hall regime. Phys. Rev. Lett. 108, 256802 (2012).

    Article  ADS  Google Scholar 

  55. Duprez, H. et al. Macroscopic electron quantum coherence in a solid-state circuit. Phys. Rev. X 9, 021030 (2019).

    Google Scholar 

  56. Chirolli, L., Venturelli, D., Taddei, F., Fazio, R. & Giovannetti, V. Proposal for a Datta-Das transistor in the quantum Hall regime. Phys. Rev. B 85, 155317 (2012).

    Article  ADS  Google Scholar 

  57. Chirolli, L., Taddei, F., Fazio, R. & Giovannetti, V. Interactions in electronic Mach-Zehnder interferometers with copropagating edge channels. Phys. Rev. Lett. 111, 036801 (2013).

    Article  ADS  Google Scholar 

  58. Karmakar, B. et al. Nanoscale Mach-Zehnder interferometer with spin-resolved quantum Hall edge states. Phys. Rev. B 92, 195303 (2015).

    Article  ADS  Google Scholar 

  59. Deviatov, E. V., Ganczarczyk, A., Lorke, A., Biasiol, G. & Sorba, L. Quantum Hall Mach-Zehnder interferometer far beyond equilibrium. Phys. Rev. B 84, 235313 (2011).

    Article  ADS  Google Scholar 

  60. Deviatov, E. V., Egorov, S. V., Biasiol, G. & Sorba, L. Quantum Hall Mach-Zehnder interferometer at fractional filling factors. EPL 100, 67009 (2012).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  62. 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 

  63. Paradiso, N. et al. Spatially resolved analysis of edge-channel equilibration in quantum Hall circuits. Phys. Rev. B 83, 155305 (2011).

    Article  ADS  Google Scholar 

  64. Paradiso, N. et al. Imaging fractional incompressible stripes in integer quantum Hall systems. Phys. Rev. Lett. 108, 246801 (2012).

    Article  ADS  Google Scholar 

  65. Wei, D. S. et al. Mach-Zehnder interferometry using spin- and valley-polarized quantum Hall edge states in graphene. Sci. Adv. 3, e1700600 (2017).

    Article  ADS  Google Scholar 

  66. Jo, M. et al. Quantum Hall valley splitters and a tunable Mach-Zehnder interferometer in graphene. Phys. Rev. Lett. 126, 146803 (2021).

    Article  ADS  Google Scholar 

  67. Amet, F., Williams, J. R., Watanabe, K., Taniguchi, T. & Goldhaber-Gordon, D. Selective equilibration of spin-polarized quantum Hall edge states in graphene. Phys. Rev. Lett. 112, 196601 (2014).

    Article  ADS  Google Scholar 

  68. Zimmermann, K. et al. Tunable transmission of quantum Hall edge channels with full degeneracy lifting in split-gated graphene devices. Nat. Commun. 8, 14983 (2017).

    Article  ADS  Google Scholar 

  69. Idrisov, E. G., Levkivskyi, I. P. & Sukhorukov, E. V. Dephasing in a Mach-Zehnder interferometer by an Ohmic contact. Phys. Rev. Lett. 121, 026802 (2018).

    Article  ADS  Google Scholar 

  70. Duprez, H. et al. Transmitting the quantum state of electrons across a metallic island with Coulomb interaction. Science 366, 1243–1247 (2019).

    Article  ADS  Google Scholar 

  71. 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 

  72. 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 

  73. 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 

  74. 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 

  75. Byers, N. & Yang, C. N. Theoretical considerations concerning quantized magnetic flux in superconducting cylinders. Phys. Rev. Lett. 7, 46–49 (1961).

    Article  ADS  Google Scholar 

  76. 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 

  77. Jonckheere, T., Devillard, P., Crépieux, A. & Martin, T. Electronic Mach-Zehnder interferometer in the fractional quantum Hall effect. Phys. Rev. B 72, 201305 (2005).

    Article  ADS  Google Scholar 

  78. 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 

  79. Kane, C. L. & Fisher, M. P. A. Impurity scattering and transport of fractional quantum Hall edge states. Phys. Rev. B 51, 13449–13466 (1995).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  81. Wen, X. G. Electrodynamical properties of gapless edge excitations in the fractional quantum Hall states. Phys. Rev. Lett. 64, 2206–2209 (1990).

    Article  ADS  Google Scholar 

  82. Wen, X. G. Chiral Luttinger liquid and the edge excitations in the fractional quantum Hall states. Phys. Rev. B 41, 12838–12844 (1990).

    Article  ADS  Google Scholar 

  83. 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 

  84. Wang, J., Meir, Y. & Gefen, Y. Edge reconstruction in the ν = 2/3 fractional quantum Hall state. Phys. Rev. Lett. 111, 246803 (2013).

    Article  ADS  Google Scholar 

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

    Article  Google Scholar 

  86. Park, J., Rosenow, B. & Gefen, Y. Symmetry-related transport on a fractional quantum Hall edge. Phys. Rev. Res. 3, 023083 (2021).

    Article  Google Scholar 

  87. de C. Chamon, 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 

  88. 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 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  91. Grivnin, A. et al. Nonequilibrated counterpropagating edge modes in the fractional quantum Hall regime. Phys. Rev. Lett. 113, 266803 (2014).

    Article  ADS  Google Scholar 

  92. 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 

  93. Ngo Dinh, S. & Bagrets, D. A. Influence of Coulomb interaction on the Aharonov-Bohm effect in an electronic Fabry-Pérot interferometer. Phys. Rev. B 85, 073403 (2012).

    Article  ADS  Google Scholar 

  94. van Wees, B. J. et al. Observation of zero-dimensional states in a one-dimensional electron interferometer. Phys. Rev. Lett. 62, 2523–2526 (1989).

    Article  ADS  Google Scholar 

  95. 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 

  96. 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 

  97. Godfrey, M. D. et al. Aharonov-Bohm-like oscillations in quantum Hall corrals. Preprint at arXiv https://arxiv.org/abs/0708.2448 (2007).

  98. Deviatov, E. V. & Lorke, A. Experimental realization of a Fabry-Perot-type interferometer by copropagating edge states in the quantum Hall regime. Phys. Rev. B 77, 161302 (2008).

    Article  ADS  Google Scholar 

  99. Zhang, Y. 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 

  100. 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 

  101. 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 

  102. Lin, P. V., Camino, F. E. & Goldman, V. J. Superperiods in interference of e/3 Laughlin quasiparticles encircling filling 2/5 fractional quantum Hall island. Phys. Rev. B 80, 235301 (2009).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  104. 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 

  105. 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 

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

    Article  ADS  Google Scholar 

  107. 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 

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

    Article  ADS  Google Scholar 

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

    Article  Google Scholar 

  110. Röösli, M. P. et al. Observation of quantum Hall interferometer phase jumps due to a change in the number of bulk quasiparticles. Phys. Rev. B 101, 125302 (2020).

    Article  ADS  Google Scholar 

  111. Simmons, J. A., Wei, H. P., Engel, L. W., Tsui, D. C. & Shayegan, M. Resistance fluctuations in narrow AlGaAs/GaAs heterostructures: direct evidence of fractional charge in the fractional quantum Hall effect. Phys. Rev. Lett. 63, 1731–1734 (1989).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  113. Maasilta, I. J. & Goldman, V. J. Tunneling through a coherent “quantum antidot molecule”. Phys. Rev. Lett. 84, 1776–1779 (2000).

    Article  ADS  Google Scholar 

  114. Goldman, V. J., Karakurt, I., Liu, J. & Zaslavsky, A. Invariance of charge of Laughlin quasiparticles. Phys. Rev. B 64, 085319 (2001).

    Article  ADS  Google Scholar 

  115. Goldman, V. J. The quantum antidot electrometer: direct observation of fractional charge. J. Korean Phys. Soc. 39, 512–518 (2003).

    Google Scholar 

  116. Kivelson, S. Semiclassical theory of localized many-anyon states. Phys. Rev. Lett. 65, 3369–3372 (1990).

    Article  ADS  Google Scholar 

  117. Lee, P. A. Comment on “Resistance fluctuations in narrow AlGaAs/GaAs heterostructures: Direct evidence of fractional charge in the fractional quantum Hall effect”. Phys. Rev. Lett. 65, 2206–2206 (1990).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  119. Gefen, Y. & Thouless, D. J. Detection of fractional charge and quenching of the quantum Hall effect. Phys. Rev. B 47, 10423–10436 (1993).

    Article  ADS  Google Scholar 

  120. Camino, F. E., Zhou, W. & Goldman, V. J. Experimental realization of Laughlin quasiparticle interferometers. Physica E 40, 949–953 (2008).

    Article  ADS  Google Scholar 

  121. Ferraro, D. & Sukhorukov, E. Interaction effects in a multi-channel Fabry-Pérot interferometer in the Aharonov-Bohm regime. SciPost Phys. 3, 014 (2017).

    Article  ADS  Google Scholar 

  122. Frigeri, G. A., Scherer, D. D. & Rosenow, B. Sub-periods and apparent pairing in integer quantum Hall interferometers. EPL 126, 67007 (2019).

    Article  Google Scholar 

  123. Frigeri, G. A. & Rosenow, B. Electron pairing in the quantum Hall regime due to neutralon exchange. Phys. Rev. Res. 2, 043396 (2020).

    Article  Google Scholar 

  124. 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 

  125. 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 

  126. Rosenow, B. & Stern, A. Flux superperiods and periodicity transitions in quantum Hall interferometers. Phys. Rev. Lett. 124, 106805 (2020).

    Article  ADS  Google Scholar 

  127. Das Sarma, S., 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 

  128. Fendley, P. & Fradkin, E. Realizing non-Abelian statistics in time-reversal-invariant systems. Phys. Rev. B 72, 024412 (2005).

    Article  ADS  Google Scholar 

  129. Freedman, M., Nayak, C. & Walker, K. Towards universal topological quantum computation in the \(\nu =\frac{5}{2}\) fractional quantum Hall state. Phys. Rev. B 73, 245307 (2006).

    Article  ADS  Google Scholar 

  130. Kitaev, A. Anyons in an exactly solved model and beyond. Ann. Phys. 321, 2–111 (2006).

    Article  MathSciNet  MATH  ADS  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

  132. Morf, R. H. Transition from quantum Hall to compressible states in the second Landau level: new light on the ν = 5/2 enigma. Phys. Rev. Lett. 80, 1505–1508 (1998).

    Article  ADS  Google Scholar 

  133. Chung, Y. C., Heiblum, M. & Umansky, V. Scattering of bunched fractionally charged quasiparticles. Phys. Rev. Lett. 91, 216804 (2003).

    Article  ADS  Google Scholar 

  134. Levin, M., Halperin, B. I. & Rosenow, B. Particle-hole symmetry and the Pfaffian state. Phys. Rev. Lett. 99, 236806 (2007).

    Article  ADS  Google Scholar 

  135. Bishara, W., Fiete, G. A. & Nayak, C. Quantum Hall states at \(\nu =\frac{2}{k+2}\): analysis of the particle-hole conjugates of the general level-k Read-Rezayi states. Phys. Rev. B 77, 241306 (2008).

    Article  ADS  Google Scholar 

  136. Dolev, M., Heiblum, M., Umansky, V., Stern, A. & Mahalu, D. Observation of a quarter of an electron charge at the ν = 5/2 quantum Hall state. Nature 452, 829–834 (2008).

    Article  ADS  Google Scholar 

  137. Carrega, M., Ferraro, D., Braggio, A., Magnoli, N. & Sassetti, M. Anomalous charge tunneling in fractional quantum Hall edge states at a filling factor ν = 5/2. Phys. Rev. Lett. 107, 146404 (2011).

    Article  ADS  Google Scholar 

  138. 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 

  139. Fendley, P., Fisher, M. P. A. & Nayak, C. Edge states and tunneling of non-Abelian quasiparticles in the ν = 5/2 quantum Hall state and p + ip superconductors. Phys. Rev. B 75, 045317 (2007).

    Article  ADS  Google Scholar 

  140. Bishara, W., Bonderson, P., Nayak, C., Shtengel, K. & Slingerland, J. K. Interferometric signature of non-Abelian anyons. Phys. Rev. B 80, 155303 (2009).

    Article  ADS  Google Scholar 

  141. Tiemann, L., Gamez, G., Kumada, N. & Muraki, K. Unraveling the spin polarization of the ν = 5/2 fractional quantum Hall state. Science 335, 828–831 (2012).

    Article  ADS  Google Scholar 

  142. Banerjee, M. et al. Observation of half-integer thermal Hall conductance. Nature 559, 205–210 (2018).

    Article  ADS  Google Scholar 

  143. Willett, R. L. et al. Interference measurements of non-Abelian e/4 & Abelian e/2 quasiparticle braiding. Preprint at arXiv https://arxiv.org/abs/1905.10248 (2019).

  144. 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 

  145. Déprez, C. et al. A tunable Fabry–Pérot quantum Hall interferometer in graphene. Nat. Nanotechnol. 16, 555–562 (2021).

    Article  ADS  Google Scholar 

  146. Ronen, Y. et al. Aharonov–Bohm effect in graphene-based Fabry–Pérot quantum Hall interferometers. Nat. Nanotechnol. 16, 563–569 (2021).

    Article  ADS  Google Scholar 

  147. Ferraro, D., Jonckheere, T., Rech, J. & Martin, T. Electronic quantum optics beyond the integer quantum Hall effect. Phys. Status Solidi B 254, 1600531 (2017).

    Article  ADS  Google Scholar 

  148. Oliver, W. D., Kim, J., Liu, R. C. & Yamamoto, Y. Hanbury Brown and Twiss-type experiment with electrons. Science 284, 299–301 (1999).

    Article  ADS  Google Scholar 

  149. Henny, M. et al. The fermionic Hanbury Brown and Twiss experiment. Science 284, 296–298 (1999).

    Article  ADS  Google Scholar 

  150. Oberholzer, S. et al. The Hanbury Brown and Twiss experiment with fermions. Physica E 6, 314–317 (2000).

    Article  ADS  Google Scholar 

  151. 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 

  152. Samuelsson, P., Sukhorukov, E. V. & Büttiker, M. Two-particle Aharonov-Bohm effect and entanglement in the electronic Hanbury Brown–Twiss setup. Phys. Rev. Lett. 92, 026805 (2004).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  154. Campagnano, G., Zilberberg, O., Gornyi, I. V. & Gefen, Y. Hanbury Brown and Twiss correlations in quantum Hall systems. Phys. Rev. B 88, 235415 (2013).

    Article  ADS  Google Scholar 

  155. Jonckheere, T., Rech, J., Wahl, C. & Martin, T. Electron and hole Hong-Ou-Mandel interferometry. Phys. Rev. B 86, 125425 (2012).

    Article  ADS  Google Scholar 

  156. Freulon, V. et al. Hong-Ou-Mandel experiment for temporal investigation of single-electron fractionalization. Nat. Commun. 6, 6854 (2015).

    Article  ADS  Google Scholar 

  157. Beenakker, C. W. J. & van Houten, H. Quantum transport in semiconductor nanostructures. Solid State Phys. 44, 1–228 (1991).

    Article  Google Scholar 

  158. Landauer, R. Spatial variation of currents and fields due to localized scatterers in metallic conduction. IBM J. Res. Dev. 1, 223–231 (1957).

    Article  MathSciNet  Google Scholar 

  159. Landauer, R. Spatial variation of currents and fields due to localized scatterers in metallic conduction. IBM J. Res. Dev. 32, 306–316 (1988).

    Article  Google Scholar 

  160. van Wees, B. J. et al. Quantized conductance of point contacts in a two-dimensional electron gas. Phys. Rev. Lett. 60, 848 (1988).

    Article  ADS  Google Scholar 

  161. Wharam, D. A. et al. One-dimensional transport and the quantisation of the ballistic resistance. J. Phys. C 21, L209 (1988).

    Article  Google Scholar 

  162. Schäpers, T. Superconductor/Semiconductor Junctions (Springer, 2001).

  163. Braggio, A., Ferraro, D., Carrega, M., Magnoli, N. & Sassetti, M. Environmental induced renormalization effects in quantum Hall edge states due to 1/f noise and dissipation. New J. Phys. 14, 093032 (2012).

    Article  ADS  Google Scholar 

  164. Cohen, Y. et al. Synthesizing a ν = 2/3 fractional quantum Hall effect edge state from counter-propagating ν = 1 and ν = 1/3 states. Nat. Commun. 10, 1920 (2019).

    Article  ADS  Google Scholar 

  165. Nosiglia, C., Park, J., Rosenow, B. & Gefen, Y. Incoherent transport on the ν = 2/3 quantum Hall edge. Phys. Rev. B 98, 115408 (2018).

    Article  ADS  Google Scholar 

  166. Protopopov, I., Gefen, Y. & Mirlin, A. Transport in a disordered ν = 2/3 fractional quantum Hall junction. Ann. Phys. 385, 287–327 (2017).

    Article  MathSciNet  MATH  ADS  Google Scholar 

Download references

Acknowledgements

This activity was partially supported by the SuperTOP project, QuantERA ERA-NET Cofund in Quantum Technologies and by the FET-Open project AndQC. L.C. acknowledges funding by the EU Marie Curie Global Fellowship TOPOCIRCUS 841894 - Simulations of Topological Phases in Superconducting Circuits.

Author information

Authors and Affiliations

Authors

Contributions

All authors contributed to the writing of the manuscript.

Corresponding author

Correspondence to Lucia Sorba.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Peer review information

Nature Reviews Physics thanks Yuval Gefen, Gwendal Feve and the other, anonymous, reviewers for their contribution to the peer review of this work.

Publisher’s note

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

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Carrega, M., Chirolli, L., Heun, S. et al. Anyons in quantum Hall interferometry. Nat Rev Phys 3, 698–711 (2021). https://doi.org/10.1038/s42254-021-00351-0

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s42254-021-00351-0

This article is cited by

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