nLab anyons in the quantum Hall effect -- references

Anyons in fractional quantum Hall systems

References on anyon-excitations (satisfying braid group statistics) in the quantum Hall effect (for more on the application to topological quantum computation see the references there):

The prediction of abelian anyon-excitations in the quantum Hall effect (i.e. satisfying braid group statistics in 1-dimensional linear representations of the braid group) by computation of Berry phases of Laughlin wavefunctions via the quantum adiabatic theorem:

• Bertrand I. Halperin: Statistics of Quasiparticles and the Hierarchy of Fractional Quantized Hall States, Phys. Rev. Lett. 52 (1984) 1583 [doi:10.1103/PhysRevLett.52.1583]

  Erratum, Phys. Rev. Lett. 52 (1984) 2390 [doi:10.1103/PhysRevLett.52.2390.4]

• Daniel P. Arovas, John Robert Schrieffer, Frank Wilczek, Fractional Statistics and the Quantum Hall Effect, Phys. Rev. Lett. 53 (1984) 722 [doi:10.1103/PhysRevLett.53.722]

  (for filling fraction $\nu = 1/q$)

• W. P. Su: Statistics of the fractionally charged excitations in the quantum Hall effect, Phys. Rev. B 34 (1986) 1031 [doi:10.1103/PhysRevB.34.1031]

  (for general filling fraction $\nu = p/q$)

The original discussion of non-abelian anyon-excitations in the quantum Hall effect (i.e. satisfying braid group statistics in higher dimensional linear representations of the braid group, related to modular tensor categories):

• Gregory Moore, Nicholas Read, Nonabelions in the fractional quantum Hall effect, Nucl. Phys. 360B(1991)362 (pdf, doi:10.1016/0550-3213(91)90407-O)

Review:

• Ady Stern, Anyons and the quantum Hall effect – A pedagogical review, Annals of Physics 323 1 (2008) 204-249 [doi:10.1016/j.aop.2007.10.008, arXiv:0711.4697]

• Menelaos Zikidis: Abelian Anyons and Fractional Quantum Hall Effect, Seminar notes (2017) [pdf, pdf]

• Ady Stern: Engineering Non-Abelian Quasi-Particles in Fractional Quantum Hall States – A Pedagogical Introduction, Ch. 9 in: Fractional Quantum Hall Effects, World Scientific (2020) 435-486 [doi:10.1142/9789811217494_0009]

• D. E. Feldman, Bertrand Halperin: Fractional charge and fractional statistics in the quantum Hall effects, Rep. Prog. Phys. 84 (2021) 076501 [doi:10.1088/1361-6633/ac03aa, arXiv:2102.08998]

As potential hardware for topological quantum computing:

• D. V. Averin, V. J. Goldman: Quantum computation with quasiparticles of the fractional quantum Hall effect, Solid State Communications 121 1 (2001) 25-28 [doi:10.1016/S0038-1098(01)00447-1, arXiv:cond-mat/0110193]

• Sankar Das Sarma, Michael Freedman, Chetan Nayak: Topologically-Protected Qubits from a Possible Non-Abelian Fractional Quantum Hall State, Phys. Rev. Lett. 94 166802 (2005) [doi:10.1103/PhysRevLett.94.166802, arXiv:cond-mat/0412343]

• Sergey Bravyi: Universal Quantum Computation with the $\nu = 5/2$ Fractional Quantum Hall State, Phys. Rev. A 73 042313 (2006) [doi:10.1103/PhysRevA.73.042313, arXiv:quant-ph/0511178]

• Maissam Barkeshli, Xiao-Liang Qi: Synthetic Topological Qubits in Conventional Bilayer Quantum Hall Systems, Phys. Rev. X 4 (2014) 041035 [doi:10.1103/PhysRevX.4.041035, arXiv:1302.2673]

• Roger S. K. Mong et al.: Universal Topological Quantum Computation from a Superconductor-Abelian Quantum Hall Heterostructure, Phys. Rev. X 4 (2014) 011036 [doi:10.1103/PhysRevX.4.011036, arXiv:1307.4403]

Observation of anyons in fractional quantum Hall systems

While the occurrence of anyon-excitations in the fractional quantum Hall effect is a robust theoretical prediction (see the references above), and while the fractional quantum Hall effect itself has long been established in experiment, the actual observation of anyons in these systems is subtle.

An early claim of the observation of non-abelian anyons seems to remain unconfirmed:

• Sanghun An, P. Jiang, H. Choi, W. Kang, S. H. Simon, L. N. Pfeiffer, K. W. West, K. W. Baldwin, Braiding of Abelian and Non-Abelian Anyons in the Fractional Quantum Hall Effect [arXiv:1112.3400]

Observation in gallium arsenide ($GaAs$) semiconductor heterostructures:

• H. Bartolomei, et al.: Fractional statistics in anyon collisions, Science 368 6487 (2020) 173-177 [doi:10.1126/science.aaz5601, arXiv:2006.13157]

• James Nakamura et al.: Aharonov–Bohm interference of fractional quantum Hall edge modes, Nature Physics 15 563–569 (2019) [doi:10.1038/s41567-019-0441-8, arXiv:1901.08452]

• James Nakamura et al.: Direct observation of anyonic braiding statistics, Nat. Phys. 16 (2020) 931–936 [doi:10.1038/s41567-020-1019-1, arXiv:2006.14115]

• Bob Yirka, Best evidence yet for existence of anyons, PhysOrg News (July 10, 2020) [phys.org/news/2020-07]

• James Nakamura et al.: Impact of bulk-edge coupling on observation of anyonic braiding statistics in quantum Hall interferometers, Nature Communications 13 344 (2022) [doi:10.1038/s41467-022-27958-w, arXiv:2107.02136]

• James Nakamura et al.: Fabry-Perot interferometry at the $\nu = 2/5$ fractional quantum Hall state, Phys. Rev. X 13 (2023) 041012 [doi:10.1103/PhysRevX.13.041012, arXiv:2304.12415]

• M. Ruelle et al.: Comparing fractional quantum Hall Laughlin and Jain topological orders with the anyon collider, Physical Review X 13 (2023) 011031 [doi:10.1103/PhysRevX.13.011031, arXiv:2210.01066]

• Pierre Glidic et al: Cross-Correlation Investigation of Anyon Statistics in the $\nu = 1/3$ and $2/5$ Fractional Quantum Hall States, Phys. Rev. X 13 011030 (2023) [doi:10.1103/PhysRevX.13.011030, arXiv:2210.01054]

• Pierre Glidic et al.: Signature of anyonic statistics in the integer quantum Hall regime, Nature Commun. 15 6578 (2024) 1 [doi:10.1038/s41467-024-50820-0, arXiv:2401.06069]

and in graphene heterostructures:

• Noah Samuelson et al.: Anyonic statistics and slow quasiparticle dynamics in a graphene fractional quantum Hall interferometer [arXiv:2403.19628]

• Jehyun Kim et al.: Aharonov-Bohm Interference in Even-Denominator Fractional Quantum Hall States [arXiv:2412.19886]