Direct observation of anyonic braiding statistics

Nakamura, James; Liang, Shuang; Gardner, Geoffrey C.; Manfra, Michael J.

doi:10.1038/s41567-020-1019-1

Title: Direct observation of anyonic braiding statistics

Journal Article · Thu Sep 03 00:00:00 EDT 2020 · Nature Physics

DOI:https://doi.org/10.1038/s41567-020-1019-1· OSTI ID:1656816

Nakamura, James ^[1]; Liang, Shuang ^[1];

^[1];

^[1]

Purdue Univ., West Lafayette, IN (United States)

Anyons are quasiparticles that, unlike fermions and bosons, show fractional statistics when two of them are exchanged. Here, we report experimental observation of anyonic braiding statisticsfor the ν 1/3 fractional quantum Hall state using a device that is equivalent to a Fabry-Perot interferometer. Strong Aharonov-Bohm interference of the edge mode is punctuated by discrete phase slips that indicate an anyonic phase of $$\theta$$_anyon = 2π/3. Here, our results are consistent with a recent theory for an interferometer operated in a regime in which device charging energy is small compared to the energy of formation of charged quasiparticles, indicating that we have observed anyonic braiding.

View Accepted Manuscript (DOE)

Cite

Export

Save

Research Organization:: Purdue Univ., West Lafayette, IN (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES)

Grant/Contract Number:: SC0020138

OSTI ID:: 1656816

Journal Information:: Nature Physics, Vol. 16, Issue 9; ISSN 1745-2473

Publisher:: Nature Publishing Group (NPG)Copyright Statement

Country of Publication:: United States

Language:: English

References (55)

Optimization of edge state velocity in the integer quantum Hall regime Sahasrabudhe, H.; Novakovic, B.; Nakamura, J. Physical Review B, Vol. 97, Issue 8 https://doi.org/10.1103/PhysRevB.97.085302	journal	February 2018
Aharonov–Bohm interference of fractional quantum Hall edge modes Nakamura, J.; Fallahi, S.; Sahasrabudhe, H. Nature Physics, Vol. 15, Issue 6 https://doi.org/10.1038/s41567-019-0441-8	journal	March 2019
Flux Superperiods and Periodicity Transitions in Quantum Hall Interferometers Rosenow, Bernd; Stern, Ady Physical Review Letters, Vol. 124, Issue 10 https://doi.org/10.1103/PhysRevLett.124.106805	journal	March 2020
Statistics of Quasiparticles and the Hierarchy of Fractional Quantized Hall States Halperin, B. I. Physical Review Letters, Vol. 52, Issue 18 https://doi.org/10.1103/PhysRevLett.52.1583	journal	April 1984
Interference, Coulomb blockade, and the identification of non-Abelian quantum Hall states Stern, Ady; Rosenow, Bernd; Ilan, Roni Physical Review B, Vol. 82, Issue 8 https://doi.org/10.1103/PhysRevB.82.085321	journal	August 2010
Proposed Experiments to Probe the Non-Abelian $ν = 5 / 2$ Quantum Hall State Stern, Ady; Halperin, Bertrand I. Physical Review Letters, Vol. 96, Issue 1 https://doi.org/10.1103/PhysRevLett.96.016802	journal	January 2006
Charge and statistics of quantum Hall quasi-particles — a numerical study of mean values and fluctuations Kjønsberg, H.; Leinaas, J. M. Nuclear Physics B, Vol. 559, Issue 3 https://doi.org/10.1016/S0550-3213(99)00353-3	journal	October 1999
Detecting Non-Abelian Statistics in the $ν = 5 / 2$ Fractional Quantum Hall State Bonderson, Parsa; Kitaev, Alexei; Shtengel, Kirill Physical Review Letters, Vol. 96, Issue 1 https://doi.org/10.1103/PhysRevLett.96.016803	journal	January 2006
Berry phases for composite fermions: Effective magnetic field and fractional statistics Jeon, Gun Sang; Graham, Kenneth L.; Jain, Jainendra K. Physical Review B, Vol. 70, Issue 12 https://doi.org/10.1103/PhysRevB.70.125316	journal	September 2004
Observation of neutral modes in the fractional quantum Hall regime Bid, Aveek; Ofek, N.; Inoue, H. Nature, Vol. 466, Issue 7306 https://doi.org/10.1038/nature09277	journal	July 2010
Resonant Tunneling in the Quantum Hall Regime: Measurement of Fractional Charge Goldman, V. J.; Su, B. Science, Vol. 267, Issue 5200 https://doi.org/10.1126/science.267.5200.1010	journal	February 1995
Quantized Hall conductance, current-carrying edge states, and the existence of extended states in a two-dimensional disordered potential Halperin, B. I. Physical Review B, Vol. 25, Issue 4 https://doi.org/10.1103/PhysRevB.25.2185	journal	February 1982
Interferometric signature of non-Abelian anyons Bishara, Waheb; Bonderson, Parsa; Nayak, Chetan Physical Review B, Vol. 80, Issue 15 https://doi.org/10.1103/PhysRevB.80.155303	journal	October 2009
Theory of the Fabry-Pérot quantum Hall interferometer Halperin, Bertrand I.; Stern, Ady; Neder, Izhar Physical Review B, Vol. 83, Issue 15 https://doi.org/10.1103/PhysRevB.83.155440	journal	April 2011
Two point-contact interferometer for quantum Hall systems de C. Chamon, C.; Freed, D. E.; Kivelson, S. A. Physical Review B, Vol. 55, Issue 4 https://doi.org/10.1103/PhysRevB.55.2331	journal	January 1997
Observation of interaction-induced modulations of a quantum Hall liquid’s area Sivan, I.; Choi, H. K.; Park, Jinhong Nature Communications, Vol. 7, Issue 1 https://doi.org/10.1038/ncomms12184	journal	July 2016
Experimental realization of a Fabry-Perot-type interferometer by copropagating edge states in the quantum Hall regime Deviatov, E. V.; Lorke, A. Physical Review B, Vol. 77, Issue 16 https://doi.org/10.1103/PhysRevB.77.161302	journal	April 2008
Fractional statistics in anyon collisions Bartolomei, H.; Kumar, M.; Bisognin, R. Science, Vol. 368, Issue 6487 https://doi.org/10.1126/science.aaz5601	journal	April 2020
Direct observation of a fractional charge de-Picciotto, R.; Reznikov, M.; Heiblum, M. Nature, Vol. 389, Issue 6647 https://doi.org/10.1038/38241	journal	September 1997
Fractional Statistics and the Quantum Hall Effect Arovas, Daniel; Schrieffer, J. R.; Wilczek, Frank Physical Review Letters, Vol. 53, Issue 7 https://doi.org/10.1103/PhysRevLett.53.722	journal	August 1984
Measurement of filling factor 5/2 quasiparticle interference with observation of charge e/4 and e/2 period oscillations Willett, R. L.; Pfeiffer, L. N.; West, K. W. Proceedings of the National Academy of Sciences, Vol. 106, Issue 22 https://doi.org/10.1073/pnas.0812599106	journal	May 2009
Topologically Protected Qubits from a Possible Non-Abelian Fractional Quantum Hall State Das Sarma, Sankar; Freedman, Michael; Nayak, Chetan Physical Review Letters, Vol. 94, Issue 16 https://doi.org/10.1103/PhysRevLett.94.166802	journal	April 2005
Edge-channel interference controlled by Landau level filling Litvin, L. V.; Helzel, A.; Tranitz, H. -P. Physical Review B, Vol. 78, Issue 7 https://doi.org/10.1103/PhysRevB.78.075303	journal	August 2008
Two-Dimensional Magnetotransport in the Extreme Quantum Limit Tsui, D. C.; Stormer, H. L.; Gossard, A. C. Physical Review Letters, Vol. 48, Issue 22 https://doi.org/10.1103/PhysRevLett.48.1559	journal	May 1982
Observation of quantum Hall interferometer phase jumps due to a change in the number of bulk quasiparticles Röösli, Marc P.; Brem, Lars; Kratochwil, Benedikt Physical Review B, Vol. 101, Issue 12 https://doi.org/10.1103/PhysRevB.101.125302	journal	March 2020
Aharanov-Bohm Interference and Fractional Statistics in a Quantum Hall Interferometer Kim, Eun-Ah Physical Review Letters, Vol. 97, Issue 21 https://doi.org/10.1103/PhysRevLett.97.216404	journal	November 2006
Anomalous Quantum Hall Effect: An Incompressible Quantum Fluid with Fractionally Charged Excitations Laughlin, R. B. Physical Review Letters, Vol. 50, Issue 18 https://doi.org/10.1103/PhysRevLett.50.1395	journal	May 1983
Incompressible states of the fractionally quantized Hall effect in the presence of impurities: A finite-size study Rezayi, E. H.; Haldane, F. D. M. Physical Review B, Vol. 32, Issue 10 https://doi.org/10.1103/PhysRevB.32.6924	journal	November 1985
Suppression of Interference in Quantum Hall Mach-Zehnder Geometry by Upstream Neutral Modes Goldstein, Moshe; Gefen, Yuval Physical Review Letters, Vol. 117, Issue 27 https://doi.org/10.1103/PhysRevLett.117.276804	journal	December 2016
Robust electron pairing in the integer quantum hall effect regime Choi, H. K.; Sivan, I.; Rosenblatt, A. Nature Communications, Vol. 6, Issue 1 https://doi.org/10.1038/ncomms8435	journal	June 2015
Edge-mode velocities and thermal coherence of quantum Hall interferometers Hu, Zi-Xiang; Rezayi, E. H.; Wan, Xin Physical Review B, Vol. 80, Issue 23 https://doi.org/10.1103/PhysRevB.80.235330	journal	December 2009
Observation of the $e / 3$ Fractionally Charged Laughlin Quasiparticle Saminadayar, L.; Glattli, D. C.; Jin, Y. Physical Review Letters, Vol. 79, Issue 13 https://doi.org/10.1103/PhysRevLett.79.2526	journal	September 1997
Topological Quantum Computation--From Basic Concepts to First Experiments Stern, A.; Lindner, N. H. Science, Vol. 339, Issue 6124 https://doi.org/10.1126/science.1231473	journal	March 2013
Molecular Beam Epitaxy of Ultra-High-Quality AlGaAs/GaAs Heterostructures: Enabling Physics in Low-Dimensional Electronic Systems Manfra, Michael J. Annual Review of Condensed Matter Physics, Vol. 5, Issue 1 https://doi.org/10.1146/annurev-conmatphys-031113-133905	journal	March 2014
Electron interferometry in the quantum Hall regime: Aharonov-Bohm effect of interacting electrons Lin, Ping V.; Camino, F. E.; Goldman, V. J. Physical Review B, Vol. 80, Issue 12 https://doi.org/10.1103/PhysRevB.80.125310	journal	September 2009
Topological dephasing in the $ν = 2 / 3$ fractional quantum Hall regime Park, Jinhong; Gefen, Yuval; Sim, H. -S. Physical Review B, Vol. 92, Issue 24 https://doi.org/10.1103/PhysRevB.92.245437	journal	December 2015
Experimental evidence for new particles in the fractional quantum Hall effect Du, R. R.; Stormer, H. L.; Tsui, D. C. Physical Review Letters, Vol. 70, Issue 19 https://doi.org/10.1103/PhysRevLett.70.2944	journal	May 1993
Composite Fermions Jain, Jainendra K. https://doi.org/10.1017/CBO9780511607561	book	January 2007
Role of interactions in an electronic Fabry-Perot interferometer operating in the quantum Hall effect regime Ofek, N.; Bid, A.; Heiblum, M. Proceedings of the National Academy of Sciences, Vol. 107, Issue 12 https://doi.org/10.1073/pnas.0912624107	journal	March 2010
Fabry-Perot Interferometry with Fractional Charges McClure, D. T.; Chang, W.; Marcus, C. M. Physical Review Letters, Vol. 108, Issue 25 https://doi.org/10.1103/PhysRevLett.108.256804	journal	June 2012
Non-Abelian anyons and topological quantum computation Nayak, Chetan; Simon, Steven H.; Stern, Ady Reviews of Modern Physics, Vol. 80, Issue 3 https://doi.org/10.1103/RevModPhys.80.1083	journal	September 2008
Enhanced Bulk-Edge Coulomb Coupling in Fractional Fabry-Perot Interferometers von Keyserlingk, C. W.; Simon, S. H.; Rosenow, Bernd Physical Review Letters, Vol. 115, Issue 12 https://doi.org/10.1103/PhysRevLett.115.126807	journal	September 2015
Influence of Interactions on Flux and Back-Gate Period of Quantum Hall Interferometers Rosenow, B.; Halperin, B. I. Physical Review Letters, Vol. 98, Issue 10 https://doi.org/10.1103/PhysRevLett.98.106801	journal	March 2007
Dephasing of an electronic two-path interferometer Gurman, Itamar; Sabo, Ron; Heiblum, Moty Physical Review B, Vol. 93, Issue 12 https://doi.org/10.1103/PhysRevB.93.121412	journal	March 2016
Edge-State Velocity and Coherence in a Quantum Hall Fabry-Pérot Interferometer McClure, D. T.; Zhang, Yiming; Rosenow, B. Physical Review Letters, Vol. 103, Issue 20 https://doi.org/10.1103/PhysRevLett.103.206806	journal	November 2009
Semiclassical theory of localized many-anyon states Kivelson, Steven Physical Review Letters, Vol. 65, Issue 27 https://doi.org/10.1103/PhysRevLett.65.3369	journal	December 1990
Distinct signatures for Coulomb blockade and Aharonov-Bohm interference in electronic Fabry-Perot interferometers Zhang, Yiming; McClure, D. T.; Levenson-Falk, E. M. Physical Review B, Vol. 79, Issue 24 https://doi.org/10.1103/PhysRevB.79.241304	journal	June 2009
Melting of Interference in the Fractional Quantum Hall Effect: Appearance of Neutral Modes Bhattacharyya, Rajarshi; Banerjee, Mitali; Heiblum, Moty Physical Review Letters, Vol. 122, Issue 24 https://doi.org/10.1103/PhysRevLett.122.246801	journal	June 2019
Disorder and the fractional quantum Hall effect: Activation energies and the collapse of the gap MacDonald, A. H.; Liu, K. L.; Girvin, S. M. Physical Review B, Vol. 33, Issue 6 https://doi.org/10.1103/PhysRevB.33.4014	journal	March 1986
Modified MBE hardware and techniques and role of gallium purity for attainment of two dimensional electron gas mobility >35×106cm2/V s in AlGaAs/GaAs quantum wells grown by MBE Gardner, Geoffrey C.; Fallahi, Saeed; Watson, John D. Journal of Crystal Growth, Vol. 441 https://doi.org/10.1016/j.jcrysgro.2016.02.010	journal	May 2016
Telegraph noise and the Fabry-Perot quantum Hall interferometer Rosenow, B.; Simon, Steven H. Physical Review B, Vol. 85, Issue 20 https://doi.org/10.1103/PhysRevB.85.201302	journal	May 2012
Proliferation of neutral modes in fractional quantum Hall states Inoue, Hiroyuki; Grivnin, Anna; Ronen, Yuval Nature Communications, Vol. 5, Issue 1 https://doi.org/10.1038/ncomms5067	journal	June 2014
Fractional Statistics in the Fractional Quantum Hall Effect Jeon, Gun Sang; Graham, Kenneth L.; Jain, Jainendra K. Physical Review Letters, Vol. 91, Issue 3 https://doi.org/10.1103/PhysRevLett.91.036801	journal	July 2003
Edge reconstruction in fractional quantum Hall states Sabo, Ron; Gurman, Itamar; Rosenblatt, Amir Nature Physics, Vol. 13, Issue 5 https://doi.org/10.1038/nphys4010	journal	January 2017
Theory of fractional quantum Hall interferometers Levkivskyi, Ivan P.; Fröhlich, Jürg; Sukhorukov, Eugene V. Physical Review B, Vol. 86, Issue 24 https://doi.org/10.1103/PhysRevB.86.245105	journal	December 2012

Similar Records

Impact of bulk-edge coupling on observation of anyonic braiding statistics in quantum Hall interferometers

Journal Article · Mon Jan 17 00:00:00 EST 2022 · Nature Communications · OSTI ID:1656816

Nakamura, J.; Liang, S.; Gardner, G. C.; +1 more

Superperiods in Interference of eÕ3 Laughlin Quasiparticles Encircling Filling 2/5 FractionalQuantum Hall Island

Journal Article · Tue Dec 01 00:00:00 EST 2009 · Physical Review. B, Condensed Matter and Materials Physics · OSTI ID:1656816

Lin, P V; Camino, F; Goldman, V J

Braid groups, anyons and gauge invariance

Journal Article · Sat Jun 01 00:00:00 EDT 1991 · International Journal of Modern Physics B; (United States) · OSTI ID:1656816

Wu, Y S

Related Subjects

75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY

Title: Direct observation of anyonic braiding statistics

Citation Formats

References (55)

Similar Records

Related Subjects