Formation of helical domain walls in the fractional quantum Hall regime as a step toward realization of high-order non-Abelian excitations

Wu, Tailung; Wan, Zhong; Kazakov, Aleksandr; Wang, Ying; Simion, George; Liang, Jingcheng; West, Kenneth W.; Baldwin, Kirk; Pfeiffer, Loren N.; Lyanda-Geller, Yuli; Rokhinson, Leonid P.

doi:10.1103/PhysRevB.97.245304

Formation of helical domain walls in the fractional quantum Hall regime as a step toward realization of high-order non-Abelian excitations

Journal Article · Thu Jun 07 00:00:00 EDT 2018 · Physical Review. B

DOI:https://doi.org/10.1103/PhysRevB.97.245304· OSTI ID:2883476

Wu, Tailung ^[1]; Wan, Zhong ^[1]; Kazakov, Aleksandr ^[1]; Wang, Ying ^[1]; Simion, George ^[1]; Liang, Jingcheng ^[1]; West, Kenneth W. ^[2]; Baldwin, Kirk ^[2]; Pfeiffer, Loren N. ^[2]; Lyanda-Geller, Yuli ^[1]; Rokhinson, Leonid P. ^[1]

Purdue University, West Lafayette, IN (United States)
Princeton University, NJ (United States)

We propose an experimentally feasible platform to realize parafermions (high-order non-Abelian excitations) based on spin transitions in the fractional quantum Hall effect regime. As a proof of concept we demonstrate a local control of the spin transition at a filling factor 2/3 and formation of a conducting fractional helical domain wall (fhDW) along a gate boundary. Coupled to an 𝑠-wave superconductor these fhDWs are expected to support parafermionic excitations. Here, we present exact diagonalization numerical studies of fhDWs and show that they indeed possess electronic and magnetic structures needed for the formation of parafermions. A reconfigurable network of fhDWs will allow manipulation and braiding of parafermionic excitations in multigate devices.

View Accepted Manuscript (DOE)

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

Sponsoring Organization:: Department of Defense Office of Naval Research; National Science Foundation (NSF); USDOE

Grant/Contract Number:: SC0008630; SC0010544

OSTI ID:: 2883476

Alternate ID(s):: OSTI ID: 1540889
OSTI ID: 1441025

Journal Information:: Physical Review. B, Journal Name: Physical Review. B Journal Issue: 24 Vol. 97; ISSN 2469-9969; ISSN 2469-9950

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

References (35)

Composite Fermions Jain, Jainendra K. https://doi.org/10.1017/CBO9780511607561	book	January 2007
Quantum Theory of the Electron Liquid Giuliani, Gabriele; Vignale, Giovanni https://doi.org/10.1017/CBO9780511619915	book	August 2012
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
Exotic non-Abelian anyons from conventional fractional quantum Hall states Clarke, David J.; Alicea, Jason; Shtengel, Kirill Nature Communications, Vol. 4, Issue 1 https://doi.org/10.1038/ncomms2340	journal	January 2013
Induced superconductivity in high-mobility two-dimensional electron gas in gallium arsenide heterostructures Wan, Zhong; Kazakov, Aleksandr; Manfra, Michael J. Nature Communications, Vol. 6, Issue 1 https://doi.org/10.1038/ncomms8426	journal	June 2015
Real-space imaging of fractional quantum Hall liquids Hayakawa, Junichiro; Muraki, Koji; Yusa, Go Nature Nanotechnology, Vol. 8, Issue 1 https://doi.org/10.1038/nnano.2012.209	journal	December 2012
Local thermometry of neutral modes on the quantum Hall edge Venkatachalam, Vivek; Hart, Sean; Pfeiffer, Loren Nature Physics, Vol. 8, Issue 9 https://doi.org/10.1038/nphys2384	journal	August 2012
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
Microscopic manifestation of the spin phase transition at filling factor 2/3 Verdene, Basile; Martin, Jens; Gamez, Gerardo Nature Physics, Vol. 3, Issue 6 https://doi.org/10.1038/nphys588	journal	April 2007
Parafermionic edge zero modes in Z _n -invariant spin chains Fendley, Paul Journal of Statistical Mechanics: Theory and Experiment, Vol. 2012, Issue 11 https://doi.org/10.1088/1742-5468/2012/11/P11020	journal	November 2012
Resources required for topological quantum factoring Baraban, M.; Bonesteel, N. E.; Simon, S. H. Physical Review A, Vol. 81, Issue 6 https://doi.org/10.1103/PhysRevA.81.062317	journal	June 2010
Evidence for a spin transition in the ν=2/3 fractional quantum Hall effect Eisenstein, J. P.; Stormer, H. L.; Pfeiffer, L. N. Physical Review B, Vol. 41, Issue 11 https://doi.org/10.1103/PhysRevB.41.7910	journal	April 1990
Topological structures, universality classes, and statistics screening in the anyon superfluid Wen, X. G.; Zee, A. Physical Review B, Vol. 44, Issue 1 https://doi.org/10.1103/PhysRevB.44.274	journal	July 1991
Sharp and smooth boundaries of quantum Hall liquids Chamon, C. de C.; Wen, X. G. Physical Review B, Vol. 49, Issue 12 https://doi.org/10.1103/PhysRevB.49.8227	journal	March 1994
Structure of fractional edge states: A composite-fermion approach Chklovskii, Dmitri B. Physical Review B, Vol. 51, Issue 15 https://doi.org/10.1103/PhysRevB.51.9895	journal	April 1995
Topological phase transition in the ν=2/3 quantum Hall effect McDonald, I. A.; Haldane, F. D. M. Physical Review B, Vol. 53, Issue 23 https://doi.org/10.1103/PhysRevB.53.15845	journal	June 1996
Edge excitations of the ν= spin-singlet quantum Hall state Moore, J. E.; Haldane, F. D. M. Physical Review B, Vol. 55, Issue 12 https://doi.org/10.1103/PhysRevB.55.7818	journal	March 1997
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
Microscopic study of edge excitations of spin-polarized and spin-unpolarized ν = 2 / 3 fractional quantum Hall effect Wu, Ying-Hai; Sreejith, G. J.; Jain, Jainendra K. Physical Review B, Vol. 86, Issue 11 https://doi.org/10.1103/PhysRevB.86.115127	journal	September 2012
In-plane electric fields and the ν = 5 2 fractional quantum Hall effect in a disk geometry Tylan-Tyler, Anthony; Lyanda-Geller, Yuli Physical Review B, Vol. 95, Issue 12 https://doi.org/10.1103/PhysRevB.95.121302	journal	March 2017
Impurity-generated non-Abelions Simion, G.; Kazakov, A.; Rokhinson, L. P. Physical Review B, Vol. 97, Issue 24 https://doi.org/10.1103/PhysRevB.97.245107	journal	June 2018
Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures Lutchyn, Roman M.; Sau, Jay D.; Das Sarma, S. Physical Review Letters, Vol. 105, Issue 7 https://doi.org/10.1103/PhysRevLett.105.077001	journal	August 2010
Helical Liquids and Majorana Bound States in Quantum Wires Oreg, Yuval; Refael, Gil; von Oppen, Felix Physical Review Letters, Vol. 105, Issue 17 https://doi.org/10.1103/PhysRevLett.105.177002	journal	October 2010
Mesoscopic Transport in Electrostatically Defined Spin-Full Channels in Quantum Hall Ferromagnets Kazakov, Aleksandr; Simion, George; Lyanda-Geller, Yuli Physical Review Letters, Vol. 119, Issue 4 https://doi.org/10.1103/PhysRevLett.119.046803	journal	July 2017
Fractional Quantization of the Hall Effect: A Hierarchy of Incompressible Quantum Fluid States Haldane, F. D. M. Physical Review Letters, Vol. 51, Issue 7 https://doi.org/10.1103/PhysRevLett.51.605	journal	August 1983
Edge channels for the fractional quantum Hall effect Beenakker, C. W. J. Physical Review Letters, Vol. 64, Issue 2 https://doi.org/10.1103/PhysRevLett.64.216	journal	January 1990
Edge states in the fractional-quantum-Hall-effect regime MacDonald, A. H. Physical Review Letters, Vol. 64, Issue 2 https://doi.org/10.1103/PhysRevLett.64.220	journal	January 1990
Randomness at the edge: Theory of quantum Hall transport at filling ν=2/3 Kane, C. L.; Fisher, Matthew P. A.; Polchinski, J. Physical Review Letters, Vol. 72, Issue 26 https://doi.org/10.1103/PhysRevLett.72.4129	journal	June 1994
Spin-Orbit Coupling Effect on Quantum Hall Ferromagnets with Vanishing Zeeman Energy Fal'ko, Vladimir I.; Iordanskii, S. V. Physical Review Letters, Vol. 84, Issue 1 https://doi.org/10.1103/PhysRevLett.84.127	journal	January 2000
Ising Ferromagnetism and Domain Morphology in the Fractional Quantum Hall Regime Smet, J. H.; Deutschmann, R. A.; Wegscheider, W. Physical Review Letters, Vol. 86, Issue 11 https://doi.org/10.1103/PhysRevLett.86.2412	journal	March 2001
Universal Topological Quantum Computation from a Superconductor-Abelian Quantum Hall Heterostructure Mong, Roger S. K.; Clarke, David J.; Alicea, Jason Physical Review X, Vol. 4, Issue 1 https://doi.org/10.1103/PhysRevX.4.011036	journal	March 2014
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
Topological Phases with Parafermions: Theory and Blueprints Alicea, Jason; Fendley, Paul Annual Review of Condensed Matter Physics, Vol. 7, Issue 1 https://doi.org/10.1146/annurev-conmatphys-031115-011336	journal	March 2016
Three-Dimensional Topological Insulators Hasan, M. Zahid; Moore, Joel E. Annual Review of Condensed Matter Physics, Vol. 2, Issue 1 https://doi.org/10.1146/annurev-conmatphys-062910-140432	journal	March 2011
The Quantum Spin Hall Effect Maciejko, Joseph; Hughes, Taylor L.; Zhang, Shou-Cheng Annual Review of Condensed Matter Physics, Vol. 2, Issue 1 https://doi.org/10.1146/annurev-conmatphys-062910-140538	journal	March 2011

Similar Records

Parafermions, induced edge states, and domain walls in fractional quantum Hall effect spin transitions

Journal Article · Tue Aug 27 20:00:00 EDT 2019 · Physical Review. B · OSTI ID:2877773

Related Subjects

Anyons
Fractional quantum Hall effect
Topological quantum computing

Formation of helical domain walls in the fractional quantum Hall regime as a step toward realization of high-order non-Abelian excitations

Citation Formats

References (35)

Similar Records

Related Subjects