Prediction of a Non-Abelian Fractional Quantum Hall State with f -Wave Pairing of Composite Fermions in Wide Quantum Wells

Faugno, W. N.; Balram, Ajit C.; Barkeshli, Maissam; Jain, J. K.

doi:10.1103/PhysRevLett.123.016802

Title: Prediction of a Non-Abelian Fractional Quantum Hall State with $f$ -Wave Pairing of Composite Fermions in Wide Quantum Wells

Journal Article · Tue Jul 02 00:00:00 EDT 2019 · Physical Review Letters

DOI:https://doi.org/10.1103/PhysRevLett.123.016802· OSTI ID:1606392

Faugno, W. N. ^[1]; Balram, Ajit C. ^[2]; Barkeshli, Maissam ^[3];

^[1]

Pennsylvania State Univ., University Park, PA (United States)
Univ. of Copenhagen (Denmark). The Niels Bohr Inst.
Univ. of Maryland, College Park, MD (United States). Condensed Matter Theory Center and Joint Quantum Inst., Dept. of Physics

We theoretically investigate the nature of the state at quarter filled lowest Landau level and predict that, as the quantum well width is increased, a transition occurs from the composite fermion Fermi sea into a novel non-Abelian fractional quantum Hall state that is topologically equivalent to $f$ -wave pairing of composite fermions. This state is topologically distinct from the familiar $p$ -wave paired Pfaffian state. We compare our calculated phase diagram with experiments and make predictions for many observable quantities.

View Accepted Manuscript (DOE)

View Accepted Manuscript (Publisher)

Cite

Export

Save

Research Organization:: Pennsylvania State Univ., University Park, PA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES); European Union (EU); National Science Foundation (NSF); Alfred P. Sloan Foundation

Grant/Contract Number:: SC0005042

OSTI ID:: 1606392

Alternate ID(s):: OSTI ID: 1546458

Journal Information:: Physical Review Letters, Vol. 123, Issue 1; ISSN 0031-9007

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

Citation Metrics:

Cited by: 25 works

Citation information provided by
Web of Science

References (69)

Parton construction of a wave function in the anti-Pfaffian phase Balram, Ajit C.; Barkeshli, Maissam; Rudner, Mark S. Physical Review B, Vol. 98, Issue 3 https://doi.org/10.1103/PhysRevB.98.035127	journal	July 2018
Is the Composite Fermion a Dirac Particle? Son, Dam Thanh Physical Review X, Vol. 5, Issue 3 https://doi.org/10.1103/PhysRevX.5.031027	journal	September 2015
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
Observation of Chiral Luttinger Behavior in Electron Tunneling into Fractional Quantum Hall Edges Chang, A. M.; Pfeiffer, L. N.; West, K. W. Physical Review Letters, Vol. 77, Issue 12 https://doi.org/10.1103/PhysRevLett.77.2538	journal	September 1996
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
Quantized thermal transport in the fractional quantum Hall effect Kane, C. L.; Fisher, Matthew P. A. Physical Review B, Vol. 55, Issue 23 https://doi.org/10.1103/PhysRevB.55.15832	journal	June 1997
Fermi-liquid-like state in a half-filled Landau level Rezayi, E.; Read, N. Physical Review Letters, Vol. 72, Issue 6 https://doi.org/10.1103/PhysRevLett.72.900	journal	February 1994
Effective theories of the fractional quantum Hall effect: Hierarchy construction Blok, B.; Wen, X. G. Physical Review B, Vol. 42, Issue 13 https://doi.org/10.1103/PhysRevB.42.8145	journal	November 1990
Transition from Abelian to non-Abelian quantum liquids in the second Landau level Wójs, Arkadiusz Physical Review B, Vol. 80, Issue 4 https://doi.org/10.1103/PhysRevB.80.041104	journal	July 2009
Spin polarization of composite fermions and particle-hole symmetry breaking Liu, Yang; Hasdemir, S.; Wójs, A. Physical Review B, Vol. 90, Issue 8 https://doi.org/10.1103/PhysRevB.90.085301	journal	August 2014
Fractional quantum Hall effect in graphene: Quantitative comparison between theory and experiment Balram, Ajit C.; Tőke, Csaba; Wójs, A. Physical Review B, Vol. 92, Issue 7 https://doi.org/10.1103/PhysRevB.92.075410	journal	August 2015
Exotic bilayer crystals in a strong magnetic field Faugno, Wn; Duthie, Aj; Wales, David Apollo - University of Cambridge Repository https://doi.org/10.17863/cam.30571	text	January 2018
Shift and spin vector: New topological quantum numbers for the Hall fluids Wen, X. G.; Zee, A. Physical Review Letters, Vol. 69, Issue 6 https://doi.org/10.1103/PhysRevLett.69.953	journal	August 1992
Numerical exploration of trial wave functions for the particle-hole-symmetric Pfaffian Mishmash, Ryan V.; Mross, David F.; Alicea, Jason Physical Review B, Vol. 98, Issue 8 https://doi.org/10.1103/PhysRevB.98.081107	journal	August 2018
Spontaneous Magnetization of Composite Fermions Park, K.; Jain, J. K. Physical Review Letters, Vol. 83, Issue 26 https://doi.org/10.1103/PhysRevLett.83.5543	journal	December 1999
Incompressible quantum Hall states Jain, J. Physical Review B, Vol. 40, Issue 11 https://doi.org/10.1103/PhysRevB.40.8079	journal	October 1989
Quasi-Particle Properties from Tunneling in the Formula Fractional Quantum Hall State Radu, I. P.; Miller, J. B.; Marcus, C. M. Science, Vol. 320, Issue 5878 https://doi.org/10.1126/science.1157560	journal	May 2008
Observed quantization of anyonic heat flow Banerjee, Mitali; Heiblum, Moty; Rosenblatt, Amir Nature, Vol. 545, Issue 7652 https://doi.org/10.1038/nature22052	journal	April 2017
Entangled Pauli principles: The DNA of quantum Hall fluids Bandyopadhyay, Sumanta; Chen, Li; Ahari, Mostafa Tanhayi Physical Review B, Vol. 98, Issue 16 https://doi.org/10.1103/PhysRevB.98.161118	journal	October 2018
Theory of the half-filled Landau level Halperin, B. I.; Lee, Patrick A.; Read, Nicholas Physical Review B, Vol. 47, Issue 12 https://doi.org/10.1103/PhysRevB.47.7312	journal	March 1993
Microscopic wave functions for the fractional quantized Hall states at $ν = \frac{2}{5} and \frac{2}{7}$ Morf, R.; d'Ambrumenil, N.; Halperin, B. I. Physical Review B, Vol. 34, Issue 4 https://doi.org/10.1103/PhysRevB.34.3037	journal	August 1986
Particle-Hole Symmetry and the Pfaffian State Levin, Michael; Halperin, Bertrand I.; Rosenow, Bernd Physical Review Letters, Vol. 99, Issue 23 https://doi.org/10.1103/PhysRevLett.99.236806	journal	December 2007
Observation of a Fractional Quantum Hall State at $ν = 1 / 4$ in a Wide GaAs Quantum Well Luhman, D. R.; Pan, W.; Tsui, D. C. Physical Review Letters, Vol. 101, Issue 26 https://doi.org/10.1103/PhysRevLett.101.266804	journal	December 2008
Realistic calculations of correlated incompressible electronic states in GaAs- ${Al}_{x}$ ${Ga}_{1 - x}$ As heterostructures and quantum wells Ortalano, M. W.; He, Song; Das Sarma, S. Physical Review B, Vol. 55, Issue 12 https://doi.org/10.1103/PhysRevB.55.7702	journal	March 1997
Particle-Hole Symmetry and the $ν = \frac{5}{2}$ Quantum Hall State Lee, Sung-Sik; Ryu, Shinsei; Nayak, Chetan Physical Review Letters, Vol. 99, Issue 23 https://doi.org/10.1103/PhysRevLett.99.236807	journal	December 2007
Half-integral spin-singlet quantum Hall effect Belkhir, L.; Wu, X. G.; Jain, J. K. Physical Review B, Vol. 48, Issue 20 https://doi.org/10.1103/PhysRevB.48.15245	journal	November 1993
Effective theories of the fractional quantum Hall effect at generic filling fractions Blok, B.; Wen, X. G. Physical Review B, Vol. 42, Issue 13 https://doi.org/10.1103/PhysRevB.42.8133	journal	November 1990
Fractional quantum Hall state at $ν = \frac{1}{4}$ in a wide quantum well Papić, Z.; Möller, G.; Milovanović, M. V. Physical Review B, Vol. 79, Issue 24 https://doi.org/10.1103/PhysRevB.79.245325	journal	June 2009
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
Non-Abelian Parton Fractional Quantum Hall Effect in Multilayer Graphene Wu, Ying-Hai; Shi, Tao; Jain, Jainendra K. Nano Letters, Vol. 17, Issue 8 https://doi.org/10.1021/acs.nanolett.7b01080	journal	July 2017
Nonabelions in the fractional quantum hall effect Moore, Gregory; Read, Nicholas Nuclear Physics B, Vol. 360, Issue 2-3 https://doi.org/10.1016/0550-3213(91)90407-O	journal	August 1991
Alternation and interchange of e/4 and e/2 period interference oscillations consistent with filling factor 5/2 non-Abelian quasiparticles Willett, R. L.; Pfeiffer, L. N.; West, K. W. Physical Review B, Vol. 82, Issue 20 https://doi.org/10.1103/PhysRevB.82.205301	journal	November 2010
Evidence for Developing Fractional Quantum Hall States at Even Denominator $1 / 2$ and $1 / 4$ Fillings in Asymmetric Wide Quantum Wells Shabani, J.; Gokmen, T.; Chiu, Y. T. Physical Review Letters, Vol. 103, Issue 25 https://doi.org/10.1103/PhysRevLett.103.256802	journal	December 2009
Quantitative study of large composite-fermion systems Jain, J. K.; Kamilla, R. K. Physical Review B, Vol. 55, Issue 8 https://doi.org/10.1103/PhysRevB.55.R4895	journal	February 1997
Theory of the fractional quantum Hall effect Tao, R. Journal of Physics C: Solid State Physics, Vol. 19, Issue 2 https://doi.org/10.1088/0022-3719/19/2/013	journal	January 1986
Observation of an even-denominator quantum number in the fractional quantum Hall effect Willett, R.; Eisenstein, J. P.; Störmer, H. L. Physical Review Letters, Vol. 59, Issue 15 https://doi.org/10.1103/PhysRevLett.59.1776	journal	October 1987
Non-Abelian adiabatic statistics and Hall viscosity in quantum Hall states and $p_{x} + i p_{y}$ paired superfluids Read, N. Physical Review B, Vol. 79, Issue 4 https://doi.org/10.1103/PhysRevB.79.045308	journal	January 2009
Even denominator fractional quantum Hall states in higher Landau levels of graphene Kim, Youngwook; Balram, Ajit C.; Taniguchi, Takashi Nature Physics, Vol. 15, Issue 2 https://doi.org/10.1038/s41567-018-0355-x	journal	November 2018
Theory of the edge States in Fractional Quantum hall Effects Wen, Xiao-Gang International Journal of Modern Physics B, Vol. 06, Issue 10 https://doi.org/10.1142/S0217979292000840	journal	May 1992
New fractional quantum Hall state in double-layer two-dimensional electron systems Eisenstein, J. P.; Boebinger, G. S.; Pfeiffer, L. N. Physical Review Letters, Vol. 68, Issue 9 https://doi.org/10.1103/PhysRevLett.68.1383	journal	March 1992
Non-Abelian statistics in the fractional quantum Hall states Wen, X. G. Physical Review Letters, Vol. 66, Issue 6 https://doi.org/10.1103/PhysRevLett.66.802	journal	February 1991
Theory of the fractional quantum Hall effect Jain, J. K. Physical Review B, Vol. 41, Issue 11 https://doi.org/10.1103/PhysRevB.41.7653	journal	April 1990
Stabilization of the Particle-Hole Pfaffian Order by Landau-Level Mixing and Impurities That Break Particle-Hole Symmetry Zucker, P. T.; Feldman, D. E. Physical Review Letters, Vol. 117, Issue 9 https://doi.org/10.1103/PhysRevLett.117.096802	journal	August 2016
Continuum of Chiral Luttinger Liquids at the Fractional Quantum Hall Edge Grayson, M.; Tsui, D. C.; Pfeiffer, L. N. Physical Review Letters, Vol. 80, Issue 5 https://doi.org/10.1103/PhysRevLett.80.1062	journal	February 1998
Composite Fermions Jain, Jainendra K. https://doi.org/10.1017/CBO9780511607561	book	January 2007
Phase diagrams for the stability of the $ν = \frac{1}{2}$ fractional quantum Hall effect in electron systems confined to symmetric, wide GaAs quantum wells Shabani, J.; Liu, Yang; Shayegan, M. Physical Review B, Vol. 88, Issue 24 https://doi.org/10.1103/PhysRevB.88.245413	journal	December 2013
Statistics of Quasiparticles and the Hierarchy of Fractional Quantized Hall States Halperin, B. I. Physical Review Letters, Vol. 52, Issue 26 https://doi.org/10.1103/physrevlett.52.2390.4	journal	June 1984
Composite Fermions in the Hilbert Space of the Lowest Electronic Landau Level Jain, J. K.; Kamilla, R. K. International Journal of Modern Physics B, Vol. 11, Issue 22 https://doi.org/10.1142/S0217979297001301	journal	September 1997
Chiral Luttinger liquids at the fractional quantum Hall edge Chang, A. M. Reviews of Modern Physics, Vol. 75, Issue 4 https://doi.org/10.1103/RevModPhys.75.1449	journal	November 2003
Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries and the fractional quantum Hall effect Read, N.; Green, Dmitry Physical Review B, Vol. 61, Issue 15 https://doi.org/10.1103/PhysRevB.61.10267	journal	April 2000
Correlated States of Electrons in Wide Quantum Wells at Low Fillings: The Role of Charge Distribution Symmetry Shabani, J.; Gokmen, T.; Shayegan, M. Physical Review Letters, Vol. 103, Issue 4 https://doi.org/10.1103/PhysRevLett.103.046805	journal	July 2009
Non-Abelian States with Negative Flux: A New Series of Quantum Hall States Jolicoeur, Th. Physical Review Letters, Vol. 99, Issue 3 https://doi.org/10.1103/PhysRevLett.99.036805	journal	July 2007
Composite-fermion approach for the fractional quantum Hall effect Jain, J. K. Physical Review Letters, Vol. 63, Issue 2 https://doi.org/10.1103/PhysRevLett.63.199	journal	July 1989
Landau-Level Mixing and Particle-Hole Symmetry Breaking for Spin Transitions in the Fractional Quantum Hall Effect Zhang, Yuhe; Wójs, A.; Jain, J. K. Physical Review Letters, Vol. 117, Issue 11 https://doi.org/10.1103/PhysRevLett.117.116803	journal	September 2016
Observation of half-integer thermal Hall conductance Banerjee, Mitali; Heiblum, Moty; Umansky, Vladimir Nature, Vol. 559, Issue 7713 https://doi.org/10.1038/s41586-018-0184-1	journal	June 2018
On Classification of Modular Tensor Categories Rowell, Eric; Stong, Richard; Wang, Zhenghan Communications in Mathematical Physics, Vol. 292, Issue 2 https://doi.org/10.1007/s00220-009-0908-z	journal	August 2009
Exotic bilayer crystals in a strong magnetic field Faugno, W. N.; Duthie, A. J.; Wales, D. J. Physical Review B, Vol. 97, Issue 24 https://doi.org/10.1103/PhysRevB.97.245424	journal	June 2018
Particle-hole symmetry and the Pfaffian state Levin, Michael; Halperin, Bertrand I.; Rosenow, Bernd arXiv https://doi.org/10.48550/arxiv.0707.0483	text	January 2007
Measurement of filling factor 5/2 quasiparticle interference: observation of charge e/4 and e/2 period oscillations Willett, R. L.; Pfeiffer, L. N.; West, K. W. arXiv https://doi.org/10.48550/arxiv.0807.0221	text	January 2008
Transition from Abelian to non-Abelian quantum liquids in the second Landau level Wojs, Arkadiusz arXiv https://doi.org/10.48550/arxiv.0811.4072	text	January 2008
Spin-Polarization of Composite Fermions and Particle-Hole Symmetry Breaking Liu, Yang; Hasdemir, S.; Wójs, A. arXiv https://doi.org/10.48550/arxiv.1406.2387	text	January 2014
Is the Composite Fermion a Dirac Particle? Son, Dam Thanh arXiv https://doi.org/10.48550/arxiv.1502.03446	text	January 2015
Fractional Quantum Hall Effect in Graphene: Quantitative Comparison between Theory and Experiment Balram, Ajit C.; Tőke, Csaba; Wójs, A. arXiv https://doi.org/10.48550/arxiv.1508.01758	text	January 2015
Non-Abelian Parton Fractional Quantum Hall Effect in Multilayer Graphene Wu, Ying-Hai; Shi, Tao; Jain, Jainendra K. arXiv https://doi.org/10.48550/arxiv.1603.02153	text	January 2016
Entangled Pauli Principles: the DNA of Quantum Hall Fluids Bandyopadhyay, Sumanta; Chen, Li; Ahari, Mostafa Tanhayi arXiv https://doi.org/10.48550/arxiv.1803.00975	text	January 2018
Numerical exploration of trial wave functions for the particle-hole-symmetric Pfaffian Mishmash, Ryan V.; Mross, David F.; Alicea, Jason arXiv https://doi.org/10.48550/arxiv.1804.01107	text	January 2018
Even denominator fractional quantum Hall states in higher Landau levels of graphene Kim, Youngwook; Balram, Ajit C.; Taniguchi, Takashi arXiv https://doi.org/10.48550/arxiv.1807.08375	text	January 2018
Composite Fermions in the Hilbert Space of the Lowest Electronic Landau Level Jain, J. K.; Kamilla, R. K. arXiv https://doi.org/10.48550/arxiv.cond-mat/9704031	text	January 1997
Spontaneous Magnetization of Composite Fermions Park, K.; Jain, J. K. arXiv https://doi.org/10.48550/arxiv.cond-mat/9910285	text	January 1999

Cited By (1)

Identification of topological order in the fractional quantum Hall state at $ν = 1 / 4$ Ma, Ken K. W. Physical Review B, Vol. 100, Issue 20 https://doi.org/10.1103/physrevb.100.205306	journal	November 2019

Figures / Tables (12)

Similar Records

Next-generation even-denominator fractional quantum Hall states of interacting composite fermions

Journal Article · Tue Dec 19 00:00:00 EST 2023 · Proceedings of the National Academy of Sciences of the United States of America · OSTI ID:1606392

Wang, Chengyu; Gupta, Adbhut; Madathil, Pranav T.; +5 more

Even denominator fractional quantum Hall states in higher Landau levels of graphene

Journal Article · Mon Nov 26 00:00:00 EST 2018 · Nature Physics · OSTI ID:1606392

Kim, Youngwook; Balram, Ajit C.; Taniguchi, Takashi; +3 more

Partons as unique ground states of quantum Hall parent Hamiltonians: The case of Fibonacci anyons

Journal Article · Wed Aug 02 00:00:00 EDT 2023 · SciPost Physics · OSTI ID:1606392

Tanhayi Ahari, Mostafa; Bandyopadhyay, Sumanta; Nussinov, Zohar; +2 more

Related Subjects

75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
topological superconductivity
composite fermions
fractional quantum Hall effect

Title: Prediction of a Non-Abelian Fractional Quantum Hall State with f -Wave Pairing of Composite Fermions in Wide Quantum Wells

Citation Formats