Fractional Quantum Hall Effect at : The Parton Paradigm for the Second Landau Level
Abstract
Here, the unexpected appearance of a fractional quantum Hall effect (FQHE) plateau at ν = 2 + 6/13 offers a clue into the physical mechanism of the FQHE in the second Landau level (SLL). Here we propose a “ $$\bar{3}$$ $$\bar{2}$$111” parton wave function, which is topologically distinct from the 6/13 state in the lowest Landau level. We demonstrate the $$\bar{3}$$ $$\bar{2}$$111 state to be a good candidate for the ν = 2 + 6/13 FQHE, and make predictions for experimentally measurable properties that can reveal the nature of this state. Furthermore, we propose that the “n$$\bar{2}$$111” family of parton states naturally describes many observed SLL FQHE plateaus.
- Authors:
-
- Univ. of Copenhagen, Copenhagen (Denmark)
- Korea Institute for Advanced Study, Seoul (Korea)
- Univ. of Maryland, College Park, MD (United States)
- Pennsylvania State Univ., University Park, PA (United States)
- Publication Date:
- Research Org.:
- Pennsylvania State Univ., University Park, PA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES)
- OSTI Identifier:
- 1489111
- Alternate Identifier(s):
- OSTI ID: 1480372
- Grant/Contract Number:
- SC0005042
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review Letters
- Additional Journal Information:
- Journal Volume: 121; Journal Issue: 18; Journal ID: ISSN 0031-9007
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; fractional quantum Hall effect; composite fermions; partons
Citation Formats
Balram, Ajit C., Mukherjee, Sutirtha, Park, Kwon, Barkeshli, Maissam, Rudner, Mark S., and Jain, J. K. Fractional Quantum Hall Effect at ν=2+6/13 : The Parton Paradigm for the Second Landau Level. United States: N. p., 2018.
Web. doi:10.1103/PhysRevLett.121.186601.
Balram, Ajit C., Mukherjee, Sutirtha, Park, Kwon, Barkeshli, Maissam, Rudner, Mark S., & Jain, J. K. Fractional Quantum Hall Effect at ν=2+6/13 : The Parton Paradigm for the Second Landau Level. United States. https://doi.org/10.1103/PhysRevLett.121.186601
Balram, Ajit C., Mukherjee, Sutirtha, Park, Kwon, Barkeshli, Maissam, Rudner, Mark S., and Jain, J. K. Thu .
"Fractional Quantum Hall Effect at ν=2+6/13 : The Parton Paradigm for the Second Landau Level". United States. https://doi.org/10.1103/PhysRevLett.121.186601. https://www.osti.gov/servlets/purl/1489111.
@article{osti_1489111,
title = {Fractional Quantum Hall Effect at ν=2+6/13 : The Parton Paradigm for the Second Landau Level},
author = {Balram, Ajit C. and Mukherjee, Sutirtha and Park, Kwon and Barkeshli, Maissam and Rudner, Mark S. and Jain, J. K.},
abstractNote = {Here, the unexpected appearance of a fractional quantum Hall effect (FQHE) plateau at ν = 2 + 6/13 offers a clue into the physical mechanism of the FQHE in the second Landau level (SLL). Here we propose a “ $\bar{3}$ $\bar{2}$111” parton wave function, which is topologically distinct from the 6/13 state in the lowest Landau level. We demonstrate the $\bar{3}$ $\bar{2}$111 state to be a good candidate for the ν = 2 + 6/13 FQHE, and make predictions for experimentally measurable properties that can reveal the nature of this state. Furthermore, we propose that the “n$\bar{2}$111” family of parton states naturally describes many observed SLL FQHE plateaus.},
doi = {10.1103/PhysRevLett.121.186601},
journal = {Physical Review Letters},
number = 18,
volume = 121,
place = {United States},
year = {2018},
month = {11}
}
Free Publicly Available Full Text
Publisher's Version of Record
Other availability
Search WorldCat to find libraries that may hold this journal
Cited by: 1 work
Citation information provided by
Web of Science
Web of Science
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.
Works referenced in this record:
Parton construction of a wave function in the anti-Pfaffian phase
journal, July 2018
- Balram, Ajit C.; Barkeshli, Maissam; Rudner, Mark S.
- Physical Review B, Vol. 98, Issue 3
Activation gaps of fractional quantum Hall effect in the second Landau level
journal, February 2008
- Choi, H. C.; Kang, W.; Das Sarma, S.
- Physical Review B, Vol. 77, Issue 8
Fractional Quantization of the Hall Effect: A Hierarchy of Incompressible Quantum Fluid States
journal, August 1983
- Haldane, F. D. M.
- Physical Review Letters, Vol. 51, Issue 7
Beyond paired quantum Hall states: Parafermions and incompressible states in the first excited Landau level
journal, March 1999
- Read, N.; Rezayi, E.
- Physical Review B, Vol. 59, Issue 12
Effective theories of the fractional quantum Hall effect: Hierarchy construction
journal, November 1990
- Blok, B.; Wen, X. G.
- Physical Review B, Vol. 42, Issue 13
Transition from Abelian to non-Abelian quantum liquids in the second Landau level
journal, July 2009
- Wójs, Arkadiusz
- Physical Review B, Vol. 80, Issue 4
Electron Correlation in the Second Landau Level: A Competition Between Many Nearly Degenerate Quantum Phases
journal, October 2004
- Xia, J. S.; Pan, W.; Vicente, C. L.
- Physical Review Letters, Vol. 93, Issue 17
Shift and spin vector: New topological quantum numbers for the Hall fluids
journal, August 1992
- Wen, X. G.; Zee, A.
- Physical Review Letters, Vol. 69, Issue 6
Fractional Quantum Hall Effect of Composite Fermions
journal, January 2003
- Pan, W.; Stormer, H. L.; Tsui, D. C.
- Physical Review Letters, Vol. 90, Issue 1
Observation of neutral modes in the fractional quantum Hall regime
journal, July 2010
- Bid, Aveek; Ofek, N.; Inoue, H.
- Nature, Vol. 466, Issue 7306
Excitation gap in the fractional quantum Hall effect: Finite layer thickness corrections
journal, February 1986
- Zhang, F. C.; Das Sarma, S.
- Physical Review B, Vol. 33, Issue 4
Classification of disordered phases of quantum Hall edge states
journal, April 1998
- Moore, Joel E.; Wen, Xiao-Gang
- Physical Review B, Vol. 57, Issue 16
Incompressible quantum Hall states
journal, October 1989
- Jain, J.
- Physical Review B, Vol. 40, Issue 11
Excitation gaps in fractional quantum Hall states: An exact diagonalization study
journal, August 2002
- Morf, R. H.; d’Ambrumenil, N.; Das Sarma, S.
- Physical Review B, Vol. 66, Issue 7
Observed quantization of anyonic heat flow
journal, April 2017
- Banerjee, Mitali; Heiblum, Moty; Rosenblatt, Amir
- Nature, Vol. 545, Issue 7652
Fractional quantum Hall states in higher Landau levels
journal, January 1988
- d'Ambrumenil, N.; Reynolds, A. M.
- Journal of Physics C: Solid State Physics, Vol. 21, Issue 1
Theory of the half-filled Landau level
journal, March 1993
- Halperin, B. I.; Lee, Patrick A.; Read, Nicholas
- Physical Review B, Vol. 47, Issue 12
Enigmatic 12/5 fractional quantum Hall effect
journal, August 2016
- Pakrouski, Kiryl; Troyer, Matthias; Wu, Yang-Le
- Physical Review B, Vol. 94, Issue 7
Particle-Hole Symmetry and the Pfaffian State
journal, December 2007
- Levin, Michael; Halperin, Bertrand I.; Rosenow, Bernd
- Physical Review Letters, Vol. 99, Issue 23
Fermi wave vector for the partially spin-polarized composite-fermion Fermi sea
journal, December 2017
- Balram, Ajit C.; Jain, J. K.
- Physical Review B, Vol. 96, Issue 23
Particle-Hole Symmetry and the Quantum Hall State
journal, December 2007
- Lee, Sung-Sik; Ryu, Shinsei; Nayak, Chetan
- Physical Review Letters, Vol. 99, Issue 23
Spinful composite fermions in a negative effective field
journal, June 2012
- Davenport, Simon C.; Simon, Steven H.
- Physical Review B, Vol. 85, Issue 24
Effective theories of the fractional quantum Hall effect at generic filling fractions
journal, November 1990
- Blok, B.; Wen, X. G.
- Physical Review B, Vol. 42, Issue 13
Non-Abelian Parton Fractional Quantum Hall Effect in Multilayer Graphene
journal, July 2017
- Wu, Ying-Hai; Shi, Tao; Jain, Jainendra K.
- Nano Letters, Vol. 17, Issue 8
Tunable interacting composite fermion phases in a half-filled bilayer-graphene Landau level
journal, September 2017
- Zibrov, A. A.; Kometter, C.; Zhou, H.
- Nature, Vol. 549, Issue 7672
Nonabelions in the fractional quantum hall effect
journal, August 1991
- Moore, Gregory; Read, Nicholas
- Nuclear Physics B, Vol. 360, Issue 2-3
Spontaneous polarization of composite fermions in the Landau level of graphene
journal, November 2015
- Balram, Ajit C.; Tőke, Csaba; Wójs, A.
- Physical Review B, Vol. 92, Issue 20
Competing Topological Orders in the Quantum Hall State
journal, January 2012
- Bonderson, Parsa; Feiguin, Adrian E.; Möller, Gunnar
- Physical Review Letters, Vol. 108, Issue 3
Fractional quantum Hall states of clustered composite fermions
journal, May 2004
- Wójs, Arkadiusz; Yi, Kyung-Soo; Quinn, John J.
- Physical Review B, Vol. 69, Issue 20
Observation of an even-denominator quantum number in the fractional quantum Hall effect
journal, October 1987
- Willett, R.; Eisenstein, J. P.; Störmer, H. L.
- Physical Review Letters, Vol. 59, Issue 15
Two-Dimensional Magnetotransport in the Extreme Quantum Limit
journal, May 1982
- Tsui, D. C.; Stormer, H. L.; Gossard, A. C.
- Physical Review Letters, Vol. 48, Issue 22
Quasiholes of and quantum Hall states: Size estimates via exact diagonalization and density-matrix renormalization group
journal, March 2014
- Johri, Sonika; Papić, Z.; Bhatt, R. N.
- Physical Review B, Vol. 89, Issue 11
Collective states of non-Abelian quasiparticles in a magnetic field
journal, May 2009
- Levin, Michael; Halperin, Bertrand I.
- Physical Review B, Vol. 79, Issue 20
Non-Abelian adiabatic statistics and Hall viscosity in quantum Hall states and paired superfluids
journal, January 2009
- Read, N.
- Physical Review B, Vol. 79, Issue 4
Nonconventional Odd-Denominator Fractional Quantum Hall States in the Second Landau Level
journal, December 2010
- Kumar, A.; Csáthy, G. A.; Manfra, M. J.
- Physical Review Letters, Vol. 105, Issue 24
Theory of the edge States in Fractional Quantum hall Effects
journal, May 1992
- Wen, Xiao-Gang
- International Journal of Modern Physics B, Vol. 06, Issue 10
Transition from Quantum Hall to Compressible States in the Second Landau Level: New Light on the Enigma
journal, February 1998
- Morf, R. H.
- Physical Review Letters, Vol. 80, Issue 7
Skyrmions in the fractional quantum Hall effect
journal, July 1996
- Kamilla, R. K.; Wu, X. G.; Jain, J. K.
- Solid State Communications, Vol. 99, Issue 4
Phase Diagram of the Fractional Quantum Hall Effect: Effects of Landau-Level Mixing and Nonzero Width
journal, April 2015
- Pakrouski, Kiryl; Peterson, Michael R.; Jolicoeur, Thierry
- Physical Review X, Vol. 5, Issue 2
Spontaneous Particle-Hole Symmetry Breaking in the Fractional Quantum Hall Effect
journal, October 2008
- Peterson, Michael R.; Park, Kwon; Das Sarma, S.
- Physical Review Letters, Vol. 101, Issue 15
Upstream Neutral Modes in the Fractional Quantum Hall Effect Regime: Heat Waves or Coherent Dipoles
journal, May 2012
- Gross, Yaron; Dolev, Merav; Heiblum, Moty
- Physical Review Letters, Vol. 108, Issue 22
Nature of composite fermions and the role of particle-hole symmetry: A microscopic account
journal, June 2016
- Balram, Ajit C.; Jain, J. K.
- Physical Review B, Vol. 93, Issue 23
Non-Abelian statistics in the fractional quantum Hall states
journal, February 1991
- Wen, X. G.
- Physical Review Letters, Vol. 66, Issue 6
Composite fermions in a negative effective magnetic field: A Monte Carlo study
journal, July 2005
- Möller, Gunnar; Simon, Steven H.
- Physical Review B, Vol. 72, Issue 4
Surprising robustness of particle-hole symmetry for composite-fermion liquids
journal, September 2017
- Sreejith, G. J.; Zhang, Yuhe; Jain, J. K.
- Physical Review B, Vol. 96, Issue 12
Competing states for the fractional quantum Hall effect in the 1/3-filled second Landau level
journal, September 2017
- Jeong, Jae-Seung; Lu, Hantao; Lee, Ki Hoon
- Physical Review B, Vol. 96, Issue 12
Theory of the fractional quantum Hall effect
journal, April 1990
- Jain, J. K.
- Physical Review B, Vol. 41, Issue 11
Enigmatic State: A Prototype for Unconventional Fractional Quantum Hall Effect
journal, January 2014
- Mukherjee, Sutirtha; Mandal, Sudhansu S.; Wu, Ying-Hai
- Physical Review Letters, Vol. 112, Issue 1
Fibonacci anyons and charge density order in the 12/5 and 13/5 quantum Hall plateaus
journal, March 2017
- Mong, Roger S. K.; Zaletel, Michael P.; Pollmann, Frank
- Physical Review B, Vol. 95, Issue 11
Mixed states of composite fermions carrying two and four vortices
journal, November 2000
- Park, K.; Jain, J. K.
- Physical Review B, Vol. 62, Issue 20
Role of Exciton Screening in the Fractional Quantum Hall Effect
journal, April 2013
- Balram, Ajit C.; Wu, Ying-Hai; Sreejith, G. J.
- Physical Review Letters, Vol. 110, Issue 18
Fractional Quantum Hall States at and and Their Non-Abelian Nature
journal, September 2015
- Zhu, W.; Gong, S. S.; Haldane, F. D. M.
- Physical Review Letters, Vol. 115, Issue 12
Excitation gaps of incompressible composite fermion states: Approach to the Fermi sea
journal, October 2002
- Scarola, V. W.; Lee, S. -Y.; Jain, J. K.
- Physical Review B, Vol. 66, Issue 15
Phase diagram for bilayer quantum Hall effect at total filling
journal, April 2008
- Shi, Chuntai; Jolad, Shivakumar; Regnault, Nicolas
- Physical Review B, Vol. 77, Issue 15
Composite fermions and broken symmetries in graphene
journal, January 2015
- Amet, F.; Bestwick, A. J.; Williams, J. R.
- Nature Communications, Vol. 6, Issue 1
Finite-temperature behavior in the second Landau level of the two-dimensional electron gas
journal, June 2018
- Shingla, V.; Kleinbaum, E.; Kumar, A.
- Physical Review B, Vol. 97, Issue 24
Abelian and non-Abelian states in bilayer fractional quantum Hall systems
journal, July 2015
- Peterson, Michael R.; Wu, Yang-Le; Cheng, Meng
- Physical Review B, Vol. 92, Issue 3
Composite-fermion approach for the fractional quantum Hall effect
journal, July 1989
- Jain, J. K.
- Physical Review Letters, Vol. 63, Issue 2
Observation of half-integer thermal Hall conductance
journal, June 2018
- Banerjee, Mitali; Heiblum, Moty; Umansky, Vladimir
- Nature, Vol. 559, Issue 7713
Experimental studies of the fractional quantum Hall effect in the first excited Landau level
journal, February 2008
- Pan, W.; Xia, J. S.; Stormer, H. L.
- Physical Review B, Vol. 77, Issue 7
Tripartite composite fermion states
journal, June 2013
- Sreejith, G. J.; Wu, Ying-Hai; Wójs, A.
- Physical Review B, Vol. 87, Issue 24
Proliferation of neutral modes in fractional quantum Hall states
journal, June 2014
- Inoue, Hiroyuki; Grivnin, Anna; Ronen, Yuval
- Nature Communications, Vol. 5, Issue 1
Non-Abelian quantized Hall states of electrons at filling factors 12/5 and 13/5 in the first excited Landau level
journal, February 2009
- Rezayi, E. H.; Read, N.
- Physical Review B, Vol. 79, Issue 7
Characterizing Neutral Modes of Fractional States in the Second Landau Level
journal, July 2011
- Dolev, M.; Gross, Y.; Sabo, R.
- Physical Review Letters, Vol. 107, Issue 3
Edge Excitations in the Fractional Quantum hall States at General Filling Fractions
journal, January 1991
- Wen, X. G.
- Modern Physics Letters B, Vol. 05, Issue 01
Shift and Spin Vector: New Topological Quantum Numbers for the Hall Fluids
journal, November 1992
- Wen, X. G.; Zee, A.
- Physical Review Letters, Vol. 69, Issue 20
Theory of the fractional quantum Hall effect
journal, January 1986
- Tao, R.
- Journal of Physics C: Solid State Physics, Vol. 19, Issue 2
Phase Diagram of the ν=5/2 Fractional Quantum Hall Effect: Effects of Landau-Level Mixing and Nonzero Width
text, January 2015
- Pakrouski, Kiryl; Peterson, Michael R.; Jolicoeur, Thierry
- ETH Zurich
Particle-hole symmetry and the Pfaffian state
text, January 2007
- Levin, Michael; Halperin, Bertrand I.; Rosenow, Bernd
- arXiv
Transition from Abelian to non-Abelian quantum liquids in the second Landau level
text, January 2008
- Wojs, Arkadiusz
- arXiv
Collective states of non-abelian quasiparticles in a magnetic field
text, January 2008
- Levin, Michael; Halperin, Bertrand I.
- arXiv
Observation of neutral modes in the fractional quantum Hall regime
text, January 2010
- Bid, Aveek; Ofek, Nissim; Inoue, Hiroyuki
- arXiv
Nonconventional odd denominator fractional quantum Hall states in the second Landau level
text, January 2010
- Kumar, A.; Manfra, M. J.; Csáthy, G. A.
- arXiv
Characterizing Neutral Modes of Fractional States in the Second Landau Level
text, January 2011
- Dolev, M.; Gross, Y.; Sabo, R.
- arXiv
Competing states for the fractional quantum Hall effect in the 1/3-filled second Landau level
text, January 2016
- Jeong, Jae-Seung; Lu, Hantao; Lee, Ki Hoon
- arXiv
Non-Abelian Parton Fractional Quantum Hall Effect in Multilayer Graphene
text, January 2016
- Wu, Ying-Hai; Shi, Tao; Jain, Jainendra K.
- arXiv
The enigmatic 12/5 fractional quantum Hall effect
text, January 2016
- Pakrouski, Kiryl; Troyer, Matthias; Wu, Yang-Le
- arXiv
Fermi wave vector for the non-fully spin polarized composite-fermion Fermi sea
text, January 2017
- Balram, Ajit C.; Jain, J. K.
- arXiv
Excitation gaps in fractional quantum Hall states: An exact diagonalization study
text, January 2002
- Morf, R. H.; d'Ambrumenil, N.; Sarma, S. Das
- arXiv
Fractional Quantum Hall Effect of Composite Fermions
text, January 2003
- Pan, W.; Stormer, H. L.; Tsui, D. C.
- arXiv
Composite Fermions in Negative Effective Magnetic Field: A Monte-Carlo Study
text, January 2005
- Moller, Gunnar; Simon, Steven H.
- arXiv
Non-Abelian quantized Hall states of electrons at filling factors 12/5 and 13/5 in the first excited Landau level
text, January 2006
- Rezayi, E. H.; Read, N.
- arXiv
Skyrmions in the Fractional Quantum Hall Effect
text, January 1996
- Kamilla, R. K.; Wu, X. G.; Jain, J. K.
- arXiv
Beyond paired quantum Hall states: parafermions and incompressible states in the first excited Landau level
text, January 1998
- Read, N.; Rezayi, E.
- arXiv
Works referencing / citing this record:
Parton construction of particle-hole-conjugate Read-Rezayi parafermion fractional quantum Hall states and beyond
journal, June 2019
- Balram, Ajit C.; Barkeshli, Maissam; Rudner, Mark S.
- Physical Review B, Vol. 99, Issue 24
Parton construction of particle-hole-conjugate Read-Rezayi parafermion fractional quantum Hall states and beyond
text, January 2019
- Balram, Ajit C.; Barkeshli, Maissam; Rudner, Mark S.
- arXiv