Theoretical phase diagram of twocomponent composite fermions in doublelayer graphene
Abstract
Theory predicts that double layer systems realize “twocomponent composite fermions,” which are formed when electrons capture both intra and interlayer vortices, to produce a wide variety of new strongly correlated liquid and crystal states as a function of the layer separation. Recent experiments in double layer graphene have revealed a large number of layercorrelated fractional quantum Hall states in the lowest Landau level, many of which have not been studied quantitatively in previous theoretical works. We consider the competition between various liquid and crystal states at several of these filling factors (specifically, the states at total filling factors ν = 3/7, 4/9, 6/11, 4/7, 3/5, 2/3, and 4/5) to determine the theoretical phase diagram as a function of the layer separation. We compare our results with experiments and identify various observed states. In particular, we show that at small layer separations the states at total fillings ν = 3/7 and ν = 3/5 are partially pseudospin polarized, where pseudospin refers to the layer index. For certain fractions, such as ν = 3/7, interlayer correlations are predicted to survive to surprisingly large interlayer separations.
 Authors:

 Pennsylvania State Univ., University Park, PA (United States); Univ. ParisSaclay, GifsurYvette (France)
 Homi Bhabha National Inst., Chennai (India)
 Wroclaw Univ. of Science and Technology (Poland)
 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:
 1606395
 Alternate Identifier(s):
 OSTI ID: 1601060
 Grant/Contract Number:
 SC0005042
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Physical Review B
 Additional Journal Information:
 Journal Volume: 101; Journal Issue: 8; Journal ID: ISSN 24699950
 Publisher:
 American Physical Society (APS)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; Bilayer graphene; fractional quantum Hall effect; composite fermions
Citation Formats
Faugno, W. N., Balram, Ajit C., Wójs, A., and Jain, J. K. Theoretical phase diagram of twocomponent composite fermions in doublelayer graphene. United States: N. p., 2020.
Web. doi:10.1103/PhysRevB.101.085412.
Faugno, W. N., Balram, Ajit C., Wójs, A., & Jain, J. K. Theoretical phase diagram of twocomponent composite fermions in doublelayer graphene. United States. doi:https://doi.org/10.1103/PhysRevB.101.085412
Faugno, W. N., Balram, Ajit C., Wójs, A., and Jain, J. K. Wed .
"Theoretical phase diagram of twocomponent composite fermions in doublelayer graphene". United States. doi:https://doi.org/10.1103/PhysRevB.101.085412. https://www.osti.gov/servlets/purl/1606395.
@article{osti_1606395,
title = {Theoretical phase diagram of twocomponent composite fermions in doublelayer graphene},
author = {Faugno, W. N. and Balram, Ajit C. and Wójs, A. and Jain, J. K.},
abstractNote = {Theory predicts that double layer systems realize “twocomponent composite fermions,” which are formed when electrons capture both intra and interlayer vortices, to produce a wide variety of new strongly correlated liquid and crystal states as a function of the layer separation. Recent experiments in double layer graphene have revealed a large number of layercorrelated fractional quantum Hall states in the lowest Landau level, many of which have not been studied quantitatively in previous theoretical works. We consider the competition between various liquid and crystal states at several of these filling factors (specifically, the states at total filling factors ν = 3/7, 4/9, 6/11, 4/7, 3/5, 2/3, and 4/5) to determine the theoretical phase diagram as a function of the layer separation. We compare our results with experiments and identify various observed states. In particular, we show that at small layer separations the states at total fillings ν = 3/7 and ν = 3/5 are partially pseudospin polarized, where pseudospin refers to the layer index. For certain fractions, such as ν = 3/7, interlayer correlations are predicted to survive to surprisingly large interlayer separations.},
doi = {10.1103/PhysRevB.101.085412},
journal = {Physical Review B},
number = 8,
volume = 101,
place = {United States},
year = {2020},
month = {2}
}
Works referenced in this record:
Anomalous Quantum Hall Effect: An Incompressible Quantum Fluid with Fractionally Charged Excitations
journal, May 1983
 Laughlin, R. B.
 Physical Review Letters, Vol. 50, Issue 18
Observation of a ν=1/2 fractional quantum Hall state in a doublelayer electron system
journal, March 1992
 Suen, Y. W.; Engel, L. W.; Santos, M. B.
 Physical Review Letters, Vol. 68, Issue 9
New fractional quantum Hall state in doublelayer twodimensional electron systems
journal, March 1992
 Eisenstein, J. P.; Boebinger, G. S.; Pfeiffer, L. N.
 Physical Review Letters, Vol. 68, Issue 9
Phase diagram of bilayer composite fermion states
journal, August 2001
 Scarola, V. W.; Jain, J. K.
 Physical Review B, Vol. 64, Issue 8
Compositefermion approach for the fractional quantum Hall effect
journal, July 1989
 Jain, J. K.
 Physical Review Letters, Vol. 63, Issue 2
Fractional Quantum Hall Effect at HalfFilled Landau Level in a MultipleLayer Electron System
journal, December 1987
 Chakraborty, Tapash; Pietiläinen, Pekka
 Physical Review Letters, Vol. 59, Issue 24
Fractional quantum Hall effect in twolayered systems
journal, January 1989
 Yoshioka, D.; MacDonald, A. H.; Girvin, S. M.
 Physical Review B, Vol. 39, Issue 3
Quantum Hall effect in doublequantumwell systems
journal, April 1991
 He, Song; Xie, X. C.; Das Sarma, S.
 Physical Review B, Vol. 43, Issue 11
Quantized Hall effect and quantum phase transitions in coupled twolayer electron systems
journal, February 1993
 He, Song; Das Sarma, S.; Xie, X. C.
 Physical Review B, Vol. 47, Issue 8
Phase Diagram of the Spin Polarization of Composite Fermions and a New Effective Mass
journal, May 1998
 Park, K.; Jain, J. K.
 Physical Review Letters, Vol. 80, Issue 19
Twocomponent fractional quantum Hall effect in the halffilled lowest Landau level in an asymmetric wide quantum well
journal, May 2014
 Thiebaut, N.; Goerbig, M. O.; Regnault, N.
 Physical Review B, Vol. 89, Issue 19
Phase diagram of fractional quantum Hall effect of composite fermions in multicomponent systems
journal, January 2015
 Balram, Ajit C.; Tőke, Csaba; Wójs, A.
 Physical Review B, Vol. 91, Issue 4
Fractional quantum Hall effect in graphene: Quantitative comparison between theory and experiment
journal, August 2015
 Balram, Ajit C.; Tőke, Csaba; Wójs, A.
 Physical Review B, Vol. 92, Issue 7
Interlayer fractional quantum Hall effect in a coupled graphene double layer
journal, June 2019
 Liu, Xiaomeng; Hao, Zeyu; Watanabe, Kenji
 Nature Physics, Vol. 15, Issue 9
Pairing states of composite fermions in doublelayer graphene
journal, June 2019
 Li, J. I. A.; Shi, Q.; Zeng, Y.
 Nature Physics, Vol. 15, Issue 9
Nextlevel composite fermions
journal, June 2019
 Csáthy, Gábor A.; Jain, Jainendra K.
 Nature Physics, Vol. 15, Issue 9
Mixedspin incompressible states in the fractional quantum Hall effect
journal, July 1993
 Wu, X. G.; Dev, G.; Jain, J. K.
 Physical Review Letters, Vol. 71, Issue 1
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
Spinful composite fermions in a negative effective field
journal, June 2012
 Davenport, Simon C.; Simon, Steven H.
 Physical Review B, Vol. 85, Issue 24
Ground state of twodimensional electrons and the reversed spins in the fractional quantum Hall effect
journal, December 1984
 Zhang, F. C.; Chakraborty, Tapash
 Physical Review B, Vol. 30, Issue 12
Excitation Energies of the Fractional Quantum Hall Effect
journal, March 1986
 Yoshioka, Daijiro
 Journal of the Physical Society of Japan, Vol. 55, Issue 3
Fractional quantum Hall effect with spin reversal
journal, August 1989
 Xie, X. C.; Guo, Yin; Zhang, F. C.
 Physical Review B, Vol. 40, Issue 5
Fractional Quantum Hall Effect around $\nu =\frac{3}{2}$ : Composite Fermions with a Spin
journal, November 1995
 Du, R. R.; Yeh, A. S.; Stormer, H. L.
 Physical Review Letters, Vol. 75, Issue 21
Effective Mass and $\mathit{g}$ Factor of FourFluxQuanta Composite Fermions
journal, January 1999
 Yeh, A. S.; Stormer, H. L.; Tsui, D. C.
 Physical Review Letters, Vol. 82, Issue 3
Spin Polarization of Composite Fermions: Measurements of the Fermi Energy
journal, May 1999
 Kukushkin, I. V.; v. Klitzing, K.; Eberl, K.
 Physical Review Letters, Vol. 82, Issue 18
The spin physics of composite fermions
journal, July 2001
 Park, K.; Jain, J. K.
 Solid State Communications, Vol. 119, Issue 45
LandauLevel Mixing and ParticleHole Symmetry Breaking for Spin Transitions in the Fractional Quantum Hall Effect
journal, September 2016
 Zhang, Yuhe; Wójs, A.; Jain, J. K.
 Physical Review Letters, Vol. 117, Issue 11
Group Theory and its Applications to Physical Problems
journal, October 1962
 Hamermesh, Morton; Mullin, Albert A.
 American Journal of Physics, Vol. 30, Issue 10
Composite Fermions in the Hilbert Space of the Lowest Electronic Landau Level
journal, September 1997
 Jain, J. K.; Kamilla, R. K.
 International Journal of Modern Physics B, Vol. 11, Issue 22
Exotic bilayer crystals in a strong magnetic field
journal, June 2018
 Faugno, W. N.; Duthie, A. J.; Wales, D. J.
 Physical Review B, Vol. 97, Issue 24
Nonabelions in the fractional quantum hall effect
journal, August 1991
 Moore, Gregory; Read, Nicholas
 Nuclear Physics B, Vol. 360, Issue 23
Incompressible quantum Hall states
journal, October 1989
 Jain, J.
 Physical Review B, Vol. 40, Issue 11
NonAbelian Parton Fractional Quantum Hall Effect in Multilayer Graphene
journal, July 2017
 Wu, YingHai; Shi, Tao; Jain, Jainendra K.
 Nano Letters, Vol. 17, Issue 8
Entangled Pauli principles: The DNA of quantum Hall fluids
journal, October 2018
 Bandyopadhyay, Sumanta; Chen, Li; Ahari, Mostafa Tanhayi
 Physical Review B, Vol. 98, Issue 16
Even denominator fractional quantum Hall states in higher Landau levels of graphene
journal, November 2018
 Kim, Youngwook; Balram, Ajit C.; Taniguchi, Takashi
 Nature Physics, Vol. 15, Issue 2
Nature of composite fermions and the role of particlehole symmetry: A microscopic account
journal, June 2016
 Balram, Ajit C.; Jain, J. K.
 Physical Review B, Vol. 93, Issue 23
ParticleHole Symmetry and the Pfaffian State
journal, December 2007
 Levin, Michael; Halperin, Bertrand I.; Rosenow, Bernd
 Physical Review Letters, Vol. 99, Issue 23
ParticleHole Symmetry and the $\nu =\frac{5}{2}$ Quantum Hall State
journal, December 2007
 Lee, SungSik; Ryu, Shinsei; Nayak, Chetan
 Physical Review Letters, Vol. 99, Issue 23
Parton construction of a wave function in the antiPfaffian phase
journal, July 2018
 Balram, Ajit C.; Barkeshli, Maissam; Rudner, Mark S.
 Physical Review B, Vol. 98, Issue 3
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
Microscopic wave functions for the fractional quantized Hall states at $\nu =\frac{2}{5}\mathrm{and}\frac{2}{7}$
journal, August 1986
 Morf, R.; d'Ambrumenil, N.; Halperin, B. I.
 Physical Review B, Vol. 34, Issue 4
Prediction of a NonAbelian Fractional Quantum Hall State with $f$ Wave Pairing of Composite Fermions in Wide Quantum Wells
journal, July 2019
 Faugno, W. N.; Balram, Ajit C.; Barkeshli, Maissam
 Physical Review Letters, Vol. 123, Issue 1
Gauge Fields and Pairing in DoubleLayer Composite Fermion Metals
journal, September 1996
 Bonesteel, N. E.; McDonald, I. A.; Nayak, C.
 Physical Review Letters, Vol. 77, Issue 14
Topological phase transition in the ν=2/3 quantum Hall effect
journal, June 1996
 McDonald, I. A.; Haldane, F. D. M.
 Physical Review B, Vol. 53, Issue 23
Interacting composite fermions: Nature of the 4/5, 5/7, 6/7, and 6/17 fractional quantum Hall states
journal, October 2016
 Balram, Ajit C.
 Physical Review B, Vol. 94, Issue 16
SU(4) composite fermions in graphene: Fractional quantum Hall states without analog in GaAs
journal, June 2007
 Tőke, Csaba; Jain, J. K.
 Physical Review B, Vol. 75, Issue 24
SU(3) and SU(4) Singlet Quantum Hall States at $\nu =2/3$
journal, October 2015
 Wu, Fengcheng; Sodemann, Inti; MacDonald, Allan H.
 Physical Review Letters, Vol. 115, Issue 16