Numerical Study of Quantum Hall Bilayers at Total Filling ${\nu}_{T}=1$ : A New Phase at Intermediate Layer Distances
Abstract
We view the phase diagram of quantum Hall bilayer systems with total filing ${\nu}_{T}=\mathrm{1/2}$ + 1/2 of the lowest Landau level as a function of layer distances d. Based on numerical exact diagonalization calculations, we obtain three distinct phases, including an exciton superfluid phase with spontaneous interlayer coherence at small d, a composite Fermi liquid at large d, and an intermediate phase for 1.1 < d/l _{B} < 1.8 (l _{B} is the magnetic length). The transition from the exciton superfluid to the intermediate phase is identified by (i) a dramatic change in the Berry curvature of the ground state under twisted boundary conditions on the two layers and (ii) an energy level crossing of the first excited state. The transition from the intermediate phase to the composite Fermi liquid is identified by the vanishing of the exciton superfluid stiffness. Moreover, from our finitesize study, the energy cost of transferring one electron between the layers shows an evenodd effect and possibly extrapolates to a finite value in the thermodynamic limit, indicating the enhanced intralayer correlation. Our identification of an intermediate phase and its distinctive features shed new light on the theoretical understanding of the quantum Hall bilayer system at total filling ${\nu}_{T}=1$.
 Authors:

 Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
 California State Univ. Northridge (CSUN), Northridge, CA (United States)
 Publication Date:
 Research Org.:
 Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States); California State Univ. Northridge (CSUN), Northridge, CA (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC22)
 OSTI Identifier:
 1505729
 Alternate Identifier(s):
 OSTI ID: 1402172
 Grant/Contract Number:
 FG0206ER46305; SC0010526
 Resource Type:
 Journal Article: Accepted Manuscript
 Journal Name:
 Physical Review Letters
 Additional Journal Information:
 Journal Volume: 119; Journal Issue: 17; Journal ID: ISSN 00319007
 Publisher:
 American Physical Society (APS)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY
Citation Formats
Zhu, Zheng, Fu, Liang, and Sheng, D. N. Numerical Study of Quantum Hall Bilayers at Total Filling νT=1 : A New Phase at Intermediate Layer Distances. United States: N. p., 2017.
Web. doi:10.1103/physrevlett.119.177601.
Zhu, Zheng, Fu, Liang, & Sheng, D. N. Numerical Study of Quantum Hall Bilayers at Total Filling νT=1 : A New Phase at Intermediate Layer Distances. United States. doi:10.1103/physrevlett.119.177601.
Zhu, Zheng, Fu, Liang, and Sheng, D. N. Mon .
"Numerical Study of Quantum Hall Bilayers at Total Filling νT=1 : A New Phase at Intermediate Layer Distances". United States. doi:10.1103/physrevlett.119.177601. https://www.osti.gov/servlets/purl/1505729.
@article{osti_1505729,
title = {Numerical Study of Quantum Hall Bilayers at Total Filling νT=1 : A New Phase at Intermediate Layer Distances},
author = {Zhu, Zheng and Fu, Liang and Sheng, D. N.},
abstractNote = {We view the phase diagram of quantum Hall bilayer systems with total filing νT=1/2 + 1/2 of the lowest Landau level as a function of layer distances d. Based on numerical exact diagonalization calculations, we obtain three distinct phases, including an exciton superfluid phase with spontaneous interlayer coherence at small d, a composite Fermi liquid at large d, and an intermediate phase for 1.1 < d/lB < 1.8 (lB is the magnetic length). The transition from the exciton superfluid to the intermediate phase is identified by (i) a dramatic change in the Berry curvature of the ground state under twisted boundary conditions on the two layers and (ii) an energy level crossing of the first excited state. The transition from the intermediate phase to the composite Fermi liquid is identified by the vanishing of the exciton superfluid stiffness. Moreover, from our finitesize study, the energy cost of transferring one electron between the layers shows an evenodd effect and possibly extrapolates to a finite value in the thermodynamic limit, indicating the enhanced intralayer correlation. Our identification of an intermediate phase and its distinctive features shed new light on the theoretical understanding of the quantum Hall bilayer system at total filling νT=1.},
doi = {10.1103/physrevlett.119.177601},
journal = {Physical Review Letters},
issn = {00319007},
number = 17,
volume = 119,
place = {United States},
year = {2017},
month = {10}
}
Web of Science
Figures / Tables:
Works referenced in this record:
Is the Composite Fermion a Dirac Particle?
journal, September 2015
 Son, Dam Thanh
 Physical Review X, Vol. 5, Issue 3
Meron deconfinement in the quantum Hall bilayer at intermediate distances
journal, November 2015
 Milovanović, M. V.; Dobardžić, E.; Papić, Z.
 Physical Review B, Vol. 92, Issue 19
Microscopic functional integral theory of quantum fluctuations in doublelayer quantum Hall ferromagnets
journal, September 2001
 Joglekar, Yogesh N.; MacDonald, Allan H.
 Physical Review B, Vol. 64, Issue 15
Fermiliquidlike state in a halffilled Landau level
journal, February 1994
 Rezayi, E.; Read, N.
 Physical Review Letters, Vol. 72, Issue 6
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
Coulomb drag
journal, May 2016
 Narozhny, B. N.; Levchenko, A.
 Reviews of Modern Physics, Vol. 88, Issue 2
Strong Correlation to Weak Correlation Phase Transition in Bilayer Quantum Hall Systems
journal, February 2001
 Schliemann, John; Girvin, S. M.; MacDonald, A. H.
 Physical Review Letters, Vol. 86, Issue 9
Activated Transport in the Separate Layers that Form the ${\nu}_{T}=1$ Exciton Condensate
journal, December 2004
 Wiersma, R. D.; Lok, J. G. S.; Kraus, S.
 Physical Review Letters, Vol. 93, Issue 26
SpinDependent Phase Diagram of the ${\nu}_{T}=1$ Bilayer Electron System
journal, March 2008
 Giudici, P.; Muraki, K.; Kumada, N.
 Physical Review Letters, Vol. 100, Issue 10
Quantum Hall Exciton Condensation at Full Spin Polarization
journal, January 2010
 Finck, A. D. K.; Eisenstein, J. P.; Pfeiffer, L. N.
 Physical Review Letters, Vol. 104, Issue 1
Bosonization Approach for Bilayer Quantum Hall Systems at ${\nu}_{T}=1$
journal, October 2006
 Doretto, R. L.; Caldeira, A. O.; Smith, C. Morais
 Physical Review Letters, Vol. 97, Issue 18
Spontaneous pseudospin spiral order in bilayer quantum Hall systems
journal, January 2004
 Park, K.
 Physical Review B, Vol. 69, Issue 4
Resonantly Enhanced Tunneling in a Double Layer Quantum Hall Ferromagnet
journal, June 2000
 Spielman, I. B.; Eisenstein, J. P.; Pfeiffer, L. N.
 Physical Review Letters, Vol. 84, Issue 25
Metallic phase of the quantum Hall system at evendenominator filling fractions
journal, October 1992
 Kalmeyer, Vadim; Zhang, ShouCheng
 Physical Review B, Vol. 46, Issue 15
Strong Enhancement of Drag and Dissipation at the Weak to StrongCoupling Phase Transition in a Bilayer System at a Total Landau Level Filling $\mathit{\nu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1\mathrm{}$
journal, February 2002
 Stern, Ady; Halperin, B. I.
 Physical Review Letters, Vol. 88, Issue 10
Collapse of integer Hall gaps in a doublequantumwell system
journal, August 1990
 MacDonald, A. H.; Platzman, P. M.; Boebinger, G. S.
 Physical Review Letters, Vol. 65, Issue 6
Phase Diagram for Quantum Hall Bilayers at $\nu =1$
journal, September 2003
 Sheng, D. N.; Balents, Leon; Wang, Ziqiang
 Physical Review Letters, Vol. 91, Issue 11
Tunable fractional quantum Hall phases in bilayer graphene
journal, July 2014
 Maher, Patrick; Wang, Lei; Gao, Yuanda
 Science, Vol. 345, Issue 6192
Theory of the halffilled Landau level
journal, March 1993
 Halperin, B. I.; Lee, Patrick A.; Read, Nicholas
 Physical Review B, Vol. 47, Issue 12
Neutral superfluid modes and ‘‘magnetic’’ monopoles in multilayered quantum Hall systems
journal, September 1992
 Wen, XiaoGang; Zee, A.
 Physical Review Letters, Vol. 69, Issue 12
Ground state of the twodimensional charged particles in a strong magnetic field and the fractional quantum Hall effect
journal, June 1984
 Yoshioka, Daijiro
 Physical Review B, Vol. 29, Issue 12
Exciton Condensation in Bilayer Quantum Hall Systems
journal, March 2014
 Eisenstein, J. P.
 Annual Review of Condensed Matter Physics, Vol. 5, Issue 1
Observation of Even Denominator Fractional Quantum Hall Effect in Suspended Bilayer Graphene
journal, March 2014
 Ki, DongKeun; Fal’ko, Vladimir I.; Abanin, Dmitry A.
 Nano Letters, Vol. 14, Issue 4
Interlayer Coherent Composite Fermi Liquid Phase in Quantum Hall Bilayers
journal, December 2009
 Alicea, Jason; Motrunich, Olexei I.; Refael, G.
 Physical Review Letters, Vol. 103, Issue 25
Observation of a Linearly Dispersing Collective Mode in a Quantum Hall Ferromagnet
journal, July 2001
 Spielman, I. B.; Eisenstein, J. P.; Pfeiffer, L. N.
 Physical Review Letters, Vol. 87, Issue 3
Spontaneous symmetry breaking and exotic quantum orders in integer quantum Hall systems under a tilted magnetic field
journal, October 2003
 Wang, DawWei; Demler, Eugene; Das Sarma, S.
 Physical Review B, Vol. 68, Issue 16
Correlation energy, quantum phase transition, and bias potential effects in quantum Hall bilayers at ν=1
journal, January 2003
 Schliemann, John
 Physical Review B, Vol. 67, Issue 3
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
Trial wave functions for $\nu ={\scriptstyle \frac{1}{2}}+{\scriptstyle \frac{1}{2}}$ quantum Hall bilayers
journal, March 2009
 Möller, Gunnar; Simon, Steven H.; Rezayi, Edward H.
 Physical Review B, Vol. 79, Issue 12
Theory of Interlayer Tunneling in Bilayer Quantum Hall Ferromagnets
journal, February 2001
 Stern, Ady; Girvin, S. M.; MacDonald, A. H.
 Physical Review Letters, Vol. 86, Issue 9
Gauge fluctuations and interlayer coherence in bilayer composite fermion metals
journal, February 2014
 Cipri, R.; Bonesteel, N. E.
 Physical Review B, Vol. 89, Issue 8
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
Finitemomentum condensate of magnetic excitons in a bilayer quantum Hall system
journal, July 2012
 Doretto, R. L.; Morais Smith, C.; Caldeira, A. O.
 Physical Review B, Vol. 86, Issue 3
Quantized Hall Conductance in a TwoDimensional Periodic Potential
journal, August 1982
 Thouless, D. J.; Kohmoto, M.; Nightingale, M. P.
 Physical Review Letters, Vol. 49, Issue 6
Incompressible Paired Hall State, Stripe Order, and the Composite Fermion Liquid Phase in HalfFilled Landau Levels
journal, May 2000
 Rezayi, E. H.; Haldane, F. D. M.
 Physical Review Letters, Vol. 84, Issue 20
Electronhole asymmetric integer and fractional quantum Hall effect in bilayer graphene
journal, May 2014
 Kou, A.; Feldman, B. E.; Levin, A. J.
 Science, Vol. 345, Issue 6192
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
Coexistence of Composite Bosons and Composite Fermions in $\nu =\frac{1}{2}+\frac{1}{2}$ Quantum Hall Bilayers
journal, July 2003
 Simon, Steven H.; Rezayi, E. H.; Milovanovic, Milica V.
 Physical Review Letters, Vol. 91, Issue 4
Manybody integer quantum Hall effect: Evidence for new phase transitions
journal, January 1994
 Murphy, S. Q.; Eisenstein, J. P.; Boebinger, G. S.
 Physical Review Letters, Vol. 72, Issue 5
Intrinsic Gap and Exciton Condensation in the ${\nu}_{T}=1$ Bilayer System
journal, February 2010
 Giudici, P.; Muraki, K.; Kumada, N.
 Physical Review Letters, Vol. 104, Issue 5
Spontaneous interlayer coherence in doublelayer quantum Hall systems: Symmetrybreaking interactions, inplane fields, and phase solitons
journal, October 1996
 Yang, Kun; Moon, K.; Belkhir, Lotfi
 Physical Review B, Vol. 54, Issue 16
Quantized Hall conductance as a topological invariant
journal, March 1985
 Niu, Qian; Thouless, D. J.; Wu, YongShi
 Physical Review B, Vol. 31, Issue 6
Bilayer paired quantum Hall states and Coulomb drag
journal, April 2001
 Kim, Yong Baek; Nayak, Chetan; Demler, Eugene
 Physical Review B, Vol. 63, Issue 20
Observation of Collapse of Pseudospin Order in Bilayer Quantum Hall Ferromagnets
journal, April 2005
 Luin, Stefano; Pellegrini, Vittorio; Pinczuk, Aron
 Physical Review Letters, Vol. 94, Issue 14
Interlayer Tunneling in DoubleLayer Quantum Hall Pseudoferromagnets
journal, February 2001
 Balents, L.; Radzihovsky, L.
 Physical Review Letters, Vol. 86, Issue 9
Interlayer Pairing Symmetry of Composite Fermions in Quantum Hall Bilayers
journal, April 2017
 Isobe, Hiroki; Fu, Liang
 Physical Review Letters, Vol. 118, Issue 16
Ground State of ν=1 Bilayer Quantum Hall Systems
journal, April 2006
 Shibata, Naokazu; Yoshioka, Daijiro
 Journal of the Physical Society of Japan, Vol. 75, Issue 4
Composite fermion duality for halffilled multicomponent Landau levels
journal, February 2017
 Sodemann, Inti; Kimchi, Itamar; Wang, Chong
 Physical Review B, Vol. 95, Issue 8
Paired states in halffilled Landau levels
journal, June 2017
 Milovanović, M. V.
 Physical Review B, Vol. 95, Issue 23
Bilayer Quantum Hall Systems at ${\nu}_{T}=1$ : Coulomb Drag and the Transition from Weak to Strong Interlayer Coupling
journal, June 2003
 Kellogg, M.; Eisenstein, J. P.; Pfeiffer, L. N.
 Physical Review Letters, Vol. 90, Issue 24
Nondissipative drag conductance as a topological quantum number
journal, January 2001
 Yang, Kun; MacDonald, A. H.
 Physical Review B, Vol. 63, Issue 7
Paired Composite Fermion Phase of Quantum Hall Bilayers at $\nu =\frac{1}{2}+\frac{1}{2}$
journal, October 2008
 Möller, Gunnar; Simon, Steven H.; Rezayi, Edward H.
 Physical Review Letters, Vol. 101, Issue 17
Quasiparticles in the 111 state and its compressible ancestors
journal, October 2002
 Veillette, M. Y.; Balents, L.; Fisher, Matthew P. A.
 Physical Review B, Vol. 66, Issue 15
Composite Fermion Theory of Exotic Fractional Quantum Hall Effect
journal, March 2015
 Jain, Jainendra K.
 Annual Review of Condensed Matter Physics, Vol. 6, Issue 1
ManyParticle Translational Symmetries of TwoDimensional Electrons at Rational LandauLevel Filling
journal, November 1985
 Haldane, F. D. M.
 Physical Review Letters, Vol. 55, Issue 20
Bose–Einstein condensation of excitons in bilayer electron systems
journal, December 2004
 Eisenstein, J. P.; MacDonald, A. H.
 Nature, Vol. 432, Issue 7018
Topological structures, universality classes, and statistics screening in the anyon superfluid
journal, July 1991
 Wen, X. G.; Zee, A.
 Physical Review B, Vol. 44, Issue 1
Quantum SpinHall Effect and Topologically Invariant Chern Numbers
journal, July 2006
 Sheng, D. N.; Weng, Z. Y.; Sheng, L.
 Physical Review Letters, Vol. 97, Issue 3
Compositefermion approach for the fractional quantum Hall effect
journal, July 1989
 Jain, J. K.
 Physical Review Letters, Vol. 63, Issue 2
Vanishing Hall Resistance at High Magnetic Field in a DoubleLayer TwoDimensional Electron System
journal, July 2004
 Kellogg, M.; Eisenstein, J. P.; Pfeiffer, L. N.
 Physical Review Letters, Vol. 93, Issue 3
Counterflow Measurements in Strongly Correlated GaAs Hole Bilayers: Evidence for ElectronHole Pairing
journal, July 2004
 Tutuc, E.; Shayegan, M.; Huse, D. A.
 Physical Review Letters, Vol. 93, Issue 3
Brokensymmetry ground states for the twodimensional electron gas in a doublequantumwell system
journal, October 1992
 Côté, R.; Brey, L.; MacDonald, A. H.
 Physical Review B, Vol. 46, Issue 16
Fractional quantum Hall effect in the absence of Landau levels
journal, July 2011
 Sheng, D. N.; Gu, ZhengCheng; Sun, Kai
 Nature Communications, Vol. 2, Issue 1
Spontaneous interlayer coherence in doublelayer quantum Hall systems: Charged vortices and KosterlitzThouless phase transitions
journal, February 1995
 Moon, K.; Mori, H.; Yang, Kun
 Physical Review B, Vol. 51, Issue 8