Tunnel transport and interlayer excitons in bilayer fractional quantum Hall systems

Zhang, Yuhe; Jain, J. K.; Eisenstein, J. P.

doi:10.1103/PhysRevB.95.195105

Tunnel transport and interlayer excitons in bilayer fractional quantum Hall systems

Journal Article · Wed May 03 04:00:00 EDT 2017 · Physical Review B

DOI:https://doi.org/10.1103/PhysRevB.95.195105· OSTI ID:1489115

Zhang, Yuhe ^[1]; Jain, J. K. ^[2]; Eisenstein, J. P. ^[3]

The Pennsylvania State Univ., University Park, PA (United States); Penn State University
The Pennsylvania State Univ., University Park, PA (United States)
California Inst. of Technology (CalTech), Pasadena, CA (United States)

In a bilayer system consisting of a composite-fermion Fermi sea in each layer, the tunnel current is exponentially suppressed at zero bias, followed by a strong peak at a finite bias voltage V_max. This behavior, which is qualitatively different from that observed for the electron Fermi sea, provides fundamental insight into the strongly correlated non-Fermi liquid nature of the CF Fermi sea and, in particular, offers a window into the short-distance high-energy physics of this highly non-trivial state. We identify the exciton responsible for the peak current and provide a quantitative account of the value of V_max. The excitonic attraction is shown to be quantitatively significant, and its variation accounts for the increase of V_max with the application of an in-plane magnetic field. Here, we also estimate the critical Zeeman energy where transition occurs from a fully spin polarized composite fermion Fermi sea to a partially spin polarized one, carefully incorporating corrections due to finite width and Landau level mixing, and find it to be in satisfactory agreement with the Zeeman energy where a qualitative change has been observed for the onset bias voltage. For fractional quantum Hall states, we predict a substantial discontinuous jump in V_max when the system undergoes a transition from a fully spin polarized state to a spin singlet or a partially spin polarized state.

View Accepted Manuscript (DOE)

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

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)

Grant/Contract Number:: SC0005042

OSTI ID:: 1489115

Alternate ID(s):: OSTI ID: 1355070

Journal Information:: Physical Review B, Journal Name: Physical Review B Journal Issue: 19 Vol. 95; ISSN 2469-9950; ISSN PRBMDO

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

References (59)

Many-Particle Physics Mahan, Gerald D. Physics of Solids and Liquids (PSLI) https://doi.org/10.1007/978-1-4757-5714-9	book	January 2000
Breakdown of particle–hole symmetry in the lowest Landau level revealed by tunneling spectroscopy Eisenstein, J. P.; Pfeiffer, L. N.; West, K. W. Solid State Communications, Vol. 149, Issue 43-44 https://doi.org/10.1016/j.ssc.2009.08.004	journal	November 2009
Composite Fermions Jain, Jainendra K. https://doi.org/10.1017/CBO9780511607561	book	January 2007
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
Fractional quantum Hall effect in a two-dimensional electron-hole fluid MacDonald, A. H.; Rezayi, E. H. Physical Review B, Vol. 42, Issue 5 https://doi.org/10.1103/PhysRevB.42.3224	journal	August 1990
Fractional quantum Hall effect at ν=2/3 and 3/5 in tilted magnetic fields Engel, L. W.; Hwang, S. W.; Sajoto, T. Physical Review B, Vol. 45, Issue 7 https://doi.org/10.1103/PhysRevB.45.3418	journal	February 1992
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
Classical approach to the gap in the tunneling density of states of a two-dimensional electron liquid in a strong magnetic field Efros, A. L.; Pikus, F. G. Physical Review B, Vol. 48, Issue 19 https://doi.org/10.1103/PhysRevB.48.14694	journal	November 1993
Tunneling between two-dimensional electron gases in a strong magnetic field Brown, K. M.; Turner, N.; Nicholls, J. T. Physical Review B, Vol. 50, Issue 20 https://doi.org/10.1103/PhysRevB.50.15465	journal	November 1994
Composite fermions and Landau-level mixing in the fractional quantum Hall effect Melik-Alaverdian, V.; Bonesteel, N. E. Physical Review B, Vol. 52, Issue 24 https://doi.org/10.1103/PhysRevB.52.R17032	journal	December 1995
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
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
Evidence for a spin transition in the ν= 2 5 fractional quantum Hall effect Kang, W.; Young, J. B.; Hannahs, S. T. Physical Review B, Vol. 56, Issue 20 https://doi.org/10.1103/PhysRevB.56.R12776	journal	November 1997
Rotons of composite fermions: Comparison between theory and experiment Scarola, Vito W.; Park, Kwon; Jain, Jainendra K. Physical Review B, Vol. 61, Issue 19 https://doi.org/10.1103/PhysRevB.61.13064	journal	May 2000
Phase diagram of bilayer composite fermion states Scarola, V. W.; Jain, J. K. Physical Review B, Vol. 64, Issue 8 https://doi.org/10.1103/PhysRevB.64.085313	journal	August 2001
Fermi contour anisotropy of GaAs electron-flux composite fermions in parallel magnetic fields Kamburov, D.; Mueed, M. A.; Shayegan, M. Physical Review B, Vol. 89, Issue 8 https://doi.org/10.1103/PhysRevB.89.085304	journal	February 2014
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
Exact results for model wave functions of anisotropic composite fermions in the fractional quantum Hall effect Balram, Ajit C.; Jain, J. K. Physical Review B, Vol. 93, Issue 7 https://doi.org/10.1103/PhysRevB.93.075121	journal	February 2016
Spin and the Coulomb gap in the half-filled lowest Landau level Eisenstein, J. P.; Khaire, T.; Nandi, D. Physical Review B, Vol. 94, Issue 12 https://doi.org/10.1103/PhysRevB.94.125409	journal	September 2016
Spin-Dependent Phase Diagram of the ν T = 1 Bilayer Electron System Giudici, P.; Muraki, K.; Kumada, N. Physical Review Letters, Vol. 100, Issue 10 https://doi.org/10.1103/PhysRevLett.100.106803	journal	March 2008
Quantum Hall Exciton Condensation at Full Spin Polarization Finck, A. D. K.; Eisenstein, J. P.; Pfeiffer, L. N. Physical Review Letters, Vol. 104, Issue 1 https://doi.org/10.1103/PhysRevLett.104.016801	journal	January 2010
Fractional Quantum Hall Phase Transitions and Four-Flux States in Graphene Feldman, Benjamin E.; Levin, Andrei J.; Krauss, Benjamin Physical Review Letters, Vol. 111, Issue 7 https://doi.org/10.1103/PhysRevLett.111.076802	journal	August 2013
Splitting of the Fermi Contour of Quasi-2D Electrons in Parallel Magnetic Fields Mueed, M. A.; Kamburov, D.; Shayegan, M. Physical Review Letters, Vol. 114, Issue 23 https://doi.org/10.1103/PhysRevLett.114.236404	journal	June 2015
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
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
Evidence for a phase transition in the fractional quantum Hall effect Eisenstein, J. P.; Stormer, H. L.; Pfeiffer, L. Physical Review Letters, Vol. 62, Issue 13 https://doi.org/10.1103/PhysRevLett.62.1540	journal	March 1989
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
Equilibrium tunneling from the two-dimensional electron gas in GaAs: Evidence for a magnetic-field-induced energy gap Ashoori, R. C.; Lebens, J. A.; Bigelow, N. P. Physical Review Letters, Vol. 64, Issue 6 https://doi.org/10.1103/PhysRevLett.64.681	journal	February 1990
Neutral superfluid modes and ‘‘magnetic’’ monopoles in multilayered quantum Hall systems Wen, Xiao-Gang; Zee, A. Physical Review Letters, Vol. 69, Issue 12 https://doi.org/10.1103/PhysRevLett.69.1811	journal	September 1992
Coulomb barrier to tunneling between parallel two-dimensional electron systems Eisenstein, J. P.; Pfeiffer, L. N.; West, K. W. Physical Review Letters, Vol. 69, Issue 26 https://doi.org/10.1103/PhysRevLett.69.3804	journal	December 1992
Magnetophonon shakeup in a Wigner crystal: Applications to tunneling spectroscopy in the quantum Hall regime Johansson, Peter; Kinaret, Jari M. Physical Review Letters, Vol. 71, Issue 9 https://doi.org/10.1103/PhysRevLett.71.1435	journal	August 1993
Mixed-spin incompressible states in the fractional quantum Hall effect Wu, X. G.; Dev, G.; Jain, J. K. Physical Review Letters, Vol. 71, Issue 1 https://doi.org/10.1103/PhysRevLett.71.153	journal	July 1993
New stochastic method for systems with broken time-reversal symmetry: 2D fermions in a magnetic field Ortiz, G.; Ceperley, D. M.; Martin, R. M. Physical Review Letters, Vol. 71, Issue 17 https://doi.org/10.1103/PhysRevLett.71.2777	journal	October 1993
Electron spectral function of an interacting two dimensional electron gas in a strong magnetic field Hatsugai, Y.; Bares, P. -A.; Wen, X. G. Physical Review Letters, Vol. 71, Issue 3 https://doi.org/10.1103/PhysRevLett.71.424	journal	July 1993
Tunneling into a two-dimensional electron system in a strong magnetic field He, Song; Platzman, P. M.; Halperin, B. I. Physical Review Letters, Vol. 71, Issue 5 https://doi.org/10.1103/PhysRevLett.71.777	journal	August 1993
Evidence for an Interlayer Exciton in Tunneling between Two-Dimensional Electron Systems Eisenstein, J. P.; Pfeiffer, L. N.; West, K. W. Physical Review Letters, Vol. 74, Issue 8 https://doi.org/10.1103/PhysRevLett.74.1419	journal	February 1995
Fractional Quantum Hall Effect around ν = 3 2 : Composite Fermions with a Spin Du, R. R.; Yeh, A. S.; Stormer, H. L. Physical Review Letters, Vol. 75, Issue 21 https://doi.org/10.1103/PhysRevLett.75.3926	journal	November 1995
Correlation Energy and Tunneling Density of States in the Fractional Quantum Hall Regime Haussmann, Rudolf; Mori, Hiroyuki; MacDonald, A. H. Physical Review Letters, Vol. 76, Issue 6 https://doi.org/10.1103/PhysRevLett.76.979	journal	February 1996
Quantum Hall Fluids on the Haldane Sphere: A Diffusion Monte Carlo Study Melik-Alaverdian, V.; Bonesteel, N. E.; Ortiz, G. Physical Review Letters, Vol. 79, Issue 26 https://doi.org/10.1103/PhysRevLett.79.5286	journal	December 1997
Phase Diagram of the Spin Polarization of Composite Fermions and a New Effective Mass Park, K.; Jain, J. K. Physical Review Letters, Vol. 80, Issue 19 https://doi.org/10.1103/PhysRevLett.80.4237	journal	May 1998
Spin Polarization of Composite Fermions: Measurements of the Fermi Energy Kukushkin, I. V.; v. Klitzing, K.; Eberl, K. Physical Review Letters, Vol. 82, Issue 18 https://doi.org/10.1103/PhysRevLett.82.3665	journal	May 1999
Effective Mass and g Factor of Four-Flux-Quanta Composite Fermions Yeh, A. S.; Stormer, H. L.; Tsui, D. C. Physical Review Letters, Vol. 82, Issue 3 https://doi.org/10.1103/PhysRevLett.82.592	journal	January 1999
NMR Determination of 2D Electron Spin Polarization at ν = 1 / 2 Melinte, S.; Freytag, N.; Horvatić, M. Physical Review Letters, Vol. 84, Issue 2 https://doi.org/10.1103/PhysRevLett.84.354	journal	January 2000
Resonantly Enhanced Tunneling in a Double Layer Quantum Hall Ferromagnet Spielman, I. B.; Eisenstein, J. P.; Pfeiffer, L. N. Physical Review Letters, Vol. 84, Issue 25 https://doi.org/10.1103/PhysRevLett.84.5808	journal	June 2000
Optical Investigation of Spin-Wave Excitations in Fractional Quantum Hall States and of Interaction between Composite Fermions Kukushkin, I. V.; Smet, J. H.; von Klitzing, K. Physical Review Letters, Vol. 85, Issue 17 https://doi.org/10.1103/PhysRevLett.85.3688	journal	October 2000
New Phase Transition between Partially and Fully Polarized Quantum Hall States with Charge and Spin Gaps at ν = 2 3 Freytag, N.; Tokunaga, Y.; Horvatić, M. Physical Review Letters, Vol. 87, Issue 13 https://doi.org/10.1103/PhysRevLett.87.136801	journal	September 2001
Observation of Quantized Hall Drag in a Strongly Correlated Bilayer Electron System Kellogg, M.; Spielman, I. B.; Eisenstein, J. P. Physical Review Letters, Vol. 88, Issue 12 https://doi.org/10.1103/PhysRevLett.88.126804	journal	March 2002
NMR Investigation of How Free Composite Fermions Are at ν = 1 2 Freytag, N.; Horvatić, M.; Berthier, C. Physical Review Letters, Vol. 89, Issue 24 https://doi.org/10.1103/PhysRevLett.89.246804	journal	November 2002
Vanishing Hall Resistance at High Magnetic Field in a Double-Layer Two-Dimensional Electron System Kellogg, M.; Eisenstein, J. P.; Pfeiffer, L. N. Physical Review Letters, Vol. 93, Issue 3 https://doi.org/10.1103/PhysRevLett.93.036801	journal	July 2004
Counterflow Measurements in Strongly Correlated GaAs Hole Bilayers: Evidence for Electron-Hole Pairing Tutuc, E.; Shayegan, M.; Huse, D. A. Physical Review Letters, Vol. 93, Issue 3 https://doi.org/10.1103/PhysRevLett.93.036802	journal	July 2004
Activated Transport in the Separate Layers that Form the ν T = 1 Exciton Condensate Wiersma, R. D.; Lok, J. G. S.; Kraus, S. Physical Review Letters, Vol. 93, Issue 26 https://doi.org/10.1103/PhysRevLett.93.266805	journal	December 2004
Reconstructing the Electron in a Fractionalized Quantum Fluid Jain, Jainendra K.; Peterson, Michael R. Physical Review Letters, Vol. 94, Issue 18 https://doi.org/10.1103/PhysRevLett.94.186808	journal	May 2005
Spin Transition in the Half-Filled Landau Level Tracy, L. A.; Eisenstein, J. P.; Pfeiffer, L. N. Physical Review Letters, Vol. 98, Issue 8 https://doi.org/10.1103/PhysRevLett.98.086801	journal	February 2007
Quantum Monte Carlo simulations of solids Foulkes, W. M. C.; Mitas, L.; Needs, R. J. Reviews of Modern Physics, Vol. 73, Issue 1 https://doi.org/10.1103/RevModPhys.73.33	journal	January 2001
Unraveling the Spin Polarization of the = 5/2 Fractional Quantum Hall State Tiemann, L.; Gamez, G.; Kumada, N. Science, Vol. 335, Issue 6070 https://doi.org/10.1126/science.1216697	journal	January 2012
Semiclassical theory of the Coulomb anomaly Levitov, S.; Shytov, A. V. Journal of Experimental and Theoretical Physics Letters, Vol. 66, Issue 3 https://doi.org/10.1134/1.567489	journal	August 1997
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
Exciton Condensation in Bilayer Quantum Hall Systems Eisenstein, J. P. Annual Review of Condensed Matter Physics, Vol. 5, Issue 1 https://doi.org/10.1146/annurev-conmatphys-031113-133832	journal	March 2014

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