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Cheng B, Pan C, Che S, Wang P, Wu Y, Watanabe K, Taniguchi T, Ge S, Lake R, Smirnov D, Lau CN, Bockrath M. Fractional and Symmetry-Broken Chern Insulators in Tunable Moiré Superlattices. NANO LETTERS 2019; 19:4321-4326. [PMID: 31204812 DOI: 10.1021/acs.nanolett.9b00811] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
We study dual-gated graphene bilayer/hBN moiré superlattices. Under zero magnetic field, we observe additional resistance peaks as the charge density varies. The peaks' resistivities vary approximately quadratically with an applied perpendicular displacement field D. Data fit to a continuum model yield a bilayer/hBN interaction energy scale ∼30 ± 10 meV. Under a perpendicular magnetic field, we observe Hofstadter butterfly spectra as well as symmetry-broken and fractional Chern insulator states. Their topology and lattice symmetry breaking is D-tunable, enabling the realization of new topological states in this system.
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Affiliation(s)
- Bin Cheng
- Department of Physics and Astronomy , University of California , Riverside , California 92521 , United States
| | - Cheng Pan
- Department of Physics and Astronomy , University of California , Riverside , California 92521 , United States
| | - Shi Che
- Department of Physics and Astronomy , University of California , Riverside , California 92521 , United States
- Department of Physics , The Ohio State University , Columbus , Ohio 43221 , United States
| | - Peng Wang
- Department of Physics and Astronomy , University of California , Riverside , California 92521 , United States
| | - Yong Wu
- Department of Physics and Astronomy , University of California , Riverside , California 92521 , United States
| | - Kenji Watanabe
- National Institute for Materials Science , 1-1 Namiki Tsukuba , Ibaraki 305-0044 , Japan
| | - Takashi Taniguchi
- National Institute for Materials Science , 1-1 Namiki Tsukuba , Ibaraki 305-0044 , Japan
| | - Supeng Ge
- Department of Electrical and Computer Engineering , University of California , Riverside , California 92521 , United States
| | - Roger Lake
- Department of Electrical and Computer Engineering , University of California , Riverside , California 92521 , United States
| | - Dmitry Smirnov
- National High Magnetic Field Laboratory , Tallahassee , Florida 32310 , United States
| | - Chun Ning Lau
- Department of Physics , The Ohio State University , Columbus , Ohio 43221 , United States
| | - Marc Bockrath
- Department of Physics , The Ohio State University , Columbus , Ohio 43221 , United States
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2
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Pan C, Wu Y, Cheng B, Che S, Taniguchi T, Watanabe K, Lau CN, Bockrath M. Layer Polarizability and Easy-Axis Quantum Hall Ferromagnetism in Bilayer Graphene. NANO LETTERS 2017; 17:3416-3420. [PMID: 28429942 DOI: 10.1021/acs.nanolett.7b00197] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
We report magnetotransport measurements of graphene bilayers at large perpendicular electric displacement fields, up to ∼1.5 V/nm, where we observe crossings between Landau levels with different orbital quantum numbers. The displacement fields at the studied crossings are primarily determined by energy shifts originating from the Landau level layer polarizability or polarization. Despite decreasing Landau level spacing with energy, successive crossings occur at larger displacement fields, resulting from decreasing polarizability with orbital quantum number. For particular crossings we observe resistivity hysteresis in displacement field, indicating the presence of a first-order transition between states exhibiting easy-axis quantum Hall ferromagnetism.
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Affiliation(s)
- C Pan
- Department of Physics and Astronomy, University of California , Riverside, California 92521, United States
| | - Y Wu
- Department of Physics and Astronomy, University of California , Riverside, California 92521, United States
| | - B Cheng
- Department of Physics and Astronomy, University of California , Riverside, California 92521, United States
| | - S Che
- Department of Physics and Astronomy, University of California , Riverside, California 92521, United States
| | - T Taniguchi
- Advanced Materials Laboratory, National Institute for Materials Science , Tsukuba, Ibaraki 305-0044, Japan
| | - K Watanabe
- Advanced Materials Laboratory, National Institute for Materials Science , Tsukuba, Ibaraki 305-0044, Japan
| | - C N Lau
- Department of Physics and Astronomy, University of California , Riverside, California 92521, United States
| | - M Bockrath
- Department of Physics and Astronomy, University of California , Riverside, California 92521, United States
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Chakraborty T, Manaselyan A, Barseghyan M. Interaction-driven distinctive electronic states of artificial atoms at the ZnO interface. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2017; 29:215301. [PMID: 28437254 DOI: 10.1088/1361-648x/aa6b97] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
We have investigated the electronic states of planar quantum dots at the ZnO interface containing a few interacting electrons in an externally applied magnetic field. The electron-electron interaction effects are expected to be much stronger in this case than in traditional semiconductor quantum systems, such as in GaAs or InAs quantum dots. In order to highlight that stronger Coulomb effects in the ZnO quantum dots, we have compared the energy spectra and the magnetization in this system to those of the InAs quantum dots. We have found that in the ZnO quantum dots the signatures of stronger Coulomb interaction manifests in an unique ground state that has very different properties than the corresponding ones in the InAs dot. Our results for the magnetization also exhibits behaviors never before observed in a quantum dot for a realistic set of parameters. We have found a stronger temperature dependence and other unexpected features, such as paramagnetic-like behavior at high temperatures for a quantum-dot helium.
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Affiliation(s)
- Tapash Chakraborty
- Department of Physics and Astronomy, University of Manitoba, Winnipeg, R3T 2N2, Canada
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4
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Robust fractional quantum Hall effect in the N=2 Landau level in bilayer graphene. Nat Commun 2016; 7:13908. [PMID: 28000663 PMCID: PMC5187585 DOI: 10.1038/ncomms13908] [Citation(s) in RCA: 24] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/02/2016] [Accepted: 11/11/2016] [Indexed: 11/09/2022] Open
Abstract
The fractional quantum Hall effect is a canonical example of electron-electron interactions producing new ground states in many-body systems. Most fractional quantum Hall studies have focussed on the lowest Landau level, whose fractional states are successfully explained by the composite fermion model. In the widely studied GaAs-based system, the composite fermion picture is thought to become unstable for the N≥2 Landau level, where competing many-body phases have been observed. Here we report magneto-resistance measurements of fractional quantum Hall states in the N=2 Landau level (filling factors 4<|ν|<8) in bilayer graphene. In contrast with recent observations of particle-hole asymmetry in the N=0/N=1 Landau levels of bilayer graphene, the fractional quantum Hall states we observe in the N=2 Landau level obey particle-hole symmetry within the fully symmetry-broken Landau level. Possible alternative ground states other than the composite fermions are discussed.
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5
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Luo W, Chakraborty T. Excitation gap of fractal quantum hall states in graphene. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2016; 28:015801. [PMID: 26657089 DOI: 10.1088/0953-8984/28/1/015801] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
In the presence of a magnetic field and an external periodic potential the Landau level spectrum of a two-dimensional electron gas exhibits a fractal pattern in the energy spectrum which is described as the Hofstadter's butterfly. In this work, we develop a Hartree-Fock theory to deal with the electron-electron interaction in the Hofstadter's butterfly state in a finite-size graphene with periodic boundary conditions, where we include both spin and valley degrees of freedom. We then treat the butterfly state as an electron crystal so that we could obtain the order parameters of the crystal in the momentum space and also in an infinite sample. A phase transition between the liquid phase and the fractal crystal phase can be observed. The excitation gaps obtained in the infinite sample is comparable to those in the finite-size study, and agree with a recent experimental observation.
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Affiliation(s)
- Wenchen Luo
- Departement of Physics and Astronomy, University of Manitoba, Winnipeg R3T 2N2, Canada
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6
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Kim Y, Lee DS, Jung S, Skákalová V, Taniguchi T, Watanabe K, Kim JS, Smet JH. Fractional Quantum Hall States in Bilayer Graphene Probed by Transconductance Fluctuations. NANO LETTERS 2015; 15:7445-7451. [PMID: 26479836 DOI: 10.1021/acs.nanolett.5b02876] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
We have investigated fractional quantum Hall (QH) states in Bernal-stacked bilayer graphene using transconductance fluctuation measurements. A variety of odd-denominator fractional QH states with νQH → νQH + 2 symmetry, as previously reported, are observed. However, surprising is that also particle-hole symmetric states are clearly resolved in the same measurement set. We attribute their emergence to the reversal of orbital states in the octet level scheme induced by a strong local charge imbalance, which can be captured by the transconductance fluctuations. Also the even-denominator fractional QH state at filling -1/2 is observed. However, contrary to a previous study on a suspended graphene layer [ Ki et al. Nano Lett. 2014, 14 , 2135 ], the particle-hole symmetric state at filling 1/2 is detected as well. These observations suggest that the stability of both odd and even denominator fractional QH states is very sensitive to local transverse electric fields in bilayer graphene.
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Affiliation(s)
- Youngwook Kim
- Department of Physics, Pohang University of Science and Technology , Pohang 790-784, Korea
- Max-Planck-Institut für Festköperforschung , 70569 Stuttgart, Germany
| | - Dong Su Lee
- KIST Jeonbuk Institute of Advanced Composite Materials , Jeonbuk 565-905, Korea
| | - Suyong Jung
- Center for Quantum Measurement Science, Korea Research Institute of Standards and Science , Daejeon, 305-340, Korea
| | - Viera Skákalová
- Faculty of Physics, University of Vienna , Boltzmanngasse 5, 1090 Vienna, Austria
- STU Center for Nanodiagnostics , Vazovova 5, 812 43 Bratislava, Slovakia
| | - T Taniguchi
- Advanced Materials Laboratory, National Institute for Materials Science , 1-1 Namiki, Tsukuba, 305-0044, Japan
| | - K Watanabe
- Advanced Materials Laboratory, National Institute for Materials Science , 1-1 Namiki, Tsukuba, 305-0044, Japan
| | - Jun Sung Kim
- Department of Physics, Pohang University of Science and Technology , Pohang 790-784, Korea
| | - Jurgen H Smet
- Max-Planck-Institut für Festköperforschung , 70569 Stuttgart, Germany
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7
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Ghazaryan A, Chakraborty T, Pietiläinen P. Fractional quantum Hall effect in Hofstadter butterflies of Dirac fermions. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2015; 27:185301. [PMID: 25894009 DOI: 10.1088/0953-8984/27/18/185301] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
We report on the influence of a periodic potential on the fractional quantum Hall effect (FQHE) states in monolayer graphene. We have shown that for two values of the magnetic flux per unit cell (one-half and one-third flux quantum) an increase of the periodic potential strength results in a closure of the FQHE gap and appearance of gaps due to the periodic potential. In the case of one-half flux quantum this causes a change of the ground state and consequently the change of the momentum of the system in the ground state. While there is also crossing between low-lying energy levels for one-third flux quantum, the ground state does not change with the increase of the periodic potential strength and is always characterized by the same momentum. Finally, it is shown that for one-half flux quantum the emergent gaps are due entirely to the electron-electron interaction, whereas for the one-third flux quantum per unit cell these are due to both non-interacting electrons (Hofstadter butterfly pattern) and the electron-electron interaction.
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Affiliation(s)
- Areg Ghazaryan
- Department of Physics and Astronomy, University of Manitoba, Winnipeg, MB R3T 2N2, Canada
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8
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Insulating state in tetralayers reveals an even-odd interaction effect in multilayer graphene. Nat Commun 2015; 6:6419. [PMID: 25732058 PMCID: PMC4366515 DOI: 10.1038/ncomms7419] [Citation(s) in RCA: 43] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/23/2014] [Accepted: 01/27/2015] [Indexed: 11/08/2022] Open
Abstract
Close to charge neutrality, the electronic properties of graphene and its multilayers are sensitive to electron-electron interactions. In bilayers, for instance, interactions are predicted to open a gap between valence and conduction bands, turning the system into an insulator. In mono and (Bernal-stacked) trilayers, which remain conducting at low temperature, interactions do not have equally drastic consequences. It is expected that interaction effects become weaker for thicker multilayers, whose behaviour should converge to that of graphite. Here we show that this expectation does not correspond to reality by revealing the occurrence of an insulating state close to charge neutrality in Bernal-stacked tetralayer graphene. The phenomenology-incompatible with the behaviour expected from the single-particle band structure-resembles that observed in bilayers, but the insulating state in tetralayers is visible at higher temperature. We explain our findings, and the systematic even-odd effect of interactions in Bernal-stacked layers of different thickness that emerges from experiments, in terms of a generalization of the interaction-driven, symmetry-broken states proposed for bilayers.
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9
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Kou A, Feldman BE, Levin AJ, Halperin BI, Watanabe K, Taniguchi T, Yacoby A. Electron-hole asymmetric integer and fractional quantum Hall effect in bilayer graphene. Science 2014; 345:55-7. [DOI: 10.1126/science.1250270] [Citation(s) in RCA: 84] [Impact Index Per Article: 8.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Affiliation(s)
- A. Kou
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
- Department of Applied Physics, Yale University, New Haven, CT 06520, USA
| | - B. E. Feldman
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - A. J. Levin
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - B. I. Halperin
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - K. Watanabe
- National Institute for Materials Science, Tsukuba, Japan
| | - T. Taniguchi
- National Institute for Materials Science, Tsukuba, Japan
| | - A. Yacoby
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
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10
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Maher P, Wang L, Gao Y, Forsythe C, Taniguchi T, Watanabe K, Abanin D, Papić Z, Cadden-Zimansky P, Hone J, Kim P, Dean CR. Tunable fractional quantum Hall phases in bilayer graphene. Science 2014; 345:61-4. [DOI: 10.1126/science.1252875] [Citation(s) in RCA: 122] [Impact Index Per Article: 12.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Abstract
Symmetry-breaking in a quantum system often leads to complex emergent behavior. In bilayer graphene (BLG), an electric field applied perpendicular to the basal plane breaks the inversion symmetry of the lattice, opening a band gap at the charge neutrality point. In a quantizing magnetic field, electron interactions can cause spontaneous symmetry-breaking within the spin and valley degrees of freedom, resulting in quantum Hall effect (QHE) states with complex order. Here, we report fractional QHE states in BLG that show phase transitions that can be tuned by a transverse electric field. This result provides a model platform with which to study the role of symmetry-breaking in emergent states with topological order.
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11
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Apalkov VM, Chakraborty T. Gap structure of the Hofstadter system of interacting Dirac fermions in graphene. PHYSICAL REVIEW LETTERS 2014; 112:176401. [PMID: 24836259 DOI: 10.1103/physrevlett.112.176401] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/13/2013] [Indexed: 06/03/2023]
Abstract
The effects of mutual Coulomb interactions between Dirac fermions in monolayer graphene on the Hofstadter energy spectrum are investigated. For two flux quanta per unit cell of the periodic potential, interactions open a gap in each Landau level with the smallest gap in the n=1 Landau level. For more flux quanta through the unit cell, where the noninteracting energy spectra have many gaps in each Landau level, interactions enhance the low-energy gaps and strongly suppress the high-energy gaps and almost close a high-energy gap for n=1. The signature of the interaction effects in the Hofstadter system can be probed through magnetization, which is governed by the mixing of the Landau levels and is enhanced by the Coulomb interaction.
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Affiliation(s)
- Vadim M Apalkov
- Department of Physics and Astronomy, Georgia State University, Atlanta, Georgia 30303, USA
| | - Tapash Chakraborty
- Department of Physics and Astronomy, University of Manitoba, Winnipeg, Canada R3T 2N2
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12
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Ki DK, Fal'ko VI, Abanin DA, Morpurgo AF. Observation of even denominator fractional quantum Hall effect in suspended bilayer graphene. NANO LETTERS 2014; 14:2135-2139. [PMID: 24611523 DOI: 10.1021/nl5003922] [Citation(s) in RCA: 51] [Impact Index Per Article: 5.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
We investigate low-temperature magneto-transport in recently developed, high-quality multiterminal suspended bilayer graphene devices, enabling the independent measurement of the longitudinal and transverse resistance. We observe clear signatures of the fractional quantum Hall effect with different states that are either fully developed, and exhibit a clear plateau in the transverse resistance with a concomitant dip in longitudinal resistance or incipient, and exhibit only a longitudinal resistance minimum. All observed states scale as a function of filling factor ν, as expected. An unprecedented even-denominator fractional state is observed at ν = -1/2 on the hole side, exhibiting a clear plateau in Rxy quantized at the expected value of 2h/e(2) with a precision of ∼0.5%. Many of our observations, together with a recent electronic compressibility measurement performed in graphene bilayers on hexagonal boron-nitride (hBN) substrates, are consistent with a recent theory that accounts for the effect of the degeneracy between the N = 0 and N = 1 Landau levels in the fractional quantum Hall effect and predicts the occurrence of a Moore-Read type ν = -1/2 state. Owing to the experimental flexibility of bilayer graphene, which has a gate-dependent band structure, can be easily accessed by scanning probes, and can be contacted with materials such as superconductors, our findings offer new possibilities to explore the microscopic nature of even-denominator fractional quantum Hall effect.
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Affiliation(s)
- Dong-Keun Ki
- Départment de Physique de la Matiére Condensée (DPMC) and Group of Applied Physics (GAP), University of Geneva , 24 Quai Ernest-Ansermet, CH1211 Genéve 4 Switzerland
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13
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Papić Z, Abanin DA. Topological phases in the zeroth Landau level of bilayer graphene. PHYSICAL REVIEW LETTERS 2014; 112:046602. [PMID: 24580475 DOI: 10.1103/physrevlett.112.046602] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/15/2013] [Indexed: 06/03/2023]
Abstract
We analyze the phase diagram of the zeroth Landau level of bilayer graphene, taking into account the realistic effects of screening of the Coulomb interaction and strong mixing between two degenerate sublevels. We identify robust quantum Hall states at filling factors ν=-1, -4/3, -5/3, -8/5, -1/2 and discuss the nature of their ground states, collective excitations, and relation to the more familiar states in GaAs using a tractable model. In particular, we present evidence that the ν=-1/2 state is non-Abelian and described by either the Moore-Read wave function or its particle-hole conjugate, while ruling out other candidates such as the 331 state.
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Affiliation(s)
- Z Papić
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA and Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada and Institute for Quantum Computing, Waterloo, Ontario N2L 3G1, Canada
| | - D A Abanin
- Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada and Institute for Quantum Computing, Waterloo, Ontario N2L 3G1, Canada
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14
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Feldman BE, Levin AJ, Krauss B, Abanin DA, Halperin BI, Smet JH, Yacoby A. Fractional quantum Hall phase transitions and four-flux states in graphene. PHYSICAL REVIEW LETTERS 2013; 111:076802. [PMID: 23992076 DOI: 10.1103/physrevlett.111.076802] [Citation(s) in RCA: 34] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/07/2013] [Indexed: 06/02/2023]
Abstract
Graphene and its multilayers have attracted considerable interest because their fourfold spin and valley degeneracy enables a rich variety of broken-symmetry states arising from electron-electron interactions, and raises the prospect of controlled phase transitions among them. Here we report local electronic compressibility measurements of ultraclean suspended graphene that reveal a multitude of fractional quantum Hall states surrounding filling factors ν=-1/2 and -1/4. Several of these states exhibit phase transitions that indicate abrupt changes in the underlying order, and we observe many additional oscillations in compressibility as ν approaches -1/2, suggesting further changes in spin and/or valley polarization. We use a simple model based on crossing Landau levels of composite fermions with different internal degrees of freedom to explain many qualitative features of the experimental data. Our results add to the diverse array of many-body states observed in graphene and demonstrate substantial control over their order parameters.
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Affiliation(s)
- Benjamin E Feldman
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
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15
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McCann E, Koshino M. The electronic properties of bilayer graphene. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2013; 76:056503. [PMID: 23604050 DOI: 10.1088/0034-4885/76/5/056503] [Citation(s) in RCA: 201] [Impact Index Per Article: 18.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/21/2023]
Abstract
We review the electronic properties of bilayer graphene, beginning with a description of the tight-binding model of bilayer graphene and the derivation of the effective Hamiltonian describing massive chiral quasiparticles in two parabolic bands at low energies. We take into account five tight-binding parameters of the Slonczewski-Weiss-McClure model of bulk graphite plus intra- and interlayer asymmetry between atomic sites which induce band gaps in the low-energy spectrum. The Hartree model of screening and band-gap opening due to interlayer asymmetry in the presence of external gates is presented. The tight-binding model is used to describe optical and transport properties including the integer quantum Hall effect, and we also discuss orbital magnetism, phonons and the influence of strain on electronic properties. We conclude with an overview of electronic interaction effects.
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Affiliation(s)
- Edward McCann
- Department of Physics, Lancaster University, Lancaster LA1 4YB, UK
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16
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Apalkov VM, Chakraborty T. Stable Pfaffian state in bilayer graphene. PHYSICAL REVIEW LETTERS 2011; 107:186803. [PMID: 22107662 DOI: 10.1103/physrevlett.107.186803] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/08/2011] [Indexed: 05/31/2023]
Abstract
Here, we show that the incompressible Pfaffian state originally proposed for the 5/2 fractional quantum Hall states in conventional two-dimensional electron systems can actually be found in a bilayer graphene at one of the Landau levels. The properties and stability of the Pfaffian state at this special Landau level strongly depend on the magnetic field strength. The graphene system shows a transition from the incompressible to a compressible state with increasing magnetic field. At a finite magnetic field of ~10 T, the Pfaffian state in bilayer graphene becomes more stable than its counterpart in conventional electron systems.
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Affiliation(s)
- Vadim M Apalkov
- Department of Physics and Astronomy, Georgia State University, Atlanta, Georgia 30303, USA
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