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Bilayer Wigner crystals in a transition metal dichalcogenide heterostructure. Nature 2021; 595:48-52. [PMID: 34194017 DOI: 10.1038/s41586-021-03560-w] [Citation(s) in RCA: 45] [Impact Index Per Article: 15.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/04/2020] [Accepted: 04/15/2021] [Indexed: 02/06/2023]
Abstract
One of the first theoretically predicted manifestations of strong interactions in many-electron systems was the Wigner crystal1-3, in which electrons crystallize into a regular lattice. The crystal can melt via either thermal or quantum fluctuations4. Quantum melting of the Wigner crystal is predicted to produce exotic intermediate phases5,6 and quantum magnetism7,8 because of the intricate interplay of Coulomb interactions and kinetic energy. However, studying two-dimensional Wigner crystals in the quantum regime has often required a strong magnetic field9-11 or a moiré superlattice potential12-15, thus limiting access to the full phase diagram of the interacting electron liquid. Here we report the observation of bilayer Wigner crystals without magnetic fields or moiré potentials in an atomically thin transition metal dichalcogenide heterostructure, which consists of two MoSe2 monolayers separated by hexagonal boron nitride. We observe optical signatures of robust correlated insulating states at symmetric (1:1) and asymmetric (3:1, 4:1 and 7:1) electron doping of the two MoSe2 layers at cryogenic temperatures. We attribute these features to bilayer Wigner crystals composed of two interlocked commensurate triangular electron lattices, stabilized by inter-layer interaction16. The Wigner crystal phases are remarkably stable, and undergo quantum and thermal melting transitions at electron densities of up to 6 × 1012 per square centimetre and at temperatures of up to about 40 kelvin. Our results demonstrate that an atomically thin heterostructure is a highly tunable platform for realizing many-body electronic states and probing their liquid-solid and magnetic quantum phase transitions4-8,17.
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Zarenia M, Hamilton AR, Peeters FM, Neilson D. Multiband Mechanism for the Sign Reversal of Coulomb Drag Observed in Double Bilayer Graphene Heterostructures. PHYSICAL REVIEW LETTERS 2018; 121:036601. [PMID: 30085815 DOI: 10.1103/physrevlett.121.036601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/29/2018] [Indexed: 06/08/2023]
Abstract
Coupled 2D sheets of electrons and holes are predicted to support novel quantum phases. Two experiments of Coulomb drag in electron-hole (e-h) double bilayer graphene (DBLG) have reported an unexplained and puzzling sign reversal of the drag signal. However, we show that this effect is due to the multiband character of DBLG. Our multiband Fermi liquid theory produces excellent agreement and captures the key features of the experimental drag resistance for all temperatures. This demonstrates the importance of multiband effects in DBLG: they have a strong effect not only on superfluidity, but also on the drag.
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Affiliation(s)
- M Zarenia
- Department of Physics, University of Antwerp, Groenenborgerlaan 171, 2020 Antwerp, Belgium
- Department of Physics and Astronomy, University of Missouri, Columbia, Missouri 65211, USA
| | - A R Hamilton
- ARC Centre of Excellence for Future Low Energy Electronics Technologies, School of Physics, The University of New South Wales, Sydney, New South Wales 2052, Australia
| | - F M Peeters
- Department of Physics, University of Antwerp, Groenenborgerlaan 171, 2020 Antwerp, Belgium
| | - D Neilson
- Department of Physics, University of Antwerp, Groenenborgerlaan 171, 2020 Antwerp, Belgium
- Physics Division, Science & Technology School, University of Camerino, 62032 Camerino, Italy
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Inhomogeneous phases in coupled electron-hole bilayer graphene sheets: Charge Density Waves and Coupled Wigner Crystals. Sci Rep 2017; 7:11510. [PMID: 28912465 PMCID: PMC5599685 DOI: 10.1038/s41598-017-11910-w] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/18/2017] [Accepted: 09/01/2017] [Indexed: 11/08/2022] Open
Abstract
Recently proposed accurate correlation energies are used to determine the phase diagram of strongly coupled electron-hole graphene bilayers. The control parameters of the phase diagram are the charge carrier density and the insulating barrier thickness separating the bilayers. In addition to the electron-hole superfluid phase we find two new inhomogeneous ground states, a one dimensional charge density wave phase and a coupled electron-hole Wigner crystal. The elementary crystal structure of bilayer graphene plays no role in generating these new quantum phases, which are completely determined by the electrons and holes interacting through the Coulomb interaction. The experimental parameters for the new phases lie within attainable ranges and therefore coupled electron-hole bilayer graphene presents itself as an experimental system where novel emergent many-body phases can be realized.
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Kumar K, Moudgil RK. Spin polarized and density modulated phases in symmetric electron-electron and electron-hole bilayers. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2012; 24:415601. [PMID: 22989866 DOI: 10.1088/0953-8984/24/41/415601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
We have studied symmetric electron-electron and electron-hole bilayers to explore the stable homogeneous spin phase and the feasibility of inhomogeneous charge-/spin-density ground states. The former is resolved by comparing the ground-state energies in states of different spin polarizations, while the latter is resolved by searching for a divergence in the wavevector-dependent static charge/spin susceptibility. For this endeavour, we have used the dielectric approach within the self-consistent mean-field theory of Singwi et al. We find that the inter-layer interactions tend to change an abrupt spin-polarization transition of an isolated layer into a nearly gradual one, even though the partially spin-polarized phases are not clearly stable within the accuracy of our calculation. The transition density is seen to decrease with a reduction in layer spacing, implying a suppression of spin polarization by inter-layer interactions. Indeed, the suppression shows up distinctly in the spin susceptibility computed from the spin-polarization dependence of the ground-state energy. However, below a critical layer spacing, the unpolarized liquid becomes unstable against a charge-density-wave (CDW) ground state at a density preceding full spin polarization, with the transition density for the CDW state increasing on further reduction in the layer spacing. Due to attractive e-h correlations, the CDW state is found to be more pronounced in the e-h bilayer. On the other hand, the static spin susceptibility diverges only in the long-wavelength limit, which simply represents a transition to the homogeneous spin-polarized phase.
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Affiliation(s)
- Krishan Kumar
- Department of Physics, Kurukshetra University, Kurukshetra, India
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Messina R. Electrostatics in soft matter. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2009; 21:113102. [PMID: 21693906 DOI: 10.1088/0953-8984/21/11/113102] [Citation(s) in RCA: 74] [Impact Index Per Article: 4.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
Recent progress in understanding the effect of electrostatics in soft matter is presented. A vast number of materials contain ions, ranging from the molecular scale (e.g. electrolyte) to the meso/macroscopic one (e.g. charged colloidal particles or polyelectrolytes). Their (micro)structure and physico-chemical properties are especially dictated by the famous and redoubtable long-ranged Coulomb interaction. In particular, theoretical and simulational aspects, including the experimental motivations, will be discussed.
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Affiliation(s)
- René Messina
- Institut für Theoretische Physik II, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, D-40225 Düsseldorf, Germany
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Golden KI, Kalman GJ, Kyrkos S. Charged particle layers in the Debye limit. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2002; 66:031107. [PMID: 12366099 DOI: 10.1103/physreve.66.031107] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/23/2002] [Indexed: 05/23/2023]
Abstract
We develop an equivalent of the Debye-Hückel weakly coupled equilibrium theory for layered classical charged particle systems composed of one single charged species. We consider the two most important configurations, the charged particle bilayer and the infinite superlattice. The approach is based on the link provided by the classical fluctuation-dissipation theorem between the random-phase approximation response functions and the Debye equilibrium pair correlation function. Layer-layer pair correlation functions, screened and polarization potentials, static structure functions, and static response functions are calculated. The importance of the perfect screening and compressibility sum rules in determining the overall behavior of the system, especially in the r--> infinity limit, is emphasized. The similarities and differences between the quasi-two-dimensional bilayer and the quasi-three-dimensional superlattice are highlighted. An unexpected behavior that emerges from the analysis is that the screened potential, the correlations, and the screening charges carried by the individual layers exhibit a marked nonmonotonic dependence on the layer separation.
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Affiliation(s)
- Kenneth I Golden
- Department of Mathematics and Statistics, University of Vermont, Burlington, Vermont 05401-1455, USA.
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Radtke RJ, Tamborenea PI. Spin instabilities in coupled semiconductor quantum wells. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 54:13832-13858. [PMID: 9985301 DOI: 10.1103/physrevb.54.13832] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Lu D, Golden KI, Kalman G, Wyns P, Miao L, Shi XL. Plasmon dispersion in strongly correlated superlattices. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 54:11457-11466. [PMID: 9984933 DOI: 10.1103/physrevb.54.11457] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Thakur JS, Neilson D. Frozen electron solid in the presence of small concentrations of defects. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 54:7674-7677. [PMID: 9984433 DOI: 10.1103/physrevb.54.7674] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Manoharan HC, Suen YW, Santos MB, Shayegan M. Evidence for a Bilayer Quantum Wigner Solid. PHYSICAL REVIEW LETTERS 1996; 77:1813-1816. [PMID: 10063178 DOI: 10.1103/physrevlett.77.1813] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Hamilton AR, Simmons MY, Bolton FM, Patel NK, Millard IS, Nicholls JT, Ritchie DA, Pepper M. Fractional quantum Hall effect in bilayer two-dimensional hole-gas systems. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 54:R5259-R5262. [PMID: 9986583 DOI: 10.1103/physrevb.54.r5259] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Liu L, Swierkowski L, Neilson D, Szymanski J. Static and dynamic properties of coupled electron-electron and electron-hole layers. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 53:7923-7931. [PMID: 9982246 DOI: 10.1103/physrevb.53.7923] [Citation(s) in RCA: 58] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Golden KI, Kalman G. Phenomenological electrodynamics of electronic superlattices. PHYSICAL REVIEW. B, CONDENSED MATTER 1995; 52:14719-14727. [PMID: 9980809 DOI: 10.1103/physrevb.52.14719] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Flensberg K, Hu BY. Plasmon enhancement of Coulomb drag in double-quantum-well systems. PHYSICAL REVIEW. B, CONDENSED MATTER 1995; 52:14796-14808. [PMID: 9980818 DOI: 10.1103/physrevb.52.14796] [Citation(s) in RCA: 46] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Zheng L, Fertig HA. Wigner-crystal states for the two-dimensional electron gas in a double-quantum-well system. PHYSICAL REVIEW. B, CONDENSED MATTER 1995; 52:12282-12290. [PMID: 9980371 DOI: 10.1103/physrevb.52.12282] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Platzman PM, Lenosky T. Possibilities for superconductivity in two-dimensional GaAs bilayers. PHYSICAL REVIEW. B, CONDENSED MATTER 1995; 52:10327-10329. [PMID: 9980083 DOI: 10.1103/physrevb.52.10327] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Alatalo M, Salmi MA, Pietiläinen P, Chakraborty T. Correlations in coupled electron and hole layers of finite thickness. PHYSICAL REVIEW. B, CONDENSED MATTER 1995; 52:7845-7848. [PMID: 9979769 DOI: 10.1103/physrevb.52.7845] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Wang R, Ruden PP. Electron-electron-interaction-induced instability in double quantum-wire structures. PHYSICAL REVIEW. B, CONDENSED MATTER 1995; 52:7826-7829. [PMID: 9979764 DOI: 10.1103/physrevb.52.7826] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Zhu X, Louie SG. Variational quantum Monte Carlo study of two-dimensional Wigner crystals: Exchange, correlation, and magnetic-field effects. PHYSICAL REVIEW. B, CONDENSED MATTER 1995; 52:5863-5884. [PMID: 9981777 DOI: 10.1103/physrevb.52.5863] [Citation(s) in RCA: 23] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Swierkowski L, Szymanski J, Gortel ZW. Coupled electron-hole transport: Beyond the mean field approximation. PHYSICAL REVIEW LETTERS 1995; 74:3245-3248. [PMID: 10058148 DOI: 10.1103/physrevlett.74.3245] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Szymanski J, Swierkowski L, Neilson D. Correlations in coupled layers of electrons and holes. PHYSICAL REVIEW. B, CONDENSED MATTER 1994; 50:11002-11007. [PMID: 9975207 DOI: 10.1103/physrevb.50.11002] [Citation(s) in RCA: 27] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Tamborenea PI. Vertex-correction-driven intersubband spin-density excitonic instability in double quantum well structures. PHYSICAL REVIEW LETTERS 1994; 73:1971-1974. [PMID: 10056935 DOI: 10.1103/physrevlett.73.1971] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Kalman G, Ren Y, Golden KI. Determination of the energy gap in the acoustic excitation of a superlattice. PHYSICAL REVIEW. B, CONDENSED MATTER 1994; 50:2031-2034. [PMID: 9976409 DOI: 10.1103/physrevb.50.2031] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Shimshoni E, Sondhi SL. Quantum Hall effect in Coulomb drag: Interlayer friction in strong magnetic fields. PHYSICAL REVIEW. B, CONDENSED MATTER 1994; 49:11484-11487. [PMID: 10010011 DOI: 10.1103/physrevb.49.11484] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Zheng L, MacDonald AH. Correlation in double-layer two-dimensional electron-gas systems: Singwi-Tosi-Land-Sjölander theory at B=0. PHYSICAL REVIEW. B, CONDENSED MATTER 1994; 49:5522-5530. [PMID: 10011507 DOI: 10.1103/physrevb.49.5522] [Citation(s) in RCA: 41] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Neilson D, Swierkowski L, Szymanski J, Liu L. Excitations of the strongly correlated electron liquid in coupled layers. PHYSICAL REVIEW LETTERS 1993; 71:4035-4038. [PMID: 10055137 DOI: 10.1103/physrevlett.71.4035] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Gold A, Calmels L. Correlation in Fermi liquids: Analytical results for the local-field correction in two and three dimensions. PHYSICAL REVIEW. B, CONDENSED MATTER 1993; 48:11622-11637. [PMID: 10007498 DOI: 10.1103/physrevb.48.11622] [Citation(s) in RCA: 54] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Zheng L, MacDonald AH. Coulomb drag between disordered two-dimensional electron-gas layers. PHYSICAL REVIEW. B, CONDENSED MATTER 1993; 48:8203-8209. [PMID: 10007011 DOI: 10.1103/physrevb.48.8203] [Citation(s) in RCA: 90] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Pudalov VM, D'Iorio M, Kravchenko SV, Campbell JW. Zero-magnetic-field collective insulator phase in a dilute 2D electron system. PHYSICAL REVIEW LETTERS 1993; 70:1866-1869. [PMID: 10053406 DOI: 10.1103/physrevlett.70.1866] [Citation(s) in RCA: 18] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Gold A. Charge-density-wave instability in layered charged quantum liquids. PHYSICAL REVIEW. B, CONDENSED MATTER 1993; 47:6762-6764. [PMID: 10004654 DOI: 10.1103/physrevb.47.6762] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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D'Iorio M, Pudalov VM, Semenchinsky SG. Reentrant insulating phase in Si inversion layers in low magnetic fields. PHYSICAL REVIEW. B, CONDENSED MATTER 1992; 46:15992-16004. [PMID: 10003739 DOI: 10.1103/physrevb.46.15992] [Citation(s) in RCA: 34] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Côté R, Brey L, MacDonald AH. Broken-symmetry ground states for the two-dimensional electron gas in a double-quantum-well system. PHYSICAL REVIEW. B, CONDENSED MATTER 1992; 46:10239-10250. [PMID: 10002867 DOI: 10.1103/physrevb.46.10239] [Citation(s) in RCA: 35] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Gold A. Instability of layered quantum liquids: 1. Local-field correction in superlattices. ACTA ACUST UNITED AC 1992. [DOI: 10.1007/bf01313826] [Citation(s) in RCA: 25] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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Harshman DR, Mills AP. Concerning the nature of high-Tc superconductivity: Survey of experimental properties and implications for interlayer coupling. PHYSICAL REVIEW. B, CONDENSED MATTER 1992; 45:10684-10712. [PMID: 10000975 DOI: 10.1103/physrevb.45.10684] [Citation(s) in RCA: 239] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
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Gammon D, Shanabrook BV, Ryan JC, Katzer DS, Yang MJ. Exchange and correlation in the nonhomogeneous electron gas in semiconductor heterojunctions. PHYSICAL REVIEW LETTERS 1992; 68:1884-1887. [PMID: 10045245 DOI: 10.1103/physrevlett.68.1884] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Gold A. Local-field correction of the charged Bose condensate for two and three dimensions. ACTA ACUST UNITED AC 1992. [DOI: 10.1007/bf01320822] [Citation(s) in RCA: 27] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/03/2023]
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Golden KI, Lu D. Third-frequency-moment sum rule and long-wavelength plasmon dispersion in layered electron liquids. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1992; 45:1084-1088. [PMID: 9907074 DOI: 10.1103/physreva.45.1084] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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