1983
DOI: 10.1103/physrevlett.51.605
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Fractional Quantization of the Hall Effect: A Hierarchy of Incompressible Quantum Fluid States

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Cited by 2,155 publications
(2,583 citation statements)
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“…(The case of charged fermions on CP 1 = S 2 with U (1) background field, corresponding to k = 1, was studied by Haldane several years ago [21]. In this case the background gauge field a is that of a monopole of charge n placed at the origin of S 2 .…”
Section: Quantum Hall Effect On Cp Kmentioning
confidence: 99%
“…(The case of charged fermions on CP 1 = S 2 with U (1) background field, corresponding to k = 1, was studied by Haldane several years ago [21]. In this case the background gauge field a is that of a monopole of charge n placed at the origin of S 2 .…”
Section: Quantum Hall Effect On Cp Kmentioning
confidence: 99%
“…For the Laughlin state in a pure 2DES it is 0.0276e 2 /εl 0 [43]. For the qd-liquid, the corresponding value is 0.32 meV and is expected to decrease a little further with increasing number of electrons in the system representing the incompressible liquid [42]. This result indicates that the small thermal energy of about 0.2 meV required to destroy the anomaly is in fact, the quasihole energy gap.…”
Section: Theoretical Modelmentioning
confidence: 58%
“…[39]. We model the incompressible state at ν = 1/3 filling using the spherical geometry [42] for six electrons. Electrons are treated as spinless particles corresponding to the state described by the Laughlin wave function [28].…”
Section: Theoretical Modelmentioning
confidence: 99%
“…The numerical results are obtained by numerical diagonalization of the interaction Hamiltonian of a finite number N of electrons (and, sometimes, one or more valence holes) confined on a spherical surface of radius R. In this model, the radial magnetic field B is due to a monopole in the center [5]. The monopole strength 2Q is defined in units of elementary flux φ 0 = hc/e, so that 4πR 2 B = 2Qφ 0 and the electron magnetic length is λ = R/ √ Q.…”
Section: Modelmentioning
confidence: 99%
“…The arguably most prominent macroscopic phenomena associated with the fascinating physics of the 2DEG at high B and low T are integral [1,2] and fractional [3,4] quantum Hall effects observed in transport experiments. Some of the most fundamental concepts developed to understand these phenomena are the fractionally charged Laughlin quasiparticles (QP's) [4][5][6] and composite fermions (CF's) [7]. However, also the optical and spin properties of the 2DEG have been intensively studied in this regime, both experimentally [8][9][10] and theoretically [11][12][13][14][15].…”
Section: Introductionmentioning
confidence: 99%