Ensemble Density Functional Theory for Inhomogeneous Fractional Quantum Hall Systems

  • O. Heinonen
  • M. I. Lubin
  • M. D. Johnson


The fractional quantum Hall effect (FQHE) occurs in a two-dimensional electron gas (2DEG) in a strong magnetic field oriented perpendicular to the plane of the electrons [1]. The effect was discovered as a transport anomaly. In a transport measurement it is noted that at certain strengths B*(n), which depend on the density n of the 2DEG, current can flow without any dissipation. That is, there is no voltage drop along the flow of the current. At the same time, the Hall voltage perpendicular to both the direction of the current and of the magnetic field is observed to attain a quantized value for a small, but finite, range of magnetic field or density, depending on which quantity is varied in the experiment. The effect is understood to be the result of an excitation gap in the spectrum of an infinite 2DEG at these magnetic fields. A convenient measure of the density of a 2DEG in a strong magnetic field is given by the filling factor v = 2πℓ2 B n, with \({\ell _B}{\mkern 1mu} = {\mkern 1mu} \sqrt {\hbar c/(eB)} \) the magnetic length. The filling factor gives the ratio of the number of particles to the number of available states in a magnetc sub-band (Landau level), or, equivalently, the number of particles per flux quantum Φ0 = hc/e. The quantum Hall effect was first discovered [2] at integer filling factors. In this integer quantum Hall effect, the energy gap is nothing but the kinetic energy gap ħω c = ħeB/(m*c). Later, the fractional quantum Hall effect (FQHE) was discovered [3] at certain rational filling factors of the form v = p/q, with p and q relative primes, and q odd. In the FQHE, the excitation gap is a consequence of the strong electron-electron correlations. Therefore, any computational approach to the quantum Hall effect must accurately treat the electron correlations in order to capture the FQHE at all


Filling Factor Local Density Approximation Quantum Hall Effect Slater Determinant Lower Landau Level 
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Copyright information

© Springer Science+Business Media New York 1998

Authors and Affiliations

  • O. Heinonen
    • 1
  • M. I. Lubin
    • 1
  • M. D. Johnson
    • 1
  1. 1.Department of PhysicsUniversity of Central FloridaOrlandoUSA

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