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Exact-exchange density functional theory of the integer quantum Hall effect: strict 2D limit

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Abstract

A strict bidimensional (strict-2D) exact-exchange (EE) formalism within the framework of density-functional theory (DFT) has been developed and applied to the case of an electron gas subjected to a strong perpendicular magnetic field, that drives the system to the regime of the integer quantum Hall effect (IQHE). As the filling of the emerging Landau levels proceeds, two main features results: i) the EE energy minimizes with a discontinuous derivative at every integer filling factor ν; and ii) the EE potential display sharp discontinuities at every integer ν. The present contribution provides a natural improvement as compared with the widely used local-spin-density approximation (LSDA), since the EE energy functional fully contains the effect of the magnetic field, and includes an inter-layer exchange coupling for multilayer systems. As a consistency test, the LSDA is derived as the leading term of a low-field expansion of the EE energy and potential.

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Authors and Affiliations

  1. Centro Atómico Bariloche, CNEA, CONICET, 8400 S. C. de Bariloche, Río Negro, Argentina

    D. Miravet

  2. Centro Atómico Bariloche and Instituto Balseiro, 8400 S. C. de Bariloche, Río Negro, Argentina

    C. R. Proetto

Authors
  1. D. Miravet
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Correspondence to C. R. Proetto.

Additional information

Contribution to the Topical Issue “Special issue in honor of Hardy Gross”, edited by C.A. Ullrich, F.M.S. Nogueira, A. Rubio, and M.A.L. Marques.

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Miravet, D., Proetto, C.R. Exact-exchange density functional theory of the integer quantum Hall effect: strict 2D limit. Eur. Phys. J. B 91, 129 (2018). https://doi.org/10.1140/epjb/e2018-90140-7

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