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

Abstract

A strict bidimensional (strict-2D) exact-exchange (EE) formalism within the framework of densityfunctional 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 interlayer 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.

Special issue in honor of Eberhard K.U. Gross for his 65th birthday

“…Dewhurst et al study the effect of the exchange-correlation spin-torque on spin dynamics [88], while Gorni et al look at spin-dynamics from time-dependent density-functional perturbation theory [89]. The theoretical exploration of a laser-driven, spin active, split-ring resonator as a source for high harmonic generation in the THz regime can be found in [90], while the integer quantum Hall effect in the strict 2D limit is discussed in [91]. In [92] a simple procedure to improve the magnon dispersion by taking into account gradient corrections to the ALDA at the exchange-only level is suggested.…”