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تسجيل مستخدم جديدExact-exchange density functional theory of the integer quantum Hall effect: strict 2D limit
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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 $ u$; and ii) the EE potential display sharp discontinuities at every integer $ u$. 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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It is shown here that the Exact Exchange (EE) formalism provides a natural and rigorous approach for a Density Functional Theory (DFT) of the Integer Quantum Hall Effect (IQHE). Application of a novel EE method to a quasi two-dimensional electron gas
(q2DEG) subjected to a perpendicular magnetic field leads to the following main findings. textit{i)} the microscopic exchange energy functional of the IQHE has been obtained, whose main feature being that it minimizes with a discontinuous derivative at every integer filling factor $ u$; textit{ii)} an analytical solution is found for the magnetic-field dependent EE potential, in the one-subband regime; textit{iii)} as a consequence of textit{i)}, the EE potential display sharp discontinuities at every integer $ u$; and textit{iv)} the widely used Local Spin Density Approximation (LSDA) is strongly violated for filling factors close to integer values.
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