Exact Exchange: a pathway for a Density Functional Theory of the Integer Quantum Hall Effect

Abstract

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 $\nu$; \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 $\nu$; and \textit{iv)} the widely used Local Spin Density Approximation (LSDA) is strongly violated for filling factors close to integer values.