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

TL;DR

This paper introduces a rigorous density functional theory approach using Exact Exchange for the Integer Quantum Hall Effect, revealing discontinuities in the exchange potential at integer fillings and challenging the validity of LSDA near these points.

Contribution

It develops a novel Exact Exchange method for DFT of IQHE, deriving the exchange energy functional and potential with key discontinuities at integer fillings.

Findings

Derived the microscopic exchange energy functional for IQHE.

Found an analytical solution for the EE potential in the one-subband regime.

Demonstrated sharp discontinuities in the EE potential at integer filling factors.

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.