Signatures of Discontinuity in the Exchange-Correlation Energy Functional Derived from the Subband Electronic Structure of Semiconductor Quantum Wells

Abstract

The discontinuous character of the exact exchange-correlation $(xc)$ energy functional of Density Functional Theory is shown to arise naturally in the subband spectra of semiconductor quantum wells. Using an \emph{ab-initio} $xc$ functional, including exchange exactly and correlation in an exact partial way, a discontinuity appears in the $xc$ potential, each time a subband becomes slightly occupied. Exchange and correlation give opposite contributions to the discontinuity, with correlation overcoming exchange. The jump in the intersubband energy is in excellent agreement with experimental data.