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

TL;DR

This paper demonstrates that the discontinuous nature of the exact exchange-correlation energy in Density Functional Theory naturally appears in the subband spectra of semiconductor quantum wells, with theoretical results matching experimental data.

Contribution

It reveals the origin of the exchange-correlation discontinuity in quantum wells using an ab-initio functional including exchange and correlation effects.

Findings

Discontinuity occurs each time a subband becomes occupied.

Correlation effects overcome exchange in the discontinuity.

The intersubband energy jump matches experimental observations.

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.