Novel properties of the Kohn-Sham exchange potential for open systems: application to the two-dimensional electron gas

TL;DR

This paper investigates the unique behavior of the Kohn-Sham exchange potential in open systems, specifically a 2D electron gas, revealing features relevant to semiconductor band-gap issues.

Contribution

It demonstrates how the KS exchange potential develops barrier-like structures and discontinuities during subband transitions in open systems, providing new insights into semiconductor properties.

Findings

KS exchange potential forms a barrier under slight second subband population

Discontinuous changes in potential and energy at the 1S to 2S transition

Results shed light on semiconductor band-gap underestimation and renormalization

Abstract

The properties of the Kohn-Sham (KS) exchange potential for open systems in thermodynamical equilibrium, where the number of particles is non-conserved, are analyzed with the Optimized Effective Potential (OEP) method of Density Functional Theory (DFT) at zero temperature. The quasi two-dimensional electron gas (2DEG) is used as an illustrative example. The main findings are that the KS exchange potential builds a significant barrier-like structure under slight population of the second subband, and that both the asymptotic value of the KS exchange potential and the inter-subband energy jump discontinuously at the one-subband (1S) -> two-subband (2S) transition. The results obtained in this system offer new insights on open problems of semiconductors, such as the band-gap underestimation and the band-gap renormalization by photo-excited carriers.