Electronic exchange in quantum rings

TL;DR

This paper derives an accurate exchange-hole potential approximation for quantum rings, outperforming traditional methods and effectively capturing the dimensional crossover in low-dimensional systems.

Contribution

It introduces a new density functional for quantum rings that accurately models exchange effects and handles the dimensional crossover, surpassing local-spin-density approximation.

Findings

Excellent agreement with exact-exchange results across parameters

Outperforms local-spin-density approximation in quasi-one-dimensional limit

Successfully captures the dimensional crossover in low-dimensional systems

Abstract

Quantum rings can be characterized by a specific radius and ring width. For this rich class of physical systems, an accurate approximation for the exchange-hole potential and thus for the exchange energy is derived from first principles. Excellent agreement with the exact-exchange results is obtained regardless of the ring parameters, total spin, current, or the external magnetic field. The description can be applied as a density functional outperforming the commonly used local-spin-density approximation, which is here explicitly shown to break down in the quasi-one-dimensional limit. The dimensional crossover, which is of extraordinary importance in low-dimensional systems, is fully captured by our functional.