Electron localization function for two-dimensional systems

TL;DR

This paper extends the electron localization function (ELF) concept to two-dimensional systems, demonstrating its simplicity and usefulness in visualizing electron structures and properties in quantum dots and quantum Hall systems.

Contribution

The paper introduces the ELF for 2D systems, highlighting its topological simplicity and demonstrating its application to quantum dots and magnetic fields.

Findings

ELF visualizes shell structures in quantum dots

ELF provides insights into electron bonding in quantum-dot molecules

ELF acts as a measure of vorticity in quantum-Hall droplets

Abstract

The concept of the electron localization function (ELF) is extended to two-dimensional (2D) electron systems. We show that the topological properties of the ELF in 2D are considerably simpler than in molecules studied previously. We compute the ELF and demonstrate its usefulness for various physical 2D systems, focusing on semiconductor quantum dots that effectively correspond to a confined 2D electron gas. The ELF visualizes the shell structure of harmonic quantum dots and provides insight into electron bonding in quantum-dot molecules. In external magnetic fields the ELF is found to be a useful measure of vorticity when analyzing the properties of quantum-Hall droplets. We show that the current-dependent term in the ELF expression is important in magnetic fields.