Ground-state electronic structure of quasi-one-dimensional wires in semiconductor heterostructures

TL;DR

This study uses density functional theory to analyze how Coulomb and correlation effects influence charge density patterns in quasi-one-dimensional semiconductor wires, revealing conditions for single or split-wire formations.

Contribution

It provides a detailed phase diagram of electron density configurations in quantum wires, highlighting the transition from single to split-wire states under various confinement and density conditions.

Findings

High-density regimes show efficient screening with uniform charge distribution.

Low-density, weak-confinement regimes induce small density modulations.

At very low densities, the electron density splits into two parallel quantum wires.

Abstract

We apply density functional theory, in the local density approximation, to a quasi-one-dimensional electron gas in order to quantify the effect of Coulomb and correlation effects in modulating, and therefore patterning, the charge density distribution. Our calculations are presented specifically for surface-gate-defined quasi-one-dimensional quantum wires in a GaAs-AlGaAs heterostructure but we expect our results to apply more generally for other low dimensional semiconductor systems. We show that at high densities with strong confinement, screening of electrons in the direction transverse to the wire is efficient and density modulations are not visible. In the low-density, weak-confinement regime, the exchange-correlation potential induces small density modulations as the electrons are depleted from the wire. At the weakest confinements and lowest densities, the electron density splits into two rows thereby forming a pair of quantum wires that lie beneath the surface gates. An additional double-well external potential forms at very low density which enhances this row splitting phenomenon. We produce phase diagrams that show a transition between the presence of a single quantum wire in a split-gate structure and two quantum wires. We suggest that this phenomenon can be used to pattern and modulate the electron density in low-dimensional structures with particular application to systems where a proximity effect from a surface gate would be valuable.