Density-functional theory of quantum wires and dots in a strong magnetic field

TL;DR

This paper uses density-functional theory to analyze how exchange interactions influence the structure of edge channels in a two-dimensional electron gas under strong magnetic fields, revealing a transition from incompressible to compressible edge regions.

Contribution

It demonstrates the significant impact of exchange interactions on edge channel widths and describes a transition between different edge states within experimentally accessible parameters.

Findings

Exchange reduces the spatial extent of edge channels.

Transition from incompressible to compressible edges occurs within a narrow confinement range.

Electrostatic and quantum descriptions of edge states are reconciled.

Abstract

We study the competition between the exchange and the direct Coulomb interaction near the edge of a two-dimensional electron gas in a strong magnetic field using density-functional theory in a local approximation for the exchange-energy functional. Exchange is shown to play a significant role in reducing the spatial extent of the compressible edge channel regions obtained from an electrostatic description. The transition from the incompressible edge channels of the Hartree-Fock picture to the broad, compressible strips predicted by electrostatics occurs within a narrow and experimentally accessible range of confinement strengths.