Theory of Interacting Parallel Quantum Wires

TL;DR

This paper uses density functional theory to study how Coulomb interactions cause energy levels in parallel quantum wires to lock together, revealing effects of electron interactions and geometry on their electronic structure.

Contribution

It introduces a self-consistent numerical approach to analyze energy level locking in parallel quantum wires due to Coulomb interactions and density of states effects.

Findings

Energy levels lock in similar wires when widths are comparable and separation is moderate.

Level locking persists at large separations but diminishes with increased tunneling.

Dissimilar wires show much less likelihood of energy level locking.

Abstract

We present self-consistent numerical calculations of the electronic structure of parallel Coulomb-confined quantum wires, based on the Hohenberg-Kohn-Sham density functional theory of inhomogeneous electron systems. We find that the corresponding transverse energy levels of two parallel wires lock together when the wires' widths are similar and their separation is not too small. This energy level locking is an effect of Coulomb interactions and of the the density of states singularities that are characteristic of quasi- one-dimensional Fermionic systems. In dissimilar parallel wires level lockings are much less likely to occur. Energy level locking in similar wires persists to quite large wire separations, but is gradually suppressed by inter-wire tunneling when the separation becomes small. Experimental implications of these theoretical results are discussed.