Coupled quantum wires

TL;DR

This paper investigates coupled quantum wires at crossings, revealing bound states and explaining experimental observations of localized states through a combination of theoretical modeling and approximations.

Contribution

It provides a formal solution for coupled quantum wires with interactions and external potentials, explaining experimental localized states at crossings.

Findings

Bound states can emerge at crossings of quantum wires.

External potentials and interactions influence the formation of localized states.

Theoretical results explain experimental observations of localized states in nanotube crossings.

Abstract

We study a set of crossed 1D systems, which are coupled with each other via tunnelling at the crossings. We begin with the simplest case with no electron-electron interactions and find that besides the expected level splitting, bound states can emerge. Next, we include an external potential and electron-electron interactions, which are treated within the Hartree approximation. Then, we write down a formal general solution to the problem, giving additional details for the case of a symmetric external potential. Concentrating on the case of a single crossing, we were able to explain recent experinents on crossed metallic and semiconducting nanotubes [J. W. Janssen, S. G. Lemay, L. P. Kouwenhoven, and C. Dekker, Phys. Rev. B 65, 115423 (2002)], which showed the presence of localized states in the region of crossing.