Coupled quantum wires

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.

11 pages, 10 figures

References in corpus (8)

• Electron-hole symmetry in a semiconducting carbon nanotube quantum dot
• Evidence for Luttinger liquid behavior in crossed metallic single-wall nanotubes
• Sliding Luttinger liquid phases
• High performance n-doped carbon nanotube field-effect transistors
• Regular networks of Luttinger liquids
• Plasmon excitations and 1D - 2D dimensional crossover in quantum crossbars
• Infrared Spectroscopy of Quantum Crossbars
• Ultraviolet Probing of Quantum Crossbars