An Isaac Newton Institute Workshop

Graph Models of Mesoscopic Systems, Wave-Guides and Nano-Structures

Quantum network model of zigzag carbon nanotube

10th April 2007

Authors: Evgeny Korotyaev (Institut fuer Mathematik, Humboldt Universitaet zu Berlin), Igor Lobanov (Saint Petersburg State University of Information Technologies, Mechanics and Optics)

Abstract

We consider the quantum network which is a model for a zigzag carbon nanotube under assumption that the confinement potential created by sigma electrons restricts the pi electrons to the network. A parallel magnetic field and a wide range of periodic scalar potentials are taken into account. The spectral properties of the corresponding Schroedinger operator are analyzed using the Lyapunov function technique. We explicitly calculate the point spectrum and all localized eigenstates. We prove that there are stable spectral gaps, where the endpoints are periodic and anti-periodic eigenvalues, and resonance spectral gaps, where the endpoints are resonances; the asymptotics of all endpoints at high energies are provided. All finite gap potentials are described. The dependence of the spectrum on magnetic field is also investigated.