Schrödinger Operators on a Zigzag Supergraphene-Based Carbon Nanotube

Abstract

Throughout this paper, we study the spectrum of a periodic Schrödinger operator on a zigzag super carbon nanotube, which is a generalization of the zigzag carbon nanotube. We prove that its absolutely continuous spectrum has the band structure. Moreover, we show that its eigenvalues with infinite multiplicities consisting of the Dirichlet eigenvalues and points embedded in the spectral band for some corresponding Hill operator. We also give the asymptotics for the spectral band edges.