Spectral Band Structure of Periodic Schrödinger Operators on a Generalized Degenerate Zigzag Nanotube

Abstract

We refer generalized degenerate zigzag nanotubes as periodic metric graphs which consist of segments of length 1 and rings of length 2 throughout this paper. In this paper, we consider the case where there are one segment and three rings in the basic period cell and analyze the spectrum of periodic Schrödinger operators on the generalized degenerate zigzag nanotube. We obtain the relationship between the structure of the metric graph and the nondegenerate spectral gaps of the Schrödinger operators.