Covering graphs, magnetic spectral gaps and applications to polymers and nanoribbons

Abstract

In this article, we analyze the spectrum of discrete magnetic Laplacians (DML) on an infinite covering graph G˜→G=G˜/Γ with (Abelian) lattice group Γ and periodic magnetic potential β˜ . We give sufficient conditions for the existence of spectral gaps in the spectrum of the DML and study how these depend on β˜ . The magnetic potential can be interpreted as a control parameter for the spectral bands and gaps. We apply these results to describe the spectral band/gap structure of polymers (polyacetylene) and nanoribbons in the presence of a constant magnetic field.