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 $\tilde{G}\to G=\tilde{G}/\Gamma$ with (Abelian) lattice group $\Gamma$ and periodic magnetic potential $\tilde{\beta }$. We give sufficient conditions for the existence of spectral gaps in the spectrum of the DML and study how these depend on $\tilde{\beta }$. The magnetic potential may 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 of nanoribbons in the presence of a constant magnetic field.

17 pages; 6 figures

References in corpus (3)

• Energy Band Gap Engineering of Graphene Nanoribbons
• Energy Gaps in Graphene Nanoribbons
• Energy-gap modulation of boron nitride nanoribbons by transverse electric fields: First-principles calculations