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arXiv · 1908.00292

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

John Stewart Fabila-Carrasco·Fernando Lledó
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Abstract

In this article, we analyze the spectrum of discrete magnetic Laplacians (DML) on an infinite covering graph $\widetilde{G} \rightarrow G=\widetilde{G} /\Gamma$ with (Abelian) lattice group $\Gamma$ and periodic magnetic potential $\widetilde{\beta}$. We give sufficient conditions for the existence of spectral gaps in the spectrum of the DML and study how these depend on $\widetilde{\beta}$. 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.

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John Stewart Fabila-Carrasco, Fernando Lledó. 2019-08-01. Covering graphs, magnetic spectral gaps and applications to polymers and nanoribbons. https://doi.org/10.3390/sym11091163

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