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

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 d...

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Bibliographic Details
Published in:Symmetry
Main Authors: Fabila Carrasco, John Stewart, Lledó Macau, Fernando
Other Authors: Ministerio de Economía y Competitividad (España), Ministerio de Educación, Cultura y Deporte (España)
Format: Article in Journal/Newspaper
Language:English
Published: MDPI 2019
Subjects:
Covering Graphs
Discrete Magnetic Laplacian
Magnetic Field
Nanoribbons
Polymers
Spectral Gaps
Matemáticas
DML
Online Access:http://hdl.handle.net/10016/35466
https://doi.org/10.3390/SYM11091163
Description
Summary: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.

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