Covering Graphs, Magnetic Spectral Gaps and Applications to Polymers and Nanoribbons
oleh: John Stewart Fabila-Carrasco, Fernando Lledó
| Format: | Article |
|---|---|
| Diterbitkan: | MDPI AG 2019-09-01 |
Deskripsi
In this article, we analyze the spectrum of discrete magnetic Laplacians (DML) on an infinite covering graph <inline-formula> <math display="inline"> <semantics> <mrow> <mover accent="true"> <mi mathvariant="bold">G</mi> <mo>˜</mo> </mover> <mo>→</mo> <mi mathvariant="bold">G</mi> <mo>=</mo> <mover accent="true"> <mi mathvariant="bold">G</mi> <mo>˜</mo> </mover> <mo>/</mo> <mo>Γ</mo> </mrow> </semantics> </math> </inline-formula> with (Abelian) lattice group <inline-formula> <math display="inline"> <semantics> <mo>Γ</mo> </semantics> </math> </inline-formula> and periodic magnetic potential <inline-formula> <math display="inline"> <semantics> <mover accent="true"> <mi>β</mi> <mo>˜</mo> </mover> </semantics> </math> </inline-formula>. We give sufficient conditions for the existence of spectral gaps in the spectrum of the DML and study how these depend on <inline-formula> <math display="inline"> <semantics> <mover accent="true"> <mi>β</mi> <mo>˜</mo> </mover> </semantics> </math> </inline-formula>. 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.