Strange eigenstates and anomalous transport in a Koch fractal with hierarchical interaction

Stationary states of non-interacting electrons on a Koch fractal are investigated within a tight binding approach. It is observed that if a hierarchically long range hopping is allowed, a suitable correlation between the parameters defining the Hamiltonian leads to spectacular changes in the transpo...

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Bibliographic Details
Published inPhysics letters. A Vol. 375; no. 44; pp. 3899 - 3903
Main Author Chakrabarti, Arunava
Format Journal Article
LanguageEnglish
Published Elsevier B.V 24.10.2011
Subjects
Binding
Conduction
Correlated disorder
Fractal analysis
Fractals
Hierarchies
Mathematical analysis
Self-similarity
Solid state physics
Tight binding model
Correlated disorder
Fractals
Tight binding model
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Summary:Stationary states of non-interacting electrons on a Koch fractal are investigated within a tight binding approach. It is observed that if a hierarchically long range hopping is allowed, a suitable correlation between the parameters defining the Hamiltonian leads to spectacular changes in the transport properties of finite, but arbitrarily large fractals. Topologically identical structures, that are found to support the same distribution of the amplitudes of eigenstates, are conducting in some cases and insulating in the others, depending on the choice of the hierarchy parameter. The values of the hierarchical parameter themselves display a self-similar, fractal character. ► New kind of correlations in a Koch fractal are discussed. ► There are hierarchically long range interactions. ► The extendedness of eigenfunctions are critically discussed.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
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content type line 23
ISSN:0375-9601
1873-2429
DOI:10.1016/j.physleta.2011.07.061