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

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

2011-04-29

arxiv.org/abs/1104.5679v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

6 pages, 5 figures

Scientific paper

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.

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