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

TL;DR

This paper explores how hierarchical long-range interactions in a Koch fractal influence electron states and transport, revealing that parameter correlations can cause dramatic shifts between conducting and insulating behaviors.

Contribution

It demonstrates the impact of hierarchical interaction parameters on electron eigenstates and transport properties in Koch fractals, highlighting self-similar and fractal characteristics.

Findings

Hierarchical parameters induce transitions between conducting and insulating states.

Eigenstate distributions are identical in topologically similar structures.

Hierarchical parameters exhibit self-similar, fractal patterns.

Abstract

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.