具有分级相互作用的Koch分形中的奇异本征态和反常输运
Strange eigenstates and anomalous transport in a Koch fractal with hierarchical interaction
摘要：
用紧束缚方法研究了Koch分形上无相互作用电子的定态。据观察，如果允许一个分层的长程跳跃，定义的哈密顿量的参数之间的一个合适的相关性导致壮观的变化，在有限的，但任意大的分形的输运性质。拓扑相同的结构，被发现支持相同的本征态的振幅分布，在某些情况下是导电的，在其他情况下是绝缘的，这取决于层次参数的选择。层次参数本身的值显示自相似的分形特征。
英文摘要：
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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