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Abstract: We study the hopping transport of a quantum particle through randomly dilutedpercolation clusters in two dimensions realized both on the square andtriangular lattices. We investigate the nature of localization of the particleby calculating the transmission coefficient as a function of energy -2 < E < 2in units of the hopping integral in the tight-binding Hamiltonian anddisorder, q probability that a given site of the lattice is not available tothe particle. Our study based on finite size scaling suggests the existence ofdelocalized states that depends on energy and amount of disorder present in thesystem. For energies away from the band center E = 0, delocalized statesappear only at low disorder q < 15%. The transmission near the band center isgenerally very small for any amount of disorder and therefore makes itdifficult to locate the transition to delocalized states if any, but our studydoes indicate a behavior that is weaker than power-law localization. Apart fromthis localization-delocalization transition, we also find the existence of twodifferent kinds of localization regimes depending on energy and amount ofdisorder. For a given energy, states are exponentially localized forsufficiently high disorder. As the disorder decreases, states first showpower-law localization before showing a delocalized behavior.



Autor: Md Fhokrul Islam, Hisao Nakanishi

Fuente: https://arxiv.org/







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