Localization-delocalization transition in 2D quantum percolation model

Abstract

We study the hopping transport of a quantum particle through randomly diluted percolation clusters in two dimensions realized both on the square and triangular lattices. We investigate the nature of localization of the particle by calculating the transmission coefficient as a function of energy (-2 < E < 2 in units of the hopping integral in the tight-binding Hamiltonian) and disorder, q (probability that a given site of the lattice is not available to the particle). Our study based on finite size scaling suggests the existence of delocalized states that depends on energy and amount of disorder present in the system. For energies away from the band center (E = 0), delocalized states appear only at low disorder (q < 15%). The transmission near the band center is generally very small for any amount of disorder and therefore makes it difficult to locate the transition to delocalized states if any, but our study does indicate a behavior that is weaker than power-law localization. Apart from this localization-delocalization transition, we also find the existence of two different kinds of localization regimes depending on energy and amount of disorder. For a given energy, states are exponentially localized for sufficiently high disorder. As the disorder decreases, states first show power-law localization before showing a delocalized behavior.