Two-dimensional quantum percolation with binary nonzero hopping integrals.

Abstract

In a previous work [Dillon and Nakanishi, Eur. Phys. J. B 87, 286 (2014)EPJBFY1434-602810.1140/epjb/e2014-50397-4], we numerically calculated the transmission coefficient of the two-dimensional quantum percolation problem and mapped out in detail the three regimes of localization, i.e., exponentially localized, power-law localized, and delocalized, which had been proposed earlier [Islam and Nakanishi, Phys. Rev. E 77, 061109 (2008)PLEEE81539-375510.1103/PhysRevE.77.061109]. We now consider a variation on quantum percolation in which the hopping integral (w) associated with bonds that connect to at least one diluted site is not zero, but rather a fraction of the hopping integral (V=1) between nondiluted sites. We study the latter model by calculating quantities such as the transmission coefficient and the inverse participation ratio and find the original quantum percolation results to be stable for w>0 over a wide range of energy. In particular, except in the immediate neighborhood of the band center (where increasing w to just 0.02Vappears to eliminate localization effects), increasing w only shifts the boundaries between the three regimes but does not eliminate them until w reaches 10%-40% of V.