Two-dimensional quantum percolation with binary non-zero hopping integrals

TL;DR

This study explores how non-zero hopping integrals in two-dimensional quantum percolation affect localization regimes, showing that the original localization behavior remains stable for a range of non-zero hopping values.

Contribution

It introduces a variation of quantum percolation with fractional hopping integrals and demonstrates the stability of localization regimes under this modification.

Findings

Localization regimes are stable for $w>0$ over a wide energy range.

Increasing $w$ shifts the boundaries between localization regimes.

Localization effects are eliminated only when $w$ reaches 10-40% of $V$.

Abstract

In a previous work [Dillon and Nakanishi, Eur.Phys.J B 87, 286 (2014)], 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)]. 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 non-diluted 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 $0.02*V$appears to eliminate localization effects), increasing $w$ only shifts the boundaries between the 3 regimes but does not eliminate them until $w$ reaches 10%-40% of $V$.