Localization and Quantum Percolation

Abstract

Electronic wave functions are studied on dilute lattices, at dimensionalities $1<~d<~8$. Generalized average inverse participation ratios are expanded in powers of the bond concentration, $p$. $Dlog$ Pad\'e approximants indicate that these ratios diverge as ${({p}_{q}\ensuremath{-}p)}^{{\ensuremath{\gamma}}_{q}}$, signaling the appearance of extended states for $p>{p}_{q}$. These Anderson transitions occur above classical percolation. No divergence is detected at $d=2$. These results are consistent with the existence of localized states at the center of the band.