Electronic properties of disordered corner-sharing tetrahedral lattices

TL;DR

This study investigates how noninteracting electrons behave on a disordered corner-sharing tetrahedral lattice, revealing unique localization properties and estimating the critical disorder for metal-insulator transition.

Contribution

It introduces a detailed analysis of electron localization on a tetrahedral lattice, highlighting differences from cubic lattices and estimating the critical disorder Wc.

Findings

Mobility edge trajectories differ from cubic lattices

Spectral rigidity is scale invariant at Wc

Critical disorder Wc/t=14.5

Abstract

We have examined the behaviour of noninteracting electrons moving on a corner-sharing tetrahedral lattice into which we introduce a uniform (box) distribution, of width W, of random on-site energies. We have used both the relative localization length and the spectral rigidity to analyze the nature of the eigenstates, and have determined both the mobility edge trajectories as a function of W, and the critical disorder, Wc, beyond which all states are localized. We find (i) that the mobility edge trajectories (energies Ec vs. disorder W) are qualitatively different from those found for a simple cubic lattice, and (ii) that the spectral rigidity is scale invariant at Wc and thus provides a reliable method of estimating this quantity -- we find Wc/t=14.5. We discuss our results in the context of the metal-to-insulator transition undergone by LiAlyTi{2-y}O4 in a quantum site percolation model that also includes the above-mentioned Anderson disorder, and show that the effects produced by Anderson disorder are far less important than those produced by quantum site percolation, at least in the determination of the doping concentration at which the metal-to-insulator transition is predicted to occur.