Wavefunction localization in a binary alloy

The nature (localized or extended) of the eigenstates of a large disordered system is studied by evaluating the imaginary part of the local Green's function at the specific eigenvalues over various atomic sites. The latter is obtained from the recursion method of Haydock-Heine-Kelly. An explicit calculation on an 841-atom cluster of random binary alloy in a square lattice ensures us that this approach is able to provide the relevant answers in even larger systems. In addition to confirming the usual conjectures about localization in a random binary alloy, several interesting points show up in the result of the model calculation. For example, the localized states in the minority band are correlated to certain clustering of the minority atoms. Their specific eigenvalues, which are not easily identified from the peaks in the d.o.s., are accurately found through the |ζ|² vs. energy plots at the specific sites.