Localization in paired correlated random binary alloys.

Abstract

We study both analytically and numerically the electronic structure and the transport properties of binary chains, when the site energies (${\mathrm{\ensuremath{\epsilon}}}_{\mathit{A}}$ or ${\mathrm{\ensuremath{\epsilon}}}_{\mathit{B}}$) are random in pairs. We compute the density of states and the localization length versus energy for various strengths of disorder by considering products of 2\ifmmode\times\else\texttimes\fi{}2 random matrices in the microcanonical ensemble and also within the usual canonical-ensemble method. The limiting cases of AA,BB correlation, which favor delocalization and AB,BA anticorrelation, which favor localization, as well as intermediate cases involving all pairs AA,AB,BA,BB at random, are distinguished. In the former case, if \ensuremath{\delta}=\ensuremath{\Vert}${\mathrm{\ensuremath{\epsilon}}}_{\mathit{A}}$-${\mathrm{\ensuremath{\epsilon}}}_{\mathit{B}}$\ensuremath{\Vert} is less than a critical value ${\mathrm{\ensuremath{\delta}}}_{\mathit{c}}$=2, we demonstrate that the density of states has a smooth part and associated dominant 1/${\mathit{E}}^{2}$ divergencies of the localization length which for \ensuremath{\delta}=${\mathrm{\ensuremath{\delta}}}_{\mathit{c}}$ become 1/E. Our results are explained by considering scattering from single-impurity pairs. The microcanonical-ensemble method is discussed and its limitations are pointed out.