Influence of chemical disorder on wavefunctions and optical transition rates in one-dimensional systems

Abstract

The authors investigate the influence of chemical disorder on wavefunctions and optical transition rates in a one-dimensional (ID) alloy AxB1-x. The Schrodinger equation is solved for real-space A and B potentials. Even for large disorder, where the states are localised over only a few lattice sites, the calculated spectral function shows a strong dependence on the energy E and the k-vector, which can be understood as a remnant of the virtual-crystal band structure. The dependence of the optical matrix elements on the energies of the initial and final states is explained by that of the overlaps of the respective eigenfunctions in real and in k-space. For large disorder, the overlap in real space between valence states and conduction states near the gap becomes small, and in consequence the corresponding optical transitions are suppressed. The results are compared with the coherent potential approximation (CPA). It is found that even in the case of 1D disorder, which is the most difficult for CPA, the general behaviour of the transition matrix elements can be understood within the single-site CPA.