Effective band structure of random alloys.

Random substitutional A(x)B(1-x) alloys lack formal translational symmetry and thus cannot be described by the language of band-structure dispersion E(k(→)). Yet, many alloy experiments are interpreted phenomenologically precisely by constructs derived from wave vector k(→), e.g., effective masses or van Hove singularities. Here we use large supercells with randomly distributed A and B atoms, whereby many different local environments are allowed to coexist, and transform the eigenstates into an effective band structure (EBS) in the primitive cell using a spectral decomposition. The resulting EBS reveals the extent to which band characteristics are preserved or lost at different compositions, band indices, and k(→) points, showing in (In,Ga)N the rapid disintegration of the valence band Bloch character and in Ga(N,P) the appearance of a pinned impurity band.