  Supercells are often used in ab initio calculations to model compound alloys,
surfaces and defects. One of the main challenges of supercell electronic
structure calculations is to recover the Bloch character of electronic
eigenstates perturbed by disorder. Here we apply the spectral weight approach
to unfolding the electronic structure of group III-V and II-VI semiconductor
solid solutions. The illustrative examples include: formation of donor-like
states in dilute Ga(PN) and associated enhancement of its optical activity,
direct observation of the valence band anticrossing in dilute GaAs:Bi, and a
topological band crossover in ternary (HgCd)Te alloy accompanied by emergence
of high-mobility Kane fermions. The analysis facilitates interpretation of
optical and transport characteristics of alloys that are otherwise ambiguous in
traditional first-principles supercell calculations.
