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Applying the approximate DFT-1/2 quasiparticle scheme, band structureunfolding, and generalized quasichemical approximation to describe chemical andstructural disorder, we investigate the electronic structure ofBi$_{1-x}$Sb$_x$ alloys from first principles. We calculate the importantenergy levels near the Fermi energy versus the Sb concentration $x$ where thetrivial-topological (TT) and semimetal-semiconductor (SMSC) transitions occur.We demonstrate that the energy variation of the relevant states deviatessignificantly from linear behavior and that the bowings are important tocorrectly describe the critical compositions. The influence of strain on theenergy levels is briefly discussed. It is concluded that the type or sign ofstrain applied on antimony atoms during the growth of the alloy should beheavily dependent on its composition.

Non-linear alloying and strain effects on trivial-topological and semimetal-semiconductor transitions in Bi$_{1-x}$Sb$_x$