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Transition-metal-based Heusler semiconductors are promising materials for avariety of applications ranging from spintronics to thermoelectricity.Employing the $GW$ approximation within the framework of the FLAPW method, westudy the quasi-particle band structure of a number of such compounds beingalmost gapless semiconductors. We find that in contrast to the\textit{sp}-electron based semiconductors such as Si and GaAs, in these systemsthe many-body corrections have a minimal effect on the electronic bandstructure and the energy band gap increases by less than 0.2~eV, which makesthe starting point density functional theory (DFT) a good approximation for thedescription of electronic and optical properties of these materials.Furthermore, the band gap can be tuned either by the variation of the latticeparameter or by the substitution of the \emph{sp}-chemical element.

Quasiparticle band structure of the almost-gapless transition-metal-based Heusler semiconductors