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Fully microscopic many-body models based on inputs from first principle density functional theory are used to calculate the carrier losses due to radiative- and Auger-recombinations in bulk tellurium. It is shown that Auger processes dominate the losses for carrier densities in the range typical for applications as lasers. The Auger loss depends crucially on the energetic position of the $H_6$ valence bands. At cryogenic temperatures of 50$\,$K (100$\,$K) the Auger coefficient, $C$, varies by about six (three) orders of magnitude within the range of published distances between these bands and the valence bandedge. Values for $C$ at the high and low end of these ranges are found if the distance is smaller or larger than the bandgap, respectively. At room temperature the sensitivity is reduced to about a factor of four with $C$ values ranging between $0.4$ and $1.6\times 10^{-27}$cm$^6$s$^{-1}$. Here, radiative losses dominate for carrier densities up to about $10^{16}/$cm$^3$ with a loss coefficient $B\approx 10^{-11}$cm$^3$s$^{-1}$. The radiative losses are about two to three times lower than in typical bulk III-V materials for comparable wavelengths., Comment: 5 pages, 4 figures. Submitted to Applied Physics Letters on 07/27/2022

The LDA-1/2 method is employed in density functional theory calculations for the electronic structure of III-V dilute bismide systems. For the representative example of Ga(SbBi) with Bi concentrations below $10 \%$, it is shown that this method works very efficiently, especially due to its reasonably low demand on computer memory. The resulting bandstructure and wavefunctions are used to compute the interaction matrix elements that serve as input to microscopic calculations of the optical properties and intrinsic losses relevant for optoelectronic applications of dilute bismides.