  We report the first quasiparticle calculations of the newly observed wurtzite
polymorph of InAs and GaAs. The calculations are performed in the GW
approximation using plane waves and pseudopotentials. For comparison we also
report the study of the zinc-blende phase within the same approximations. In
the InAs compound the In 4d electrons play a very important role: whether they
are frozen in the core or not, leads either to a correct or a wrong band
ordering (negative gap) within the Local Density Appproximation (LDA). We have
calculated the GW band structure in both cases. In the first approach, we have
estimated the correction to the pd repulsion calculated within the LDA and
included this effect in the calculation of the GW corrections to the LDA
spectrum. In the second case, we circumvent the negative gap problem by first
using the screened exchange approximation and then calculating the GW
corrections starting from the so obtained eigenvalues and eigenfunctions. This
approach leads to a more realistic band-structure and was also used for GaAs.
For both InAs and GaAs in the wurtzite phase we predict an increase of the
quasiparticle gap with respect to the zinc-blende polytype.
