Model GW band structure of $\mathrm{InAs}$ and $\mathrm{GaAs}$ in the wurtzite phase

We report quasiparticle calculations of the newly observed wurtzite polymorph of $\mathrm{InAs}$ and $\mathrm{GaAs}$. The calculations are performed in the GW approximation (based on a model dielectric function) using plane waves and pseudopotentials. For comparison we also report the study of the zinc-blende phase within the same approximations. In the $\mathrm{InAs}$ compound the $\mathrm{In}4d$ 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, that can be thought of as a step towards self-consistency, leads to a more realistic band structure and was also used for $\mathrm{GaAs}$. For both $\mathrm{InAs}$ and $\mathrm{GaAs}$ in the wurtzite phase we predict an increase of the quasiparticle gap with respect to the zinc-blende polytype.

Figure 1

(Color online) The normalized total energy vs volume for one $\mathrm{InAs}$ pair for the zinc-blende (diamonds) and the wurtzite (circles) polymorphs. Total energies are calculated by using US pseudopotentials.

Figure 2

Quasiparticle (solid lines) and Kohn-Sham (dashed lines) band structures of $\mathrm{InAs}$ wurtzite with the $\mathrm{In}4d$ included in the valence states: at $\Gamma$ a “negative gap” is predicted.

Figure 3

Quasiparticle (solid lines) and Kohn-Sham (dashed lines) band structures of wurtzite $\mathrm{InAs}$ with the $\mathrm{In}4d$ included among the core states.

Figure 4

Scheme for the estimation of the LDA value of the pd repulsion $\left({\Delta }_{pd}\right)$.

Figure 5

GW band structure of $\mathrm{InAs}$ wurtzite with the $\mathrm{In}4d$ included among the valence states. The quasiparticle corrections are applied on top of the SX calculation which, in turn, is started from the LDA eigenspectrum.

Figure 6

Band structure of $\mathrm{GaAs}$ wurtzite with $\mathrm{Ga}3d$ included among valence states. The quasiparticle corrections are applied on top of the SX calculation which, in turn, is started from the LDA eigenspectrum.