Polytypic nanowhiskers: electronic properties in the vicinity of the band edges

The increasing interest of nanowhiskers for technological applications has led to the observation of the zinc-blend/wurtzite polytypism. Polytypic nanowhiskers could also play, by their characteristics, an important role on the design of optical and electronic devices. In this work we propose a theoretical model to calculate the electronic properties of polytypic zinc-blend/wurtzite structure in the vicinity of the band edges. Our formulation is based on the $\vec{k} \cdot \vec{p}$ method connecting the irreducible representations in the interface of the two different crystalline phases by group theory arguments. Analyzing the composition of the states in the $\Gamma$ point and the overlap integrals of the envelope functions we predict energy transitions that agree with experimental photoluminescence spectra.