Ellipticity and spurious solutions in k⋅p calculations of III-nitride nanostructures

We analyze the ellipticity of the standard kldrp Wurtzite model for the symmetrized and the Burt-Foreman operator ordering. We find that the symmetrized Hamiltonian is unstable, leads to different results and can cause spurious solutions. We show that the operator ordering in Wurtzite must be completely asymmetric to be stable. The asymmetric operator ordering is elliptic and therefore no spurious solutions are obtained.