Real and spurious solutions of the8×8k⋅p model for nanostructures

Quantum dot wave functions are constructed in the $8\times 8$ k⋅p model from three bulk states: $k_1,k_2,$ and $k_3.$ We found that the $8\times 8$ $\mathbf{k}\cdot \mathbf{p}$ $k_2$ bulk state (far from $\Gamma ,$ belonging to the electon-light hole bands) does not exist in the more realistic atomistic pseudopotential calculation. As a result, $8\times 8$ k⋅p nanostructure solutions which critically depend on this $k_2$ bulk state are spurious. These include the $8\times 8$ k⋅p quantum dot band gap “intrinsic” surface states and oscillating hole states. On the other hand, if the contribution of this $k_2$ state is small and decays with increasing nanostructure size, the corresponding nanostructure state is real.