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In this work, we present and evaluate a (111)-rotated eight-band$\mathbf{k}\cdot\mathbf{p}$ Hamiltonian for the zinc-blende crystal lattice toinvestigate the electronic properties of site-controlled InGaAs/GaAs quantumdots grown along the [111] direction. We derive the rotated Hamiltonianincluding strain and piezoelectric potentials. In combination with ourpreviously formulated (111)-oriented continuum elasticity model, we employ thisapproach to investigate the electronic properties of a realisticsite-controlled (111)-grown InGaAs quantum dot. We combine these studies withan evaluation of single-band effective mass and eight-band$\mathbf{k}\cdot\mathbf{p}$ models, to investigate the capabilities of thesemodels for the description of electronic properties of (111)-grown zinc-blendequantum dots. Moreover, the influence of second-order piezoelectriccontributions on the polarisation potential in such systems is studied. Thedescription of the electronic structure of nanostructures grown on(111)-oriented surfaces can now be achieved with significantly reducedcomputational costs in comparison to calculations performed using theconventional (001)-oriented models.

Electronic properties of site-controlled (111)-oriented zinc-blende  InGaAs/GaAs quantum dots calculated using a symmetry adapted  $\mathbf{k}\cdot\mathbf{p}$ Hamiltonian