Magnetic field implementation in multiband k⋅p Hamiltonians of holes in semiconductor heterostructures

We propose an implementation of external homogeneous magnetic fields in k⋅p Hamiltonians for holes in heterostructures, in which we make use of the minimal coupling prior to introducing the envelope function approximation. Illustrative calculations for holes in InGaAs quantum dot molecules show that the proposed Hamiltonian outperforms the standard Luttinger model (Luttinger 1956 Phys. Rev. 102 1030) describing the experimentally observed magnetic response. The present implementation culminates our previous proposal (Planelles et al 2010 Phys. Rev. B 82 155307).