k · p Hamiltonians for quantum dots in a magnetic field

The problem of multiband k p Hamiltonians describing the hole energy structure of semiconductor nanosystems in a magnetic field is addressed. The approximate formulation given previously by Luttinger is revisited. We show that interaction with a magnetic field enters into the multiband equations for the envelope function components through the usual quadratic term and two linear Zeeman terms. The first linear term corresponds to the envelope angular momentum, while the other corresponds to the Bloch band-edge angular momentum. Several approximate ways of including the magnetic field in a four-band valence Hamiltonian are discussed and numerically compared.