Single and vertically coupled type-II quantum dots in a perpendicular magnetic field: Exciton ground-state properties

The properties of an exciton in a type-II quantum dot are studied under the influence of a perpendicular applied magnetic field. The dot is modeled by a quantum disk with radius R, thickness d and the electron is confined in the disk, whereas the hole is located in the barrier. The exciton energy and wave functions are calculated applying a self-consistent mean-field theory in the Hartree approximation using a finite difference mesh method. We distinguish two different regimes, namely, $d\ll 2R$ (the hole is located above and below the disk) and $d\gg 2R$ (the hole is located at the radial boundary of the disk), for which angular momentum (l) transitions are predicted with increasing magnetic field. We also considered a system of two vertically coupled dots where now an extra parameter is introduced, namely, the interdot distance $d_z.$ For a sufficient large magnetic field, each $l_h$ state becomes spontaneous symmetry broken with the electron and the hole moving towards one of the dots. This transition is induced by the Coulomb interaction and leads to a magnetic-field-induced dipole moment. No such symmetry-broken ground states are found for a single dot (and for three vertically coupled symmetric quantum disks). For a system of two vertically coupled truncated cones, which is asymmetric from the start, we still find angular momentum transitions. For a symmetric system of three vertically coupled quantum disks, the system resembles for small $d_z$ the pillarlike regime of a single dot, where the hole tends to stay at the radial boundary, which induces angular momentum transitions with increasing magnetic field. For larger $d_z$ the hole can sit between the disks and the $l_h=0\mathrm{}$ state remains the ground state for the whole B region.