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The properties of an exciton in a type II quantum dot are studied under theinfluence of a perpendicular applied magnetic field. The dot is modelled by aquantum disk with radius $R$, thickness $d$ and the electron is confined in thedisk, whereas the hole is located in the barrier. The exciton energy andwavefunctions are calculated using a Hartree-Fock mesh method. We distinguishtwo different regimes, namely $d<<2R$ (the hole is located at the radialboundary of the disk) and $d>>2R$ (the hole is located above and below thedisk), for which angular momentum $(l)$ transitions are predicted withincreasing magnetic field. We also considered a system of two verticallycoupled dots where now an extra parameter is introduced, namely the interdotdistance $d_{z}$. For each $l_{h}$ and for a sufficient large magnetic field,the ground state becomes spontaneous symmetry broken in which the electron andthe hole move towards one of the dots. This transition is induced by theCoulomb interaction and leads to a magnetic field induced dipole moment. Nosuch symmetry broken ground states are found for a single dot (and for threevertically coupled symmetric quantum disks). For a system of two verticallycoupled truncated cones, which is asymmetric from the start, we still findangular momentum transitions. For a symmetric system of three verticallycoupled quantum disks, the system resembles for small $d_{z}$ the pillar-likeregime of a single dot, where the hole tends to stay at the radial boundary,which induces angular momentum transitions with increasing magnetic field. Forlarger $d_{z}$ the hole can sit between the disks and the $l_{h}=0$ stateremains the groundstate for the whole $B$-region.Comment: 11 pages, 16 figure

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