In-plane magnetic-field-induced Wigner crystallization in a two-electron quantum dot

The orbital effects of the in-plane magnetic field on a two-electron harmonic quantum dot are studied using a variational method. For flat quantum dots the singlet-triplet transitions appearing in a perpendicular magnetic field are absent in a magnetic field oriented parallel to the plane of confinement. Instead, a degeneracy of orbital energies for symmetric and antisymmetric states at high in-plane magnetic field is observed. This degeneracy is due to the formation of Wigner molecules in the laboratory frame of reference with charge islands elongated along the direction of the magnetic field and localized within the plane perpendicular to it.