Electronic states in circular and ellipsoidally deformed quantum dots

The electronic properties of circular and ellipsoidally deformed quantum dot single electron transistors are studied by measuring Coulomb oscillations of circular and rectangular mesas. The filling of the few electron ground states in circular mesa devices at zero magnetic field gives rise to a pronounced shell structure characteristic of a two-dimensional harmonic confining potential with rotational symmetry, and is in accordance with Hund's first rule. These atomic like features are readily disrupted in the rectangular mesa devices due to the lifting of the single-particle level degeneracies. Measurements with a magnetic held parallel to the current allow us to identify changes in the quantum numbers labelling the electronic states which are induced by the deformation. In particular, the transition from a spin-triplet in a circular dot to a spin-singlet in elliptical dots for the four-electron ground state at zero-magnetic field is investigated. The spin-singlet in the rectangular mesa is clearly identified independently from the measurement of the Zeeman effect. These observations are in good agreement with model calculations based on spin-density functional theory, and a single particle picture is also very useful. Even for a small deformation, breaking the circular symmetry significantly modifies the shell structure and changes the total spin of a state. Finally, we argue that the magnetic field dependence for the rectangular mesa devices suggests that the anisotropy of an elliptical dot may be much higher than that suggested by the geometry of the device mesa in which the dot is located.