Vertical quantum dots are found to show distinct atom-like properties such as shell filling and the obeyance of Hund's first rule due to the well defined circular shape of the confining potential [1], A magnetic field applied parallel to the current is useful for studying the electronic properties of these artificial atoms, because one can identify the electronic states by their different orbital motion in the presence of the magnetic field. When the lateral confining potential loses the rotational symmetry, degeneracy in the single particle states is generally lifted and the way electrons fill these states is altered [2]. As a results, Hound's first rule favoring parallel electron spins no longer holds, and the spin state, for example, for electron number n chemical bounds 4 changes from triplet to singlet. We can also measure the Zeeman effect by applying a magnetic field perpendicular to the current (transverse magnetic field) to directly investigated the spin states in the artificial atoms [3].
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