The von Neumann-Wigner theorem in quantum dot molecules

We show that electrons in coupled quantum dots characterized by high aspect ratios undergo abrupt density rotations when the dots are biased into an asymmetric confinement configuration. Density rotations occur with electron transfer to a single dot, and give rise to sharp variations of the exchange coupling between electrons as a function of inter-dot detuning. Our analysis based on exact diagonalization technique indicates that this unusual behavior is in agreement with the von Neumann-Wigner theorem that dictates the variations of the energy spectrum from the symmetries of the molecular states during the detuning process. It is also shown that the overall effect is quenched by the presence of magnetic fields, which by adding angular momentum to the electron motion affects the spatial symmetry of the molecular states.