From a few to many electrons in quantum dots under strong magnetic fields: Properties of rotating electron molecules with multiple rings

Using the method of breaking circular symmetry and the subsequent symmetry restoration via projection techniques, we present calculations for the ground-state energies and excitation spectra of $N$-electron parabolic quantum dots in strong magnetic fields in the medium-size range $10⩽N⩽30$. The physical picture suggested by our calculations is that of finite rotating electron molecules (REMs) comprising multiple rings, with the rings rotating independently of each other. An analytic expression for the energetics of such nonrigid multiring REMs is derived; it is applicable to arbitrary sizes given the corresponding ring configuration of classical point charges. We show that the rotating electron molecules have a nonrigid (nonclassical) rotational inertia exhibiting simultaneous crystalline correlations and liquidlike (nonrigidity) characteristics. This mixed phase appears in high magnetic fields and contrasts with the picture of a classical rigid Wigner crystal in the lowest Landau level.