Re-entrant pinning of Wigner molecules in a magnetic field due to a Coulomb impurity

– Pinning of magnetic-field induced Wigner molecules (WMs) confined in parabolic two-dimensional quantum dots by a charged defect is studied by an exact diagonalization approach. We found a re-entrant pinning of the WMs as function of the magnetic field, a magnetic field induced re-orientation of theWMs and a qualitatively different pinning behaviour in the presence of a positive and negative Coulomb impurity. Low-density electron systems in bulk may form an ordered crystalline phase called Wigner crystal [1] in which electron charges are spatially separated. A similar collective type of electron localization in quantum dots (QDs) is called Wigner molecule (WM) [2]. WMs may be formed in large QDs [2] or be induced by a strong magnetic field [3] in the quantum Hall regime. Wigner localization is observed in the inner coordinates of the quantum system whose charge density conserves the symmetry of the external potential [4]. Therefore, in circular QDs [4, 5] the charge density will be circular symmetric even in the Wigner phase. However, a perturbation of the potential may pin [6] the charge density at a fixed orientation in the laboratory frame which should allow for the experimental observation [7] of Wigner localization. Pinning of the magnetic-field induced WMs by the anisotropy of the potential [8] or by an attractive Gaussian impurity potential [9] in the absence of a magnetic field have been studied previously. Here, we will show that the WM pinning is qualitatively very different in the presence of a positive and negative impurity. We consider WMs induced by a magnetic field in a two-dimensional harmonic QD. A strong magnetic field polarizes the spins of the confined electrons and leads to the formation of a so-called maximum density droplet (MDD) corresponding to the lowest Landau level filling factor ν = 1. Stronger fields induce the MDD to decay into a molecular phase with ν < 1, for which the distribution of electrons in the inner coordinates resembles the equilibrium configuration of a classical point-charge system [10]. The external magnetic field increases the absolute value of the angular momentum of the confined electron system inducing its changes between certain ’magic’ [11] values for which the classical distribution of electrons in the inner (’rotating’) frame of reference can be realized.