Pinning of electron densities in quantum rings by defects: symmetry   constraints and distribution of persistent currents
  We study the pinning of few-electron charge densities by weak perturbations to circular quantum ring potentials. We find that the pinning by weak defects is only allowed when the symmetry of the classical few-electron lowest-energy configuration agrees with the symmetry of the external potential. We indicate that whenever the pinning is allowed by the symmetry, its strength is an oscillatory function of the external magnetic field. In the magnetic fields for which the pinning is maximal the dipole moment generated by the persistent currents changes orientation from antiparallel to parallel to the external field in a continuous manner. For confinement potentials of a higher symmetry than the one of a classical Wigner molecule the pinning is forbidden and a discontinuous abrupt inversion of the dipole moments is observed. When the pinning of single-electron islands is absent or weak the current distribution resembles the one of a circular ring. For the maximal pinning instead of current loops running around the entire ring one observes formation of multiple current vortices circulating around each single-electron density island. We study the magnetic field generated by persistent currents and find that at the dipole moment reversal the currents tend to screen the external field in the region occupied by electrons. In consequence the magnetic field generated by the currents in the maximally pinned electron systems maps the charge distribution. 
T.Chwiej, B.Szafran