  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.
