  We predict the existence of a quantum vortex for an unusual situation. We
study the order parameter in doubly connected superconducting samples embedded
in a uniform magnetic field. For samples with perfect cylindrical symmetry, the
order parameter has been known for long and no vortices are present in the
linear regime. However, if the sample is not symmetric, there exist ranges of
the field for which the order parameter vanishes along a line, parallel to the
field. In many respects, the behavior of this line is qualitatively different
from that of the vortices encountered in type II superconductivity. For samples
with mirror symmetry, this flux-induced vortex appears at the thin side for
small fluxes and at the opposite side for large fluxes. We propose direct and
indirect experimental methods which could test our predictions.

Superconductivity;Mesoscale and Nanoscale Physics;Quantum Physics