  A quantized vortex in the Bose-Einstein condensation (BEC), which is known to
be unstable intrinsically, is demonstrated theoretically to be stabilized by
the finite temperature effect. The mean-field calculation of Popov
approximation within the Bogoliubov theory is employed, giving rise to a
self-consistent solution for BEC confined by a harmonic potential. Physical
origin of this vortex stabilization is investigated. An equivalent effect is
also proved to be induced by an additional pinning potential at the vortex
center produced by a focused laser beam even at the lowest temperature. The
self-consistent solutions give detailed properties of a stable vortex, such as
the spatial profiles of the condensate and non-condensate, the particle current
density around the core, the whole excitation spectrum, and their temperature
dependences.
