  In a harmonically-trapped rotating Bose-Einstein condensate (BEC), a vortex
of large angular momentum decays to multiple vortices of unit angular momentum
from an energetic consideration. We demonstrate the formation of a robust and
dynamically stable giant vortex of large angular momentum in a harmonically
trapped rotating BEC with a potential hill at the center, thus forming a
Mexican hat like trapping potential. For a small inter-atomic interaction
strength, a highly controllable stable giant vortex appears, whose angular
momentum slowly increases as the angular frequency of rotation is increased. As
the inter-atomic interaction strength is increased beyond a critical value,
only vortices of unit angular momentum are formed, unless the strength of the
potential hill at the center is also increased: for a stronger potential hill
at the center a giant vortex is again formed. The dynamical stability of the
giant vortex is demonstrated by real-time propagation numerically. These giant
vortices of large angular momentum can be observed and studied experimentally
in a highly controlled fashion.
