  In this work, we have analytically devised novel vortex solutions in a
rotating holographic superfluid. To achieve this result, we have considered a
static disc at the AdS boundary and let the superfluid rotate relative to it.
This idea has been numerically exploited in [1] where formation of vortices in
such a setting was reported. We have found that these vortex solutions are
eigenfunctions of angular momentum. We have also shown that vortices with
higher winding numbers are associated with higher quantized rotation of the
superfluid. We have, then, analysed the equation of motion along bulk AdS
direction using St\"urm-Liouville eigenvalue approach. A surprising outcome of
our study is that the chemical potential must be purely imaginary. We have then
observed that the winding number of the vortices decreases with the increase in
the imaginary chemical potential. We conclude from this that imaginary chemical
potential leads to less dissipation in such holographic superfluids.
