Stability of half-quantum vorticies in p_x+ip_y superconductors

We consider the stability conditions for half-quantum vortices in quasi two dimensional $p_x+ip_y$ superconductor (such as ${\rm Sr_2 RuO_4}$ is believed to be) through energetics calculations. Although the predicted exotic nature of these excitations have recently attracted much attention but they have not been observed yet. We pay particular attention to the fact that an isolated half quantum vortex has a divergent energy cost in the bulk due to the associated {\it unscreened} spin current, which requires two half-quantum vortices with opposite spin winding to pair. We show that the stability of such a pair in bulk is enhanced when the ratio of spin superfluid density to superfluid density $\rho_{{\rm sp}}/\rho_{\rm s}$ is small. As a step towards stabilizing and observing these exotic excitations, we propose using various mesoscopic geometries. We find that certain mesoscopic geometries can selectively allow only single half-quantum vortices to enter the sample for small $\rho_{{\rm sp}}/\rho_{\rm s}$.