Numerical study of the stability of half-quantum vortices in superconducting Sr$_2$RuO$_4$

We numerically solve the coupled Landau-Ginzburg-Maxwell equations for a model of a $p_x+ip_y$ superconductor in which whole or half-quanta of flux threads through a hole. We recover the pattern of stable and unstable regions for the half-flux observed in the experiments of Jang et al [1].\\[4pt] [1] J. Jang, et al, Observation of half-height magnetization steps in Sr$_2$RuO$_4$, \textit{Science}, \textbf{331}, 186-188(2011)