Vortex lattice stability in the SO(5) model

We study the energetics of superconducting vortices in the SO(5) model for high-$T_c$ materials proposed by Zhang. We show that for a wide range of parameters normally corresponding to type II superconductivity, the free energy per unit flux $\FF(m)$ of a vortex with $m$ flux quanta is a decreasing function of $m$, provided the doping is close to its critical value. This implies that the Abrikosov lattice is unstable, a behaviour typical of type I superconductors. For dopings far from the critical value, $\FF(m)$ can become very flat, indicating a less rigid vortex lattice, which would melt at a lower temperature than expected for a BCS superconductor.