Stability of vortex in a two-component superconductor

Thermodynamic stability of composite vortex in a two-component superconductor is investigated by the Ginzburg-Landau theory. The predicted nature of these vortices has recently attracted much attention. Here we consider axially symmetric quantized vortex and show that the stability of vortex depends on three independent dimensionless parameters: $\kappa _{1}$, $\kappa _{2}$, $\kappa _{\xi}$, where $\kappa _{i}(i=1,2)$ is the Ginzburg-Landau parameter of individual component, $\kappa _{\xi }=\xi _{1}/\xi _{2}$ is the ratio of two coherence lengths. We also show that there exists thermodynamic stable vortex in type-1+type-2 or type-2+type-2 materials over a range of these three parameters.