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We investigate the behavior of vortices of multi-component superconductivity,realized in $\rm{MgB_2}$ and Fe-based superconductors, within the framework ofGinzburg-Landau (GL) theory in terms of numerical calculations of thetime-dependent GL equations and the variational method. It is revealed thatclose to the critical point of the composite system the inter-componentcoupling makes the system behave as a single component superconductivity inmost cases. However, when the bare mean-field critical points of the twocomponents coincide with each other, and furthermore the inter-band couplingdisappears at the same temperature, interesting phenomena occur as follows.Vortices interact attractively at large separation and repulsively at shortdistance in certain parameter space. Because of the non-monotonic interactionprofile, phase separations between vortex clusters of triangular order and theMeissner state take place, which indicates a first-order phase transitionassociated with the penetration of the magnetic field into a superconductorsample. Phase diagrams of vortex states are then constructed with theassociated magnetization curve. It is found that all these behaviorinterpolates the features of the type I and II superconductors.

Vortex States and Phase Diagram of Multi-component Superconductors with Competing Repulsive and Attractive Vortex Interactions