Type-1.5 Superconducting State from an Intrinsic Proximity Effect in Two-Band Superconductors

We show that in multiband superconductors, even an extremely small interband proximity effect can lead to a qualitative change in the interaction potential between superconducting vortices by producing long-range intervortex attraction. This type of vortex interaction results in an unusual response to low magnetic fields leading to phase separation into domains of two-component Meissner states and vortex droplets.