Deconfinement of Vortices with Continuously Variable Fractions of the Unit Flux Quanta in Two-Gap Superconductors

We propose a new stage of confiment-decofinment transition, which can be observed in laboratory. In two-gap superconductors, two kinds of vortex exist by the presence of two different $U(1)$ phases. Each of them carries a continuously variable fraction of the unit flux quanta $\Phi_0=h c / 2 e$. The confined state of these two is a usual vortex and stable in the low temperature region of the system under a certain magnetic field above $H_{c1}$. We see an analogy to quarks in a charged pion. An entropy gain causes two fractional vortices to be deconfined above a certain temperature. We estimate the condition of the deconfinement by using parameters for a typical two-gap superconductor MgB$_2$.