  We study the Berezinskii-Kosterlitz-Thouless (BKT) transition of
two-component Bose mixtures in two spatial dimensions. When phases of both
components are decoupled, half-quantized vortex-antivortex pairs of each
component induce two-step BKT transitions. On the other hand, when phases of
the both components are synchronized through the inter-component Josephson
coupling, two species of vortices of each component are bind to form a
molecule, and in this case, we find that there is only one BKT transition by
molecule-antimolecule pairs. Our results can be tested by two weakly-connected
Bose systems such as two-component ultracold dilute Bose mixtures with the Rabi
oscillation, and multiband superconductors.
