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 both components are synchronized through the intercomponent Josephson coupling, two species of vortices of each component are bound 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 diluted Bose mixtures with the Rabi oscillation, and multiband superconductors.
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