  We theoretically investigate the superfluid-normal-state
Berezinskii-Kosterlitz-Thouless transition in a binary mixture of bosonic atoms
with Rabi coupling under balanced densities. We find the nonmonotonic behavior
of the transition temperature with respect to the intercomponent coupling and
amplification of the transition temperature for finite values of Rabi coupling,
but for small intracomponent couplings. We develop the Nelson-Kosterlitz
renormalization-group equations in the two-component Bose mixture and obtain
the Nelson-Kosterlitz criterion modified by a fractional parameter, which is
responsible for half-integer vortices, and by Rabi coupling. Adopting the
renormalization-group approach, we clarify the dependence of the
Berezinskii-Kosterlitz-Thouless transition temperature on the Rabi coupling and
the intercomponent coupling. Analysis of the first and second sound velocities
also reveals the suppression of quasicrossing of the two sound modes with a
finite Rabi coupling in the low-temperature regime. Our results for a
two-dimensional binary Bose superfluid contribute to the understanding of a
broad range of multicomponent quantum systems such as two-dimensional multiband
superconductors.
