  Counter-rotating vortices in miscible two-component Bose-Einstein
condensates, in which superflows counter-rotate between the two components
around the overlapped vortex cores, are studied theoretically in a
pancake-shaped potential. In a linear stability analysis with the Bogoliubov-de
Gennes model, we show that counter-rotating vortices are dynamically unstable
against splitting into multiple vortices. The instability shows characteristic
behaviors as a result of countersuperflow instability, which causes relaxation
of relative flows between the two components in binary condensates. The
characteristic behaviors are completely different from those of multiquantum
vortices in single-component Bose-Einstein condensates; the number of vortices
generated by the instability can become larger than the initial winding number
of the counter-rotating vortex. We also investigate the nonlinear dynamics of
the instability by numerically solving the Gross-Pitaevskii equations. The
nonlinear dynamics drastically changes when the winding number of
counter-rotating vortices becomes larger, which lead to nucleation of vortex
pairs outside of the vortex core. The instability eventually develops into
turbulence after the relaxation of the relative rotation between the two
components.
