  We construct a family of partially hyperbolic skew-product diffeomorphisms on
$\mathbb{T}^3$ that are robustly transitive and admitting two physical measures
with intermingled basins. In particularly, all these diffeomorphisms are not
topologically mixing. Moreover, for every such example, it exhibits a dichotomy
under perturbation: every perturbation of such example either has a unique
physical measure and is robustly topologically mixing, or has two physical
measures with intermingled basins.
