Is the orbital-selective Mott phase stable against inter-orbital hopping?

Orbital differentiation, seen e.g. via distinct effective electron masses, is an important notion for strongly correlated materials. An extreme form of it is the orbital-selective Mott phase (OSMP). In model studies, the OSMP can be easily realized with orbitals that have different bandwidths or occupations and do not hybridize with each other. But is the OSMP stable against inter-orbital hopping? Here, we use the single-site dynamical mean-field theory (DMFT) to show that, at zero temperature, the OSMP, involving the Mott-insulating state of one orbital, is unstable against inter-orbital hopping to another, metallic orbital. We provide a lower bound for the inter-orbital Kondo scale T^K_inter, stabilizing the metallic phase. Importantly, however, this scale can be extremely small, so that the physics at energies or temperatures far above T^K_inter is indistinguishable from a hypothetical OSMP with T^K_inter=0. We present analytical arguments supported by numerical results using the numerical renormalization group as DMFT impurity solver. We also compare our findings with previous slave-spin studies.