  The localization-delocalization transition is at the heart of strong
correlation physics. Recently, there is great interest in multiorbital systems
where this transition can be restricted to certain orbitals, leading to an
orbital-selective Mott phase (OSMP). Theoretically, the OSMP is widely studied
for kinetically decoupled orbitals, but the effect of interorbital hopping
remains unclear. Here, we show how nonlocal interorbital hopping leads to local
hybridization in single-site dynamical mean-field theory (DMFT). Under fairly
general circumstances, this implies that, at zero temperature, the OSMP,
involving the Mott-insulating state of one orbital, is unstable against
interorbital hopping to different, metallic orbital. We further show that the
coherence scale below which all electrons are itinerant is very small and gets
exponentially suppressed even if the interorbital hopping is not overly small.
Within this framework, the OSMP with interorbital hopping may thus reach down
to extremely low temperatures $T$, but not to $T=0$. Accordingly, it is part of
a coherence-incoherence crossover and not a quantum critical point. We present
analytical arguments supported by numerical results using the numerical
renormalization group as a DMFT impurity solver. We also compare our findings
with previous slave-spin studies.
