  We study by dynamical mean field theory the ground state of a quarter-filled
Hubbard model of two bands with different bandwidths. At half-filling, this
model is known to display an orbital selective Mott transition, with the
narrower band undergoing Mott localisation while the wider one being still
itinerant. At quarter-filling, the physical behaviour is different and to some
extent reversed. The interaction generates an effective crystal field
splitting, absent in the Hamiltonian, that tends to empty the narrower band in
favour of the wider one, which also become more correlated than the former at
odds with the orbital selective paradigm. Upon increasing the interaction, the
depletion of the narrower band can continue till it empties completely and the
system undergoes a topological Lifshitz transition into a half-filled
single-band metal that eventually turns insulating. Alternatively, when the two
bandwidths are not too different, a first order Mott transition intervenes
before the Lifshitz's one. The properties of the Mott insulator are
significantly affected by the interplay between spin and orbital degrees of
freedom.
