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In the framework of a two-band model, we study the phase separation regime ofdifferent kinds of strongly correlated charge carriers as a function of theenergy splitting between the two sets of bands. The narrow (wide) bandsimulates the more localized (more delocalized) type of charge carriers. Byassuming that the internal chemical pressure on the CuO$_2$ layer due tointerlayer mismatch controls the energy splitting between the two sets ofstates, the theoretical predictions are able to reproduce the regime of phaseseparation at doping higher than 1/8 in the experimental pressure-doping-$T_c$phase diagram of cuprates at large microstrain as it appears in overoxygenatedLa$_2$CuO$_4$.

A model for the phase separation controlled by doping and the internal chemical pressure in different cuprate superconductors