  Understanding the similarities and differences between adding or removing
electrons from a charge-transfer insulator may provide insights about the
origin of the electron-hole asymmetry found in cuprates. Here we study with
cellular dynamical mean-field theory the Emery model set in the charge-transfer
insulator regime, and dope it with either electrons or holes. We consider the
normal state only and focus on the doping evolution of the orbital character of
the dopants and on the nature of the doping driven transition. Regarding the
orbital character of the dopants, we found an electron-hole asymmetry: doped
electrons mostly enter the copper orbitals, whereas doped holes mostly enter
the oxygen orbitals. Regarding the nature of the doping driven transition, we
found no qualitative electron-hole asymmetry: upon either electron or hole
doping, there is a two-stage transition from a charge-transfer insulator to a
strongly correlated pseudogap and then to a metal. This shows that a strongly
correlated pseudogap is an emergent feature of doped correlated insulators in
two dimensions, in qualitative agreement with recent experiments on ambipolar
Sr$_{1-x}$La$_{x}$CuO$_{2+y}$ cuprate films. Our results indicate that merely
doping with holes or electrons a charge-transfer insulator is not sufficient
for explaining the electron-hole asymmetry observed in the normal state phase
diagram of cuprates. Our work reinforces the view that actual hole-doped
cuprates are more correlated than their electron-doped counterparts.
