Mott-Hubbard vs Charge-Transfer Insulating Behavior in the CuO$_2$ Plane

High temperature superconductivity emerges in the CuO$_2$ plane upon doping a Mott insulator. The Mott insulating state occurs in different regimes, Mott-Hubbard insulator and charge-transfer insulator. The latter is relevant especially for hole-doped cuprates. Within a three-band model we can explore both charge-transfer and Mott-Hubbard systems. Here we study the metal-insulator transitions in a three-band copper oxide model within cluster dynamical mean-field theory with continuous-time quantum Monte Carlo as an impurity solver. As a function of doping, charge-transfer energy and interaction strength, the normal state of this model shows the two types of metal-insulator transitions, metal to charge-transfer insulator and metal to Mott-Hubbard insulator.