Phase diagram for the exciton Mott transition in infinite-dimensional electron–hole systems

To understand the essence of the exciton Mott transition in three-dimensional electron–hole systems, the metal–insulator transition is studied for a two-band Hubbard model in infinite dimensions with interactions of electron–electron (hole–hole) repulsion U and electron–hole attraction image. By using the dynamical mean-field theory, the phase diagram in the U–image plane is obtained (which is exact in infinite dimensions) assuming that electron–hole pairs do not condense. When both electron and hole bands are half-filled, two types of insulating states appear: the Mott–Hubbard insulator for image and the biexciton-like insulator for image. Even when away from half-filling, we find the phase transition between the exciton- or biexciton-like insulator and a metallic state. This transition can be assigned to the exciton Mott transition, whereas the Mott–Hubbard transition is absent.