Quantum condensation in electron–hole systems: excitonic BEC–BCS crossover andbiexciton crystallization

Abstract

Quantum condensation of electron–hole (e–h) systems in photoexcited semiconductorsis reviewed from a theoretical viewpoint, stressing the exciton Bose–Einsteincondensation (BEC), the e–h BCS-type condensed state, the exciton Mott transition,and the biexciton crystallization. First, we discuss the crossover between theexciton BEC and the e–h BCS states at low temperature using the self-consistentt-matrix and local approximations, applied to the high-dimensional two-band Hubbardmodel with both repulsive and attractive on-site interactions. We also study themetal–insulator transition (called the ‘exciton Mott transition’) at zero and finitetemperatures, investigated with the dynamical mean-field theory. Away fromhalf-filling we find excitonic/biexcitonic insulating phases and the first-order transitionbetween metallic and insulating states. Second, in a one-dimensional e–h system,we employ the exciton bosonization and renormalization-group techniques toclarify quantum orders at zero temperature. The most probable ground stateexhibits the biexciton crystallization, which reflects the Tomonaga–Luttinger liquidproperties, the e–h backward scattering, and the long-range Coulomb interaction. Theone-dimensional e–h system is insulating even at the high-density limit, hencethe exciton Mott transition never occurs at zero temperature in one dimension.