Dimensionality of exciton-state renormalization in highly excited semiconductors

Renormalization of the band gap and exciton state in the presence of high-density electron-hole pairs is studied systematically for quasi-one-dimensional (q-1D), quasi-two-dimensional (q-2D), and three-dimensional (3D) systems. By introducing a universal measure of particle packing, it is shown that renormalization proceeds less effectively in lower dimensions. The exciton state disappears (Mott transition) due to the Coulomb-potential screening in the 3D system, the phase space filling in the q-1D system, and both of them in the q-2D system, although the screening is important at densities below the Mott density for every dimension.