Excitonic effects in quantum wires

We review the effects of Coulomb correlation on the linear and nonlinear optical properties of semiconductor quantum wires, with emphasis on recent results for the bound excitonic states. Our theoretical approach is based on generalized semiconductor Bloch equations, and allows full three-dimensional multisubband description of electron-hole correlation for arbitrary confinement profiles. In particular, we consider V- and T-shaped structures for which significant experimental advances were obtained recently. Above band gap, a very general result obtained by this approach is that electron-hole Coulomb correlation removes the inverse-square-root single-particle singularity in the optical spectra at band edge, in agreement with previous reports from purely one-dimensional models. Strong correlation effects on transitions in the continuum are found to persist also at high densities of photoexcited carriers. Below band gap, we find that the same potential- (Coulomb) to kinetic-energy ratio holds for quite different wire cross-sections and compositions. As a consequence, we identify a shape-and barrier-independent parameter that governs a universal scaling law for exciton binding energy with size. Previous indications that the shape of the wire cross-section may have important effects on exciton binding are discussed in the light of the present results.