The interaction between electron-electron and electron-hole pairs in semiconductor nanorods embedded in dielectric media is investigated using a configuration-interaction method. Contrary to spherical quantum dots of similar volume, the dielectric confinement is shown to bring nanorods into a regime of strong configuration mixing. The wave functions are particularly sensitive to such mixing, which leads to qualitative changes in the electronic and optical properties of the rods. DOI: 10.1103/PhysRevB.79.161301 PACS number͑s͒: 73.21.La, 77.22.Ej, 78.67.Hc, 71.27.ϩa Semiconductor quantum rods or nanorods ͑NRs͒ are colloidal quantum dots with strong radial confinement and variable length.1,2 Even though NRs were first synthesized long after spherical nanocrystals ͑NCs͒, it was soon realized that their anisotropic shape posed many benefits for optical and transport applications.3 This prompted a large number of studies, often revealing characteristic physical phenomena which stem from the weak longitudinal confinement, for NRs bridge the gap between zero-dimensional and onedimensional quantum-confined systems. [4][5][6][7][8][9][10] Similar to NCs, NRs are usually embedded in insulating media, whose dielectric constant is much lower than that of the semiconductor structure. This dielectric mismatch gives rise to a so-called dielectric confinement, which greatly enhances the Coulomb interactions inside the semiconductor. 11,12 In spherical NCs, however, owing to the strong quantum confinement, Coulomb interactions are usually a first-order perturbation effect for the low-lying states.
13Furthermore, a strong spatial confinement leads to compensations between electron and hole charge distributions, 14,15 so that the optical properties are barely affected by the dielectric environment.None of these restrictions apply to NRs, where the longitudinal confinement may be fairly weak. Indeed, the dielectric confinement has been held responsible for the large variation in the optical gap of CdSe NRs as compared to the transport one. 7,16 What is more, NRs are the zerodimensional counterpart of quantum wires, where variations in the dielectric confinement have been shown to induce drastic changes in the binding energy and oscillator strength of excitons, thus enabling Coulomb interaction engineering. [17][18][19] One may then wonder to which extent the single-particle and perturbational treatments of Coulomb interactions that dominate the literature of NRs ͑Refs. 6-10͒ provide a valid description of the optoelectronic properties.In this work, we perform a theoretical study of the effect of the dielectric confinement on interacting particles ͑two electrons or one electron and one hole͒ confined in a semiconductor NR. A numerical procedure is used which allows us to estimate the effect of the dielectric environment for arbitrary three-dimensional potentials, thus addressing realistic geometries. Electron correlations are then accounted for exactly using an effective mass-configuration-interaction ͑CI͒ scheme. We go beyond en...