Electron-hole recombination density matrices obtained from large configuration-interaction expansions

An efficient computational method for constructing general transition density matrices such as the electron-hole recombination density matrix from large configuration interaction expansions is presented. The present string-based Slater-determinant approach is completely general and can be used to describe simultaneous annihilation or creation of one or several electron-hole pairs. The method can also be applied on electron-hole annihilation processes involving excitations of remaining particles. In this work, the method has been implemented and used for obtaining the radiative recombination rates of electrons and holes confined in a semiconductor ${\mathrm{In}}_x{\mathrm{Ga}}_{1-x}\mathrm{A}\mathrm{s}/\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}$ quantum dot sample. The qualitative features of an experimental single-dot photoluminescence (PL) spectrum are well explained by the calculated PL spectra including exciton, biexciton, and triexciton transitions. The obtained exciton-biexciton and biexciton-triexciton splittings agree well with the experiment. The present computational approach provides accurate and reliable interpretations of PL spectra for quantum dots.