Excitons in core-shell nanowires with polygonal cross sections

The distinctive prismatic geometry of semiconductor core-shell nanowires leads to complex localization patterns of carriers. Here, we describe the formation of optically active in-gap excitonic states induced by the interplay between localization of carriers in the corners and their mutual Coulomb interaction. To compute the energy spectra and configurations of excitons created in the conductive shell, we use a multi-electron numerical approach based on the exact solution of the multi-particle Hamiltonian for electrons in the valence and conduction bands, which includes the Coulomb interaction in a nonperturbative manner. We expose the formation of well separated quasidegenerate levels, and focus on the implications of the electron localization in the corners or on the sides of triangular, square and hexagonal cross sections. We obtain excitonic in-gap states associated with symmetrically distributed electrons in the spin singlet configuration. They acquire large contributions due to Coulomb interaction, and thus are shifted to much higher energies than other states corresponding to the conduction electron and the vacancy localized in the same corner. We compare the results of the multi-electron method with those of an electron-hole model and we show that the latter does not reproduce the singlet excitonic states. We also obtain the exciton lifetime and explain selection rules which govern the recombination process.