Trions in cylindrical nanowires with a dielectric mismatch

Abstract

We investigated the lowest energy levels of trions (charged excitons) in freestanding nanowires with strong lateral carrier confinement. Within the adiabatic approximation, the three-particle problem reduces to an effective two-dimensional Schr\"odinger equation for the relative motion which is solved numerically. Dielectric mismatch effects are taken into account, which results in a distorted Coulomb interaction between the charged particles. We obtain the ``bright'' singlet and triplet trion binding energies and we found that the negatively charged exciton is always less stable than the positively charged exciton in a wire with a hole to electron mass ratio $\ensuremath{\sigma}>1$. The pair correlation functions and the conditional probabilities are calculated, which visualizes the correlation between the particles in the wire.