Long-range exchange interaction controls the fine structure of excited trion states in semiconductor quantum dots

Abstract

We develop a microscopic theory of the long-range electron-hole exchange interaction in charged excitons (trions) confined in semiconductor quantum dots. While the ground-state singlet trion remains degenerate in the spin component of unpaired charge carrier by time-reversal symmetry, excited trion states exhibit a rich fine structure resulting from the interplay of electron-electron and electron-hole exchange interactions. We derive the effective long-range exchange Hamiltonian for both the spin-$3/2$ heavy-hole and a simple spin-$1/2$ valence band models. The long-range exchange interaction mixes singlet and triplet trion configurations, giving rise to anisotropic fine-structure splittings and related polarization-dependent optical spectra determined by the quantum-dot shape. Analytical expressions are obtained for the long-range exchange parameters. The developed theory establishes a unified microscopic description of the fine structure of excited trions in semiconductor quantum dots and provides a framework for interpreting polarization-resolved optical spectroscopy of charged excitonic complexes.