Quantum-mechanical spin states and Zeeman-level diagrams of the positively charged exciton

Abstract

We consider the spin interaction in the Hamiltonian for the positively charged exciton ${X}^{+},$ determining the spin states and Zeeman-level diagrams for ${X}^{+}$ in which the heavy- and light-hole bands are degenerate and nondegenerate. The former case results in an ${X}^{+}$ with quintuplet and septet states in addition to the singlet and triplet states that are also observed for the negatively charged exciton ${X}^{\ensuremath{-}}.$ When the heavy- and light-hole bands are split ${X}^{+}$ can comprise two heavy holes, two light holes, or a heavy and a light hole. The heavy-hole ${X}^{+}$ Zeeman-level diagram is found to be completely analogous to that of ${X}^{\ensuremath{-}},$ while the light-hole ${X}^{+}$ has more optical transitions and a different Zeeman splitting in photoluminescence. ${X}^{+}$ consisting of a heavy and a light hole has no coupled hole states, and is truly a heavy- (or light-) hole exciton plus a light (heavy) hole.