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

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-. 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-, 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.