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 heavyand 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 heavyand 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.