Pseudo-Spin Development of the Exciton Ground State in Zincblende-Type Semiconductors

Abstract

We have seen in the foregoing chapters that the development of an effective Hamiltonian, which is adapted to the crystal symmetry, is an efficient tool to describe electronic excitations in semiconductors. The development procedure becomes, however, quite tedious and inefficient if a large basis of electron states is considered when describing a system. On the contrary, this technique is interesting if only a couple of almost degenerate states, which are well separated in energy from other states, has to be analyzed. This is the case for example in the exciton problem that has been discussed in the previous chapter. Here, the split-off exciton states (resulting from electrons and holes that transform as $\Gamma _6$ and $\Gamma _7$, respectively) are separated by the spin-orbit coupling from the exciton block obtained from electrons and holes that transform as $\Gamma _6$ and $\Gamma _8$, respectively. As we have already discussed, the two exciton blocks are coupled by the electron-hole exchange interaction, which is, however, small compared to the spin-orbit coupling. In this case, the exciton blocks are approximately decoupled and different effective Hamiltonians that are independent from each other can be developed for the two exciton blocks. This will be done in the present chapter. We understand this as a “Pseudo-Spin Development” of excitons in a subspace of almost degenerated states.