Spin-orbit coupling, semiconductors

In addition to the experimental aspects of the different types of materials, theoretical treatments also were discussed. These included the presentation of studies related to molecular vibrational dynamics, the problem of vibration-induced decay of electronic excited states, nanoscale spin-orbit coupling in two-dimensional silicon-based structures, and the growth of semiconductor clusters by combining both theoretical approaches with actual experimental data. 

Spin-orbit coupling, semiconductors, 160f Spinels, 453... 

Zinc selenide is a direct-gap semiconductor with the smallest energy gap at the center of the Brillouin zone (F). The topmost valence band (F15) is spht owing to spin-orbit coupling into a fourfold (Fg) and a twofold (F7) state. 

The levels structure of the EM acceptor centres is determined by the characteristics of the VB of their host crystal near from its absolute extremum. As mentioned before, this extremum is located at k = 0 in most semiconductors. The contribution of the atomic p states of the constituent semiconductor atoms is predominant in the VB (for the compound crystals, it is related to the most electronegative atom). When spin-orbit (s-o) coupling is included, the pseudo-angular momentum J associated with the upper VB is L + S where L = 1 corresponds to the p electrons of the host crystal. For this reason and since they correspond to the pseudo-angular momenta J = 3/2 and 1/2, in the description of the acceptor states in diamond-type semiconductors, the T8 and r7- VBs are often labelled the p3/2 and j> /2 bands, respectively. 

We first note that an isolated atom with an odd number of electrons will necessarily have a magnetic moment. In this book we discuss mainly moments on impurity centres (donors) in semiconductors, which carry one electron, and also the d-shells of transitional-metal ions in compounds, which often carry several In the latter case coupling by Hund s rule will line up all the spins parallel to one another, unless prevented from doing so by crystal-field splitting. Hund s-rule coupling arises because, if a pair of electrons in different orbital states have an antisymmetrical orbital wave function, this wave function vanishes where r12=0 and so the positive contribution to the energy from the term e2/r12 is less than for the symmetrical state. The antisymmetrical orbital state implies a symmetrical spin state, and thus parallel spins and a spin triplet. The two-electron orbital functions of electrons in states with one-electron wave functions a(x) and b(x) are, to first order,... 

The relatively simple band stmcture of a cubic perovskite becomes more complex when the electron spin is taken into account. Calculations show that the mainly tj and e bands split into two components, one for spin-up electrons and one for spin-down species. The original two bands become four. An example is provided by the perovskite CaMnOj, containing Mn (d which is an AFM semiconductor. The lower-energy t band should contain three electrons with parallel spins. As the tj state can hold up to six electrons, it is only half full in CaMnOj, thus predicting metallic conductivity. However, because of electron correlation (Hund s coupling between electrons, which results in Hund s mles for electron occupation of similar orbitals), both the t and e orbital sets are split into two sub-bands, one for spin-up (t) electrons and one for spin-down (f) electrons. The simplified density of states diagram (Figure 8.11) shows that the valence band, derived mainly from O 2p states. 

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