Interband polarization

Here u fl" and E " are the periodic part of the Bloch function, energy and Fermi-Dirac distribution functions for the n-th carrier spin subband. In the case of cubic symmetry, the susceptibility tensor is isotropic, Xcj) = Xc ij- It has been checked within the 4 x 4 Luttinger model that the values of 7c, determined from eqs (13) and (12), which do not involve explicitly u and from eqs (14) and (15) in the limit q - 0, are identical (Ferrand et al. 2001). Such a comparison demonstrates that almost 30% of the contribution to 7c originates from interband polarization, i.e. from virtual transitions between heavy and light hole subbands. 

First, we express the operator of the electron-hole interband polarization Pw in terms of the electron and hole creation and annihilation operators in the envelope function approximation, following the standard procedure (18), (39) ... 

Key words Exciton, interband transition, polarization, band structure... 

In Table 2, the calculated values of energy maxima E, and band areas Si of transverse transitions were compared for the three variants of calculations of optical function sets. These variants differ comparatively little in energy El. The principal inconsistencies are observed in the values of Si. This is caused by the differences in the experimental R(E) spectra, i.e. by using of ZnO samples of different quality and by different registration techniques for polarized reflectivity spectra. The determined components of S2 and -Ims spectra are caused by direct interband transitions or metastable excitons, except for the most long-wavelength of them, which are associated with free excitons. The theoretical band calculations of ZnO ° strongly differ in the bands dispersion and positions. This makes it difficult to propose a... 

Hydration of polar groups in the interbands, accompanied by some... 

Finally, in Sect. E the optical and magnetic properties are considered. It is found experimentally that some Zintl phases are colored and in ternary systems the color changes continuously as a function of the composition. This change can be correlated to a shift in a maximum of the imaginary part 2 of the dielectric constant e, and 2 can be interpreted by electronic interband transitions ) The magnetic susceptibility and Knight shift are discussed on the basis of spin polarized band structure calculations . Spin and orbital contributions are also considered. 

Most wurtzite-type crystals are direct band-gap materials (2fP-SiC is an exception) and interband transitions can take place between these three Fils and the T7 CB minimum. These materials are anisotropic and this anisotropy reflects on the selection rules for the optical transitions and on the effective masses. The Tg (A) —> T7 (CB) transitions are only allowed for ETc while the two T7 (B. C) —> T7 (CB) transitions are allowed for both polarizations. However, the relative values of the transition matrix elements for the T7 (B, C) —> T7 (CB) transitions can vary with the material. For instance, in w-GaN, the T7 (B) —> T7 (CB) transition is predominantly allowed for ETc while the T7 (C) — I 7 (CB) transition is predominantly allowed for E//c [22]. Table 3.7 gives band structure parameters of representative materials with the wurtzite structure. 

Figure 15. Calculated interband contribution to polar Kerr spectra of CoPt (Ref. [169]) (lower panel) for the (001) and (110) orientations of the magnetic moment. (A 0.03 Ry broadening was included). The experimental data (Ref. [170]) are for (001) oriented FePt.

Figure 1 Luminescence from n = 0 LL at filling factor i/ = 1. Recombination of initial interband exciton (a) can result either in ground state for (t+ polarization (b), or spin wave shake up for (t polarization (c).

One of the important facts regarding collagen fibril structure disclosed by electron optical studies is that the periodic band-interband patterns are polarized (193). In other words, as can be seen in Fig. 21, the fibrils possess no cross sectional planes of symmetry each has head and tail directions which are distinguishable. 

In the light of the description for intrafibrillar structure which has been presented above, the polarity has the following consequences. Since polypeptide chains, however folded in a regular manner, also possess similar polarity, the fibrillar polarity must arise because all constituent protofibrils are parallel and similarly directed. The model postulates also that the neighboring protofibrils or molecules are located axially so that corresponding features of chemical structure match across the fibril to form the bands and interbands. The important result emerges that the periodic band-interband pattern of the fibril is a direct indication. 

In ordinary optical absorption there are two components associated with intraband transitions (Drude component) and interband transitions, respectively. A similar situation is encountered in magneto-optical spectroscopy. Of special interest is the interband component which is related to the joint density of states. The intensity of the magneto-optical transitions is proportional to the product of spin-orbit coupling strength and net electron-spin polarization of states excited by the incident light (Erskine and Stern, 1973). 

As a consequence, the gap function il(k) is a matrix function of k only or its corresponding polar and azimuthal angles and (p. We have neglected indices for interband pairing because the available phase space is much smaller than in the case of intraband pairs. 

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