Transverse charge

The transverse charge motion is incoherent for a quasi-one-dimensional conductor as long as the condition h hiT is fulfilled (where the intrachain scattering time provides a broadening to the quasi-one-dimensional Fermi surface). This situation is encountered at high temperature. The interchain hopping rate is thus determined by the one-dimensional Fermi golden rule [60] ... 

The transverse charge for displacement in the y-direction is simplest. One sees immediately from F ig. 11-16 that displacement in this direction causes no changes in bond length to first order, nor does it change the bond angle to first order. Therefore, no transfer of charge is caused by the displacement, unlike what was described for the tetrahedral solid discussed in Section 9-D, and so e is simply the Z given in Eq. (11-6). 

This differs considerably from the Pantelides-Harrison prediction of transverse charge for x-displacement, which was dominated by changes in IT3. 

One other transverse-charge parameter can be evaluated. That parameter, 5p gives the change in dipole in the x-direction due to the change in distance R between the two silicons in the bonding unit (the distance between the oxygen and the Si—Si axis is held fixed). Its evaluation is closely related to the calculation of e leading to Eq. (11-17) and can be written as... 

It is interesting that these transverse charges depend so strongly upon direction this dependence comes entirely from the transfer charge. Kleinman and Spltzer... 

For oxygen, ef depends upon (he direction of displacement (Table 11-2), but if the environment of the silicon is assumed to have tetrahedral symmetry, its ef will not. Use values of ef from Table 11-2 to estimate the transverse charge for the silicon in SiO. ... 

We turn now to a matter of more direct physical relevance, the local electric dipole moment induced when a particular ion is displaced by some vector u. The transverse charge is defined to be the magnitude of that dipole moment divided by the displacement (and by the magnitude of the electronic charge). We saw in Eq. (9-22) that is directly related to an observable splitting between the longitudinal and transverse optical-mode frequencies, so that this is a quantity that can be compared with experiment. 

In Section 19-E we found contributions to the effective charge 7 of the oxygen due to the matrix clement between an sp hybrid and a d slate and due to the matrix element For an oxygen displacement perpendicular to the Ti—O axis, the predicted transverse charge is simply this Z. However, for displacements along the Ti—O axis there are contributions from the transfer of charge between ions just as there were in the alkali halides, for which we obtained the transverse charge in Section 14-C. 

Evaluate these contributions and the total transverse charge for oxygen displacements along the Ti—O axis in SrTiO, by using the relation... 

Indeed, very large couplings do occur in SrTiO., (sec Bauerle, 1974, and references contained therein), but a quantitative experimental estimate of the transverse charge is not available for comparison with this theoretical estimate. 

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