By Casalbuoni R.
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Extra info for Lectures on advanced quantum field theory (lecture notes, web draft 1999)
A complete analysis of all three dispersion branches and thus the largest possible amount of information about linear combinations of the elastic and elasto-optic constants is obtained from lowersymmetry growth directions such as  or . Along these directions the LA and TA modes partially couple and mixed quasi-longitudinal (QL), quasitransverse (QT), and pure transverse (T) modes are observed. 144]. Before that, however, it seems appropriate to summarize the fundamentals of the acoustic phonon propagation in SLs and their Raman activities.
As mentioned above, one finds that confined LOl and TO1 modes for each material at q = 0 change character and become interface modes when the crystalmomentum component qll is different from zero. This dependence of the interface phonons on qll which is obtained in microscopic calculations is shown in Fig. For qll = qz ~ O, IF1 goes over into the AlAs LOl mode. As a consequence of the simultaneous fulfilment of the electrostatic and mechanical boundary conditions the displacement pattern of this mode is significantly deformed compared to a pure sine-like half wave and shifted towards tile interfaces.
The theoretical spectra were calculated with the planar bond-charge model for the frequencies, and the bond-polarizability model was used for the scattering intensities. To facilitate the comparison with the experiment the lines in Fig. 2 c m - l and, as outlined above, shifted by 2 cm-1 towards lower frequencies. One finds good agreement of these calculations with the measurements. 3 Optic Phonons in Isotopic Superlattices 39 74Ge 7OGe c L03(~,~) /~L(:'~ ZLd I,-Z ~r L01(L14~) ~ I 80 I ' I ~'(~') 300 f I I I 1 320 280 300 520 RAMAN SHIFT (cm -~) Fig.
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