Take a look at the table below to get an idea of how well this relation holds for a few materials (reproduced from Mark Fox’s textbook Optical Properties of Solids): Not only that, the agreement with experiment in many polar semiconductors is excellent. Regardless, it turns out that all quantities in the LST relation are experimentally accessible! I find this relation quite remarkable and deep. It is an interesting question as to whether or not quantum mechanics plays a role in the long-wavelength optical response in general. Therefore, the result can be derived from classical electrodynamics, without resorting to any quantum mechanics. The beautiful thing about the LST result is that it is independent of any microscopic description, which is quite unusual in solid-state physics. All these quantities are understood to be the values in the long-wavelength limit (i.e. and refer to the static and high frequency (above the phonon frequencies, but below any electronic energy scale) dielectric constants. In the equation above, and refer to the frequencies of the longitudinal and transverse optical phonons respectively. It has wide applicability for polar insulators. In 1941, Lydanne, Sachs and Teller wrote a paper entitled “On the Polar Vibrations of Alkali Halides”, where they derived a result now known as the Lydanne-Sachs-Teller (LST) relation.
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