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Why can the energy of a photon be directly absorbed by an optical phonon but not by an acoustic phonon?

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Phonons have different modes of excitations. One kind of excitation is called the acoustic phonon. This kind of phonon has a dispersion relation like $\omega= ck$ for small k and where c is the speed of sound.

The optical phonon, however has a different dispersion relation, where $\omega\to\text{(non-zero constant)}$ as $k\to0$. In an optical phonon, neighbouring atoms move in opposite directions. In an ionic crystal, since neighbouring atoms have opposite charge, this is an oscillating dipole that radiation can interact with. It turns out that the large wavelength (small k i.e. wavenumber) optical phonons have energies similar to infrared radiation, so they can absorb light. I.e. light can excite optical phonons.

The acoustic phonons have very small energy/frequency (relative to light) for large wavelengths (small wave number) since $\omega\propto k$ for small k, so do not have strong coupling so to light. Also, they (generically) do not set up an oscillating dipole like the optical phonons.

See also Fig 22.10 of Ashcroft & Mermin.

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  • $\begingroup$ Acoustic phonons can have oscillating dipole moments, especially longitudinal ones. For example the longitudinal acoustic phonon of graphite at the M point explicitly has B1u symmetry. $\endgroup$ – KF Gauss Apr 9 at 15:56
  • $\begingroup$ @KFGauss I'm not a condensed matter physicist, so I have no idea what you're talking about! Could you explain a bit more? Also, are we talking about the short-wavelength phonons? Then I'm not so impressed. The main point is that the two phonons have qualitatively different mode behaviour. $\endgroup$ – thedoctar Apr 9 at 16:43
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You need to consider both momentum and energy conservation. The speed of sound for most materials is so low that you can't conserve both quantities for a photon to acoustic phonon absorption.

Think about the energy of a photon that is 100 meV (comparable to optical phonons). Then it has an momentum of roughly 0.5 um$^{-1}$. At this momentum, the highest acoustic phonon for any common material (e.g. diamond) is about 0.004 meV, so it cannot absorb the photon.

In pictures, look at the following figure showing the dispersion relations for light, optical phonons, and acoustic phonons $\omega=f(k)$. Which curve does the light line (red) intersect?

The light line can only intersect the optical phonon branch, never the acoustic one (except at zero energy, which is irrelevant). This is due to the velocity mismatch between the modes, which essentially means that the speed of sound is always much smaller than the speed of light.

enter image description here

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  • $\begingroup$ Your answer is not complete as absorption of light can only happen in ionic crystals, where the optical phonon sets up an oscillating dipole. If a crystals only contains neutral species, there will be no absorption by phonons. $\endgroup$ – thedoctar Apr 9 at 11:54
  • $\begingroup$ @thedoctar, no that is not true. You can have "infrared" active optical phonons (inversion breaking phonons) even in neutral compounds or molecules. For example, take a look the FTIR spectrum of graphite. It is true you need a phonon with the correct symmetry, but it does not only happen in ionic materials. $\endgroup$ – KF Gauss Apr 9 at 15:38
  • $\begingroup$ Moreover, the question is why optical phonons can be absorbed, not which ones will be absorbed. $\endgroup$ – KF Gauss Apr 9 at 15:39
  • $\begingroup$ the spectrum doesn't tell you how the light is being absorbed. But you seem like more of an expert than me. Can you explain the mechanism which gives a dipole moment in neutral species? $\endgroup$ – thedoctar Apr 9 at 16:50
  • $\begingroup$ CO$_2$ is a "neutral" molecule, so you would claim it cannot absorb light. But clearly if the Carbon atom moves transverse to the bonding direction a dipole moment is created. All you need is for the phonon distortion to break inversion symmetry, once it does then generically the dipole moment is non-zero. $\endgroup$ – KF Gauss Apr 9 at 18:14

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