Dispersion relations in diamond crystal structure

[jacare]

I know acoustic and optical phonons can interact with one another. Also, longitudinal and transverse phonons can interact with one another. I am wondering can a longitudinal phonon in one plane act with a transverse phonon from another plane to create a third phonon? Or, do these phonon-phonon interactions happen only amongst phonons in similar planes?

 

[arw75]

They can but it's rare for this to be significant because the planar separation is comparatievely large (usually). I've never seen it, but it's certainly possible. The largest effect would, i suppose, would be two TOs. The phonon modulated electron electron interaction would be interesting too, with polar coupling.

Cheers

 

[Gokul43201]

The phonon modulated electron electron interaction would be interesting too, with polar coupling.

I'm curious what you mean by this? Did you mean "phonon mediated"? Could you elaborate (and throw in some references, if possible)?

 

[arw75]

Hi again,

I got the term phonon modulated from Gerald Mahan and LM Woods. They describe it in PRB 60, 5276 (1999) for systems with one atom per unit cell. They later extend it to two which they then use to show that the effect is comparable to the deformation eph interaction in graphene. That ref is on my laptop. Anyway, there are some tidy diagrams for the interaction in the former. It's a straight e-e interaction with a phonon line added between initial or final states.

The propagation of Cooper pairs is phonon assisted transport of two electrons (PR 108, 1175 (1957)... of course!) . I don't work on superconductors so I don't know if it's an identical effect, and perhaps the word there is phonon-mediated. I don't know... It would be interesting to look at the Feynman Diagrams for that.

 

[Gokul43201]

I got the term phonon modulated from Gerald Mahan and LM Woods. They describe it in PRB 60, 5276 (1999) for systems with one atom per unit cell. They later extend it to two which they then use to show that the effect is comparable to the deformation eph interaction in graphene. That ref is on my laptop. Anyway, there are some tidy diagrams for the interaction in the former. It's a straight e-e interaction with a phonon line added between initial or final states.

Thanks for the reference. Mahan's paper talks about phonon modulated e-e interactions, which I now understand better.

But let me point out that the diagram you've described (if I'm not misinterpreting it) actually refers to a phonon mediated interaction. Read the first sentence in the second paragraph (and see ref 6, MacDonald et al, PRB 23, 2718, 1981).

 

[arw75]

Ah thanks for that. That's what you get for not reading the intro! I got the idea that ph-mediated e-e would be the exchange of a phonon, but wasn't sure. The diagrams I'm referring to (figs 1 and 2) are modulations though. The exchange mechanism is Coulombic, but the phonons alter the positions... Unless I'm mistaken. So the deformation has an indirect effect on the coulomb interaction.

Thanks again,
Will take a look at MacDonald now.

 

[arw75]

Just by the way, why the ref to Zhukov et al? My honours thesis used the Rashba effect to determine the effect of the spin orbit interaction on the dielectric function and plasma frequencies.

Cheers

 

[arw75]

the pic. I see. nevermind

 

[Gokul43201]

Didn't want to be using the picture without acknowledging the source. I used to have the acknowledgment buried somewhere in my profile, but I recently decided to put it in a more visible place.