The role of phonons in momentum conservation

[hokhani]

In an indirect transition from the valence band maximum to conduction band minimum, the momentum of electron and hole would not change but the crystal momentum would change and this change is supplied by phonons.I have two questions here:
1) phonons don't carry momentum so how they can transfer their momentum to the crystal?
2) phonons are part of the crystal. why do we separate their momentum from crystal momentum?

 

[DrDu]

Phonons don't carry momentum but they carry crystal momentum which are two completely different things.

 

[hokhani]

Phonons don't carry momentum but they carry crystal momentum which are two completely different things.

Ok, but crystal momentum's change is sum of electron momentum's change and momentum change of the crystal;Ok? If yes, in the explained situation electron momentum is not changed so the momentum of crystal must be changed by phonons!

 

[DrDu]

In an indirect transition, the electrons crystal momentum changes this is compensated by a change of crystal momentum of the phonon.
I don't see any problem here.
The true momentum of the electron doesn't interest anyone in that context, as it isn't in a momentum eigenstate anyhow.

 

[hokhani]

The true momentum of the electron doesn't interest anyone in that context, as it isn't in a momentum eigenstate anyhow.

Yes, But what I meant was the mean value of true momentum of electron which is "mass of electron times its group velocity".

 

[DrDu]

As I already explained in another thread, the lattice itself (as opposed to the phonons) can take up arbitrary amounts of momentum, so momentum conservation is always trivial.