# Photon absorption by electrons at opposite k-points

1. Jan 5, 2016

### hokhani

Transition of an electron from the valence to conduction bands (direct transition at a k-point near the band edge) would change the momentum of electron because the sign of the group velocity in valence and conduction bands are opposite. Could one infer that the direction of radiation is a determining factor in the transition? In other words, by radiating light from a specific direction, if we have transition at k we can not have the same transition at -k because if the radiation could change the group velocity at k from v to -v, it would change the group velocity at -k from -v to -2v while according to band structure the transition at -k requires changing from -v to v!

2. Jan 6, 2016

### M Quack

How large is the momentum of a photon compared to the size of the Brillouin zone?

3. Jan 6, 2016

### hokhani

The momentum of photon is too small to change the crystal momentum of electron but it changes the real momentum of electron because $v_g={1/\hbar} \nabla_k E$ and assuming parabolic valence and conduction bands (with the same effective mass) this formula says that the velocity changes from, say, v to -v in the optical transition.

4. Jan 7, 2016

### M Quack

The assumption is always that the real momentum is taken up by the whole crystal, which has a huge mass, and therefore the resulting velocity is nothing.
A very good example for this is the Moessbauer effect (OK, photons are absorbed/emitted by the nuclei, but the principle is the same).

5. Jan 7, 2016

### hokhani

No, this problem occurs even if we don't suppose the phonon effect.

6. Jan 10, 2016

### zhanghe

When a transition happens that an electron jumps from VB to CB by being excited only by a photon, the electron always jumps almost vertically in the E-k diagram. The momentum conversation is still held though the election velocity direction becomes reverse. But do not forget that its effective mass also becomes from negative into positive. As usual people prefer to use h with bar *k to describe the momentum instead of mv for simplicity. In the way. You just need to check k for the direction of momentum of electron.

7. Jan 10, 2016

### hokhani

Thanks. But I don't agree. The hole effective mass is negative (valence band) but it is not true for an electron which is still in the valence band. To describe the behavior of the whole valence band which has lost an electron, we use the hole language and consider a negative effective mass for the hole.

Last edited: Jan 10, 2016
8. Jan 10, 2016

### zhanghe

Well, the m* of hole is positive.