Simple (?) question regarding the Fermi Surface

[rwooduk]

We all see diagrams of the Fermi surface, the representation of the occupied states, but I can't seem to find a precise diagram of when an electric field is applied. Most diagrams show that the surface has moved, BUT they do not say in which direction relative to the electric field, and when they do they seem vague about which surface was the old, and which is the new, and which one is occupied.

This one does, but it's unclear which is the original fermi surface and which is the new one:

"When an electrical field is applied, the Fermi surface shifts in the direction of the field either in the positive or negative direction."

Ok, so if it has moved in the direction of the field, then the old fermi surface is still occupied. Or if it moved in the other direction then why is the new fermi surface in the centre of the axis?

So my questions:

1) Does the fermi surface move in the direction of the electric field?
2) Does the old fermi surface remain fully occupied, or does it take the electrons with it when it moves i.e. the new fermi surface is fully occupied?

thanks if anyone could clear this up a little for me.

 

[mfb]

Ok, so if it has moved in the direction of the field, then the old fermi surface is still occupied.

Only partially. Without field the sphere is centered at zero. With field, the whole sphere shifts in such a way that the electrons on average flow towards the positive side.

To get a fully occupied surface you need a temperature of zero. But the occupation of the old surface and the new surface will be the same.

 

[rwooduk]

Only partially. Without field the sphere is centered at zero. With field, the whole sphere shifts in such a way that the electrons on average flow towards the positive side.

To get a fully occupied surface you need a temperature of zero. But the occupation of the old surface and the new surface will be the same.

hmm, I'm having trouble relating that to the diagram above. which is the new and old fermi surface in the diagram?

thanks for the reply

 

[mfb]

Old is the filled sphere, centered at zero. The new one is shifted (and the electrons will shift in the same way, not shown in the diagram).

 

[rwooduk]

Old is the filled sphere, centered at zero. The new one is shifted (and the electrons will shift in the same way, not shown in the diagram).

Thanks, so the electrons will move with the Fermi surface, i.e. the new fermi surface will be fully occupied?

 

[mfb]

See above:

To get a fully occupied surface you need a temperature of zero. But the occupation of the old surface and the new surface will be the same.

 

[rwooduk]

See above:

So assuming 0K all the electrons will occupy the new fermi surface, is that right?

thanks

 

[mfb]

Or states below that, sure.