Regions in the electronic band structure

[erst]

I'm thinking mainly within the context of the useful semiconductors here (Si, GaAs, etc.)...

What does it mean for an electron to be in the L or X valley instead of the Gamma valley? If Gamma is the k = 0 point, then momentum p = 0. Does that mean being in L or X means all the electrons there are moving in some particular direction in real space (since k ≠ 0, so p ≠ 0, giving them some non-zero velocity vector). Does that mean that in the indirect bandgap materials like Si, electrons are moving together in some direction even with no applied E-field?

 

[DrDu]

There are several L (and X) valleys which are energetically degenerate. Hence while all electrons in one valey move in the same direction, on the average over all valleys, there is no net current.

 

[erst]

Ok, I see. But with just thermal energy, we have large numbers of electrons moving in a direction rather than randomly scattering about. Sure, they're canceled by another set of electrons doing the very same thing in exactly the opposite direction. But this just seems very "unnatural".

Physically in real space (just making up numbers in 1-D), do we have case of 1 A of current being canceled by -1 A, or is the net result of 0 A the only meaningful interpretation?

 

[DrDu]

Hm, finally this is a consequence of the Fermi-Dirac statistics. At finite density most electrons move at a high momentum whose absolute value is known as the Fermi-momentum. Only on the average the momentum of the electrons is zero.