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?