I'm getting very confused about the movement of electrons in the valence band. In the textbook I'm reading, the convention is that these electrons have a negative effective mass. Therefore, when a force is applied, they move in the opposite direction to what would be expected usually. An electric field would cause the electrons to move in the same direction as a positive charge. A hole in the valence band would also have this same behaviour (since it is opposite charge but also opposite effective mass). $ \vec{v}_{group} =\nabla_{k_e} E_{elec} = \nabla_{-k_{h}}(-E_{h}) = \nabla_{k_h} E_h $
So, it seems that both holes and electrons in the valence band are moving in the direction of the electric field towards the negative electrode. There are some electrons moving towards the positive electrode in the conduction band. But, overall, there is a much larger net movement of negative charges moving towards the negative electrode. This seems very wrong. In this stack exchange, Matt says that this picture is correct. We should think of the valence band as a conveyor belt with everything moving in the same direction. Are holes electrons moving in the same direction of the electric field? .
Every website I've seen with gifs trying to demonstrate this has the electrons in the valence band going the other way though.
The only workaround I can see is this: instead of thinking about the electrons in the valence band as having a negative mass, we can think about them as having a positive charge.
