I still don’t fully understand, why in the 1D electron in crystal model the electrons start accelerating in opposite direction to the field if we keep on increasing the force.
I guess that it makes sense that the effective mass starts diverging for larger and larger forces as we reach some sort of terminal velocity (due to the scattering), but why would it suddenly start moving slower again after reaching the terminal velocity? (i.e., when the effective mass becomes negative)
what model are you considering? The Drude model or the tight binding?
In tight binding we consider negative effective mass. Here, we first argue that it is reasonable to define the effective mass as the (inverse of the) curvature of the dispersion. How to understand that a negative effective mass implies movement of a particle opposite to the force acting on it is however also to me very hard. I rather see it as a parameter that describes the shape of the dispersion. In particular, it describes how the group velocity of a wave changes as a function of the wavelength.
@t.vandersar this is about the lecture (I explained Bloch oscillations).
This phenomenon is known as Bloch oscillations. It occurs only in absence of scattering. One way to see it is to observe that
- the electric field exerts a constant force on electrons
- a constant force leads to a constant increase of electron momentum and accordingly k-vector, k \propto t.
- The electron velocity in a single orbital is v \sim \sin k a, so it oscillates.
Another way to see this is to consider that the energy of an electron in a band can have energies between E_0 + 2 t and E_0 - 2t. This means that an electric field cannot increase or reduce the electron energy indefinitely, and therefore once electron reaches the point where its kinetic energy is E_0 \pm 2t it must turn back.