In the right column of page 20 in this paper, spins in few-electron quantum dots, the paper says "It is at first sight surprising that there is a net spin-orbit interaction: since the state is bound along the growth direction, the average electric field in the conduction band must be zero."
I was confused about the statement that 'the average electric field in the conduction band must be zero.' Why would the average electric field in the valence band not be zero but that in the conduction band be zero?
I think the wikipedia page on Rashba effect, wikipedia page does touch on this (Under the subtitle, 'Naive derivation', it says "the effect comes from mixing energy bands (interband matrix elements) rather from intraband term of the naive model." It sounds like the electric field in the toy model hamiltonian somehow describes the electric field in the conduction band only. I don't understand the idea that different bands experience different electric fields. Is it because they are in different orbitals?) but I wasn't able to really understand what's written there either.
Also, what causes the mixing between the conduction band and valence band, which the paper says leads to the Rashba interaction?