Rashba spin splitting and Ehrenfestʹs theorem

It is shown rigorously that the 2×2 Rashba term characterizing the spin splitting in inversion asymmetric electron systems emerges from the 8×8 Kane Hamiltonian in much the same way like the 2×2 Pauli spin–orbit coupling emerges from the 4×4 Dirac equation. The gradient of the potential that enters into the Rashba term is the gradient of the effective potential in the valence band so that Ehrenfestʹs theorem is not applicable to Rashba spin splitting.