Probability current in presence of Spin-Orbit Interaction-Spintrionics IV

We propose a procedure, based on momentum power series expansion Hamiltonian of n th general order, to obtain a coherent expression of the probability current operator that is valid also when Spin-Orbit Interaction terms are included. We prove that we recover the standard definition for a free electron-like Hamiltonian, and also in the case of the Rashba Hamiltonian. When higher-order terms are taken into account, a more general definition of the probability current operator is mandatory. This is the case of the D'yakonov-Perel' Hamiltonian.