Probability- and spin-current operators for effective Hamiltonians

We present a systematic construction of the probability-and spin-current operators, based on a momentum power expansion of effective Hamiltonians. These operators play an essential role in transport problems related to semiconductor heterostructures, in particular when spin-orbit interaction is taken into account. The result, valid whatever the momentum power and including the linear (Bychkov-Rashba) term as well as the cubic (Dresselhaus or D'yakonov-Perel) term, is of special importance for spintronics.