Transport properties related to spin-orbit interaction

We propose a novel set of boundary conditions, based on the continuity of a generalized velocity and on the continuity of the probability current at the interface of heterojunctions, which is well suited to construct the solution of the tunneling problem when spin-orbit interaction is taken into account. We illustrate this procedure in a model case: tunneling of conduction electrons through a [110]-oriented GaAs barrier. In that case, the new boundary conditions reduce to two set of equations: the first one expresses the discontinuity of the envelope function at the interface while the other one is close to the standard condition on the derivative of the envelope function.