Spin-dependent tunneling through a spin-orbit-split barrier

In a crystal without inversion center, when the spin-orbit interaction is taken into account, it has been shown that the evanescent branches inside the forbidden band gap correspond to complex wave vectors. Here, we discuss possible tunneling phenomena associated with complex wave vectors. We demonstrate that in a case where the wave vector has orthogonal real and imaginary components, an almost standard tunneling process can be restored under crude approximations, analoguous to off-normal tunneling through a potential barrier. Any more accurate analysis is an open problem. In one-dimensional tunneling with a complex wave; vector, no solution can be calculated under simple hypotheses.