  The influence of spin-orbit coupling in two-dimensional systems is
investigated within the framework of the Landauer-Buettiker coherent scattering
formalism. This formalism usually deals with spin-independent stationary states
and, therefore, it does not include a spin-orbit contribution to the current.
In this article, we will rederive the coherent scattering formalism, accounting
for the changes brought about by the spin-orbit coupling. After a short review
of the features of spin-orbit coupling in two-dimensional electron gases, we
define the creation/annihilaton operators in the stationary states of the
spin-orbit coupling Hamiltonian and use them to calculate the current operator
within the Landauer-Buettiker formalism. The current is expressed as it is in
the standard spin-independent case, but with the spin label replaced by a new
label which we call the spin-orbit coupling label. The spin-orbit coupling
effects can then be represented in a scattering matrix which relates the
spin-orbit coupling stationary states in different leads. This scattering
matrix is calculated in the case of a four-port beamsplitter, and it is shown
to mix states with different spin-orbit coupling labels in a manner that
depends on the angle between the leads. The formalism is then used to calculate
the effect of spin-orbit coupling on the current and noise in two examples of
electron collision.
