Rashba effect within the coherent scattering formalism

The influence of spin-orbit coupling in two-dimensional systems is investigated within the framework of the Landauer-B\"uttiker coherent scattering formalism. After a short review of the features of spin-orbit coupling in two-dimensional electron gases, we define the creation and annihilation operators for the stationary states of the Rashba spin-orbit coupling Hamiltonian and use them to calculate the current operator within the Landauer-B\"uttiker 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 that relates the spin-orbit coupling stationary states in different leads. As an example, we calculate the scattering matrix in the case of a four-port beam splitter, and it is shown to mix states with different spin-orbit coupling labels in a manner that depends on the angle between the leads. A noise measurement after the collision of spin-polarized electrons at an electron beam splitter provides an experimental means to measure the Rashba parameter $\ensuremath{\alpha}.$ It is also shown that the degree of electron bunching in an entangled-electron collision experiment is reduced by the spin-orbit coupling according to the beam splitter lead angle.