Multiterminal multimode spin-dependent scattering matrix formalism: Electron and hole quantum spin transport in multiterminal junctions

We present a derivation of a scattering matrix method providing an exact multimode solution to spin-dependent quantum transport in multiterminal structures. The method is formulated in a general language such that it can readily be applied to any spin-S system with spin interactions. We apply the formalism to spin-1/2 electron and spin-3/2 hole transport in three- and four-terminal structures. It is shown that the existence of a third lead lifts constraints on the flux polarization of two-terminal electron transport. A spin-rectification property in a three-terminal system with Rashba spin-orbit interaction is demonstrated. We furthermore find that a four-terminal structure can partition a fully spin-polarized electron flux into two oppositely polarized fluxes. For holes, we calculate the polarization vector of both the injected states as well as the outgoing states in a three-terminal structure. Close to the onset of propagating channels, the hole polarization exhibits peak-dip structures attributed to the angular-momentum dependent Fano resonances in the three-terminal junction. We rigorously show that when the outgoing state is restricted to a single channel, the polarization is uniquely determined by the outgoing lead state, independent of the scattering details of the structure.