Scattering wave function approach to multi-terminal mesoscopic system with spin-orbit coupling

In this paper,we present a detailed formulation to solve the scattering wave function for a multi-terminal mesoscopic system with spin-orbit coupling. In addition to terminal currents, all local quantities can be calculated explicitly by taking proper ensemble average in the Landauer-Buttiker's spirit using the scattering wave functions. Based on this formulation, we derive some rigorous results for equilibrium state. Furthermore, some new symmetry relations are found for the typical two terminal structure in which a semiconductor bar with Rashba or/and Dresselhaus SO coupling is sandwiched symmetrically between two leads. These symmetry property can provide accuracy tests for experimental measurements and numerical calculations.