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

TL;DR

This paper develops a comprehensive scattering wave function method for multi-terminal mesoscopic systems with spin-orbit coupling, enabling detailed calculations of local quantities and revealing new symmetry relations.

Contribution

It introduces a detailed formulation for solving scattering wave functions in multi-terminal systems with spin-orbit coupling, including new symmetry relations for two-terminal structures.

Findings

Derived rigorous results for equilibrium states.

Discovered new symmetry relations in two-terminal structures.

Provided tools for accuracy testing in experiments and simulations.

Abstract

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.