Standard form of the scattering matrix for time reversal symmetric system

TL;DR

This paper derives the standard form of the scattering matrix for mesoscopic systems with spin-orbit coupling that preserve time reversal symmetry, revealing its analytical structure and relation to SU(2) matrices.

Contribution

It provides a new analytical form of the scattering matrix for such systems, highlighting its relation to SU(2) matrices and polar decomposition.

Findings

Transmission matrix is proportional to an SU(2) matrix in two-terminal mono-channel systems.

The scattering matrix exhibits specific analytical structures related to sub-matrices between channels.

Results are consistent with known polar decomposition properties.

Abstract

In this paper, we present the standard form of the scattering matrix of mesocopic system with spin-orbital coupling which preserves time reversal symmetry. We found some analytical structure of the scattering matrix related to the sub-matrices between arbitrary two channels. In particular, we proved that in the two-terminal mono-channel scattering problem, the transmission matrix is proportional to a SU(2) matrix. We obtained these properties through direct and elementary way and found it in agreement with polar decomposition known before.