Spin-current quantization in a quantum point contact with spin-orbit interaction

TL;DR

This paper models spin current generation in a quantum point contact with spin-orbit interaction, revealing quantized spin polarization peaks linked to conductance steps, with results applicable to realistic device geometries.

Contribution

It provides an analytically tractable model showing spin current quantization in QPCs with finite-region SOI, including detailed dependence on geometry and potential landscape.

Findings

Spin polarization appears in third-order perturbation theory.

Spin current is proportional to the cube of SOI strength.

Characteristic peaks in spin conductance align with charge conductance steps.

Abstract

We develop a realistic and analytically tractable model to describe the spin current which arises in a quantum point contact (QPC) with spin-orbit interaction (SOI) upon a small voltage is applied. In the model, the QPC is considered as a saddle point of two-dimensional potential landscape. The SOI acts within a finite region and is absent deep in the reservoirs. The SOI strength is not supposed to be strong. It is shown that the spin polarization appears in the third order of the perturbation theory as a result of definite combinations of electron transitions. They include two intersubband transitions to nearest subbands and one intrasubband transition. The spin current is proportional to the cube of the SOI strength and strongly depends on geometric parameters of the saddle point. The spin is polarized in the plane of the QPC and directed normally to the electron current if the SOI is of Rashba type. As a function of the saddle-point potential (i.e., the height of the QPC barrier), the spin conductance and especially the spin polarization have characteristic features (specifically, peaks) correlated with the charge conductance quantization steps. The peak shape depends on the length of the region where the SOI acts. In QPCs with sharp potential landscape, this picture is distorted by interference processes.