Theory of charge-to-spin conversion under quantum confinement

TL;DR

This paper develops a comprehensive theoretical framework to understand charge-to-spin conversion in low-dimensional systems with spin-orbit interactions, accounting for quantum confinement and magnetic effects, aligning with experimental observations.

Contribution

It introduces a generalized scattering matrix approach that explicitly describes spin and charge transport under quantum confinement and spin-orbit coupling, extending the B"uttiker formalism.

Findings

Provides explicit real-space expressions for spin and charge currents.

Captures effects of quantum confinement and magnetic fields.

Aligns theoretical predictions with experimental results.

Abstract

The interplay between spin and charge degrees of freedom in low-dimensional systems is a cornerstone of modern spintronics, where achieving all-electrical control of spin currents is a major goal. Spin-orbit interactions provide a promising mechanism for such control, yet understanding how spin and charge transport emerge from microscopic principles remains a fundamental challenge. Here we develop a spin-dependent scattering matrix approach to describe spin and charge transport in a multiterminal system in the presence of Rashba spin-orbit interaction. Our framework generalizes the B\"uttiker formalism by offering explicit real-space expressions for spin and charge current densities, along with the corresponding linear response function. It simultaneously captures the effects of quantum confinement, the orbital response to external magnetic fields, and the intrinsic (geometric) properties of the electronic bands, offering a comprehensive description of the spin-charge interconversion mechanisms at play in a Hall bar, in agreement with experiments.