Magnetic field effects on a nanowire with inhomogeneous Rashba spin-orbit coupling: Spin properties at equilibrium

TL;DR

This paper studies how a magnetic field and inhomogeneous Rashba spin-orbit coupling influence spin currents and polarizations in a nanowire, revealing effects that challenge typical interpretations of spin signatures in such systems.

Contribution

It introduces a detailed model of a Rashba nanowire with inhomogeneous coupling under magnetic fields, highlighting novel equilibrium spin phenomena and interface effects.

Findings

A spin current polarized perpendicularly to the magnetic field is generated at equilibrium.

Localized spin torques and polarizations appear at the interfaces due to inhomogeneous Rashba coupling.

Spin polarization signatures can be misleading for identifying Majorana fermions.

Abstract

By modeling a Rashba nanowire contacted to leads via an inhomogeneous spin-orbit coupling profile, we investigate the equilibrium properties of the spin sector when a uniform magnetic field is applied along the nanowire axis. We find that the interplay between magnetic field and Rashba coupling generates a spin current, polarised perpendicularly to the applied field and flowing through the nanowire even at equilibrium. In the nanowire bulk such effect persists far beyond the regime where the nanowire mimics the helical states of a quantum spin Hall system, while in the leads the spin current is suppressed. Furthermore, despite the nanowire not being proximized by superconductors, at the interfaces with the leads we predict the appearance of localized spin torques and spin polarizations, orthogonal to the magnetic field and partially penetrating into the leads. This feature, due to the inhomogeneity of the Rashba coupling, suggests to use caution in interpreting spin polarization as signatures of Majorana fermions. When the magnetic field has a component also along the Rashba field, its collinearity with the spin polarization and orthogonality to the spin current are violated in the nanowire bulk too. We analyze these quantities in terms of the magnetic field and chemical potential for both long and short nanowires in experimentally realistic regimes.