Curvature induced out of plane spin accumulation

TL;DR

This paper demonstrates that curvature in waveguides with Rashba spin orbit interaction induces out-of-plane spin accumulation, combining analytical derivations and numerical simulations to reveal new spin behaviors in curved geometries.

Contribution

It derives the RSOI Hamiltonian on curved surfaces and shows how curvature causes out-of-plane spin accumulation through analytical and numerical methods.

Findings

Curvature leads to out-of-plane spin accumulation.

Analytical predictions are verified by numerical eigenstate solutions.

Out-of-plane spin effects occur in asymmetrically curved waveguides.

Abstract

In this work we show that (real space) curvature in the geometry of curved waveguides with Rashba spin orbit interaction (RSOI) can lead to out of plane spin accumulations. We first derive the RSOI Hamiltonian on arbitrarily curved surfaces. We then analyze the effects of curvature with two distinct methods. We first apply an adiabatic approximation on gently curved, planar waveguides lying flat on the $xy$ plane to show that analogous to the acceleration of the charge carriers by an electric field, the change in momentum direction of the charge carriers as they move along the waveguide leads to an out of plane spin accumulation. We then use the Heisenberg equations of motion to establish the relationships between spin currents and accumulations on non-planar waveguides. These relations predict the existence of out of plane spin accumulation on asymmetrically curved, non-planar waveguides. We finally solve for the eigenstates on such waveguides numerically, and present numerical results to verify our earlier analytic predictions.