Unitarity of scattering and edge spin accumulation

TL;DR

This paper investigates how unitarity in scattering processes influences edge spin accumulation in 2D structures with spin-orbit coupling, revealing boundary shape and Hamiltonian form affect spin density oscillations.

Contribution

It demonstrates the critical role of scattering unitarity in determining edge spin density patterns, including cancellation of oscillations for straight boundaries and effects of boundary shape.

Findings

Unitarity causes cancellation of long-wavelength spin oscillations for straight boundaries.

Boundary shape influences the emergence of spin precession oscillations.

The form of the spin-orbit Hamiltonian significantly affects edge spin accumulation.

Abstract

We consider a 2D ballistic and quasi-ballistic structures with spin-orbit-related splitting of the electron spectrum. The ballistic region is attached to the leads with a voltage applied between them. We calculate the edge spin density which arises in the presence of a charge current through the structure. We solve the problem with the use of the method of scattering states and clarify the important role of the unitarity of scattering. In the case of a straight boundary it leads to exact cancellation of long-wavelength oscillations of the spin density. In general, however, the smooth spin oscillations with the spin precession length may arise, as it happens, e.g., for the wiggly boundary. Moreover, we show that the result crucially depends on the form of the spin-orbit Hamiltonian.