Longitudinal and spin-Hall conductance of a two-dimensional Rashba system with arbitrary disorder

TL;DR

This paper investigates the effects of disorder, Fermi energy, and spin-orbit coupling ratios on longitudinal and spin-Hall conductances in a two-dimensional Rashba system using numerical methods.

Contribution

It provides a comprehensive numerical analysis of how disorder and system parameters influence conductance in Rashba systems, confirming the persistence of the spin-Hall effect below a critical disorder threshold.

Findings

Spin-Hall effect persists below a critical disorder level.

Conductances depend on Fermi energy and spin-orbit coupling ratios.

System size influences conductance behavior.

Abstract

We calculate the longitudinal and spin-Hall conductances in four-lead bridges with Rashba - Dresselhaus spin-orbit interactions. Numerical results are obtained both within Landauer-Buttiker formalism and by the direct evaluation of the Kubo formula. The microscopic Hamiltonian is obtained in the tight-binding approximation in terms of the neareast-neighbor hopping integral $t$, the Rashba spin-orbit coupling $V_R$, the Dresselhaus spin-orbit coupling $V_D$ and an Anderson-like, on-site disorder energy strength $W$. We reconfirm that below a critical disorder threshold, the spin-Hall effect is present. Further, we study the effect on the two conductivities of the Fermi energy, Rashba/Dresselhaus coefficient ratio, and system size.