Slab Thickness Dependence of Rashba Splitting on Au(111) Surface: First-Principles and Model Analyses

TL;DR

This paper investigates how the Rashba spin splitting on Au(111) surfaces varies with slab thickness, revealing a crossover from off-center to at-center minima as layers decrease, explained through first-principles and simplified models.

Contribution

It provides a detailed analysis of the thickness-dependent Rashba splitting using first-principles calculations and introduces two models to explain the underlying mechanisms.

Findings

Rashba splitting minimum shifts towards the center as layers decrease.

For N ≤ 14, the minimum is located at the Γ point.

Surface band dispersion results from interference and spin-orbit interaction.

Abstract

We study the dependence of the spin splitting on the number $N$ of atomic layers, using first-principles calculation for Au(111) surface. When the slab of the atomic layers is sufficiently thick, the lower split state has a minimum away from $\bar{\Gamma}$, which is known as the Rashba effect. As the number of layers decreases, the minimum approaches $\bar{\Gamma}$, and it is located at $\bar{\Gamma}$ for $N \leq 14$. This crossover is analyzed in detail using two models: a tight-binding model and a bilayer nearly-free-electron model. It is demonstrated that the features of surface band dispersion are clearly understood as the result of the competition between the interference of the surface states on both sides and the spin-orbit interaction.