# Spin-polarized electronic surface states of Re(0001): an ab-initio investigation

## TL;DR

This paper investigates the electronic surface states of Re(0001) using ab-initio relativistic DFT, focusing on spin-orbit effects, surface state dispersions, and spin polarization, with comparisons to other heavy metal surfaces.

## Contribution

It provides a detailed ab-initio analysis of Re(0001) surface states, including spin-orbit effects and spin polarization, which were not previously characterized.

## Key findings

- Identified main surface states and resonances with detailed dispersion relations.
- Found spin-polarized resonances crossing the Fermi level with Rashba-like polarization.
- Observed the absence of the expected level crossing at ar{mma} with the studied slab thickness.

## Abstract

We study the electronic structure of the Re(0001) surface by means of ab-initio techniques based on the Fully Relativistic (FR) Density Functional Theory (DFT) and the Projector Augmented-Wave (PAW) method. We identify the main surface states and resonances and study in detail their energy dispersion along the main symmetry lines of the SBZ. Moreover, we discuss the effect of spin-orbit coupling on the energy splittings and the spin-polarization of the main surface states and resonances. Whenever possible, we compare the results with previously studied heavy metals surfaces. We find empty resonances, located below a gap similar to the L-gap of the (111) fcc surfaces, that have a downward dispersion and cross the Fermi level, similarly to the recently studied Os(0001) surface. Their spin polarization at the Fermi level is similar to that predicted by the Rashba model, but the usual level crossing at $\bar{\Gamma}$ is not found with our slab thickness. Moreover, for selected states, we follow the spin polarization along the high symmetry lines, discussing its behavior with respect to ${\bf k}_{\parallel}$, the wave-vector parallel to the surface.