# Relativistic response and novel spin-charge plasmon at the Tl/Si(111) surface

## TL;DR

This paper provides an  ab initio analysis of spin-charge interactions at the Tl/Si(111) surface, revealing a novel collective mode with enhanced spin character due to strong spin-orbit coupling.

## Contribution

It introduces a comprehensive relativistic response framework for spin-charge correlations, uncovering a new collective excitation at the Tl/Si(111) surface.

## Key findings

- Discovery of a novel spin-charge collective mode.
- Enhanced spin character near zero momentum.
- Relativistic tensor response function analysis.

## Abstract

We present a comprehensive \textit{ab initio} analysis of the spin-charge correlations at the Tl/Si(111) surface, where the spin-orbit interaction is so strong that a detailed treatment of the non-collinear electron spin appears decisive for the correct description of the response properties. The relativistic limit enforces a unified treatment of the spin and charge densities as a four-vector, and the response function acquires then a 4$\times$4 tensor structure. Our all-electron implementation allows to resolve the real space structure of the possible collective modes, and demonstrates the emergence of a novel collective excitation combining transverse-spin and ordinary charge oscillations of a similar order of magnitude, whose spin character is strongly enhanced as we approach the $q$$\rightarrow$0 momentum limit.