# Spatial structure of correlations around a quantum impurity at the edge of a two-dimensional topological insulator

## TL;DR

This study provides an exact real-space analysis of magnetic impurities at the edges of topological insulators, revealing how impurity position influences Kondo physics, spin correlations, and edge scattering in a realistic model.

## Contribution

It offers a detailed real-space investigation of impurity effects at topological insulator edges using advanced numerical methods, highlighting the impact of impurity location and spin-orbit coupling.

## Key findings

- Impurity position significantly affects Kondo state development.
- Spin correlations are anisotropic due to Dzyaloshinskii-Moriya interaction.
- Edge scattering patterns depend on impurity placement.

## Abstract

We calculate exact zero-temperature real space properties of a substitutional magnetic impurity coupled to the edge of a zigzag silicene-like nanoribbon. Using a Lanczos transformation [Phys. Rev. B 91, 085101 (2015)] and the density matrix renormalization group method, we obtain a realistic description of stanene and germanene that includes the bulk and the edges as boundary one-dimensional helical metallic states. Our results for substitutional impurities indicate that the development of a Kondo state and the structure of the spin correlations between the impurity and the electron spins in the metallic edge state depend considerably on the location of the impurity. More specifically, our real space resolution allows us to conclude that there is a sharp distinction between the impurity being located at a crest or a trough site at the zigzag edge. We also observe, as expected, that the spin correlations are anisotropic due to an emerging Dzyaloshinskii-Moriya interaction with the conduction electrons, and that the edges scatter from the impurity and "snake" or circle around it. Our estimates for the Kondo temperature indicate that there is a very weak enhancement due to the presence of spin-orbit coupling.