# Signature of topological phase transition in the RKKY interaction of silicene

## TL;DR

This paper demonstrates that the RKKY interaction in silicene reveals clear signatures of topological phase transitions, enabling detection through magnetic measurements, with detailed analysis of impurity configurations and phase-dependent interaction terms.

## Contribution

It introduces a method to detect phase transitions in silicene via RKKY interaction analysis, highlighting the behavior of interaction terms at critical points.

## Key findings

- In-plane and out-of-plane RKKY terms show extrema or sign changes at phase transitions.
- Magnetic measurements can unambiguously identify different topological phases.
- The analysis covers various impurity configurations along the zigzag direction.

## Abstract

Silicene offers an ideal platform for exploring the phase transition due to strong spin-orbit interaction and its unique structure with strong tunability. With applied electric field and circularly polarized light, siliccene is predicted to exhibit rich phases. We propose that these intricate phase transitions can be detected by measuring the bulk Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction. We have in detail analyzed the dependence of RKKY interaction on phase parameters for different impurity configurations along zigzag direction. Importantly, we present an interesting comparison between different terms of RKKY interaction with phase diagram. It is found that the in-plane and out-of-plane terms can exhibit the local extreme value or change of sign at the phase critical point and remarkable difference in magnitude for different phase regions. Consequently, the magnetic measurement provides unambiguous signatures to identify various types of phase transition simultaneously, which can be carried out with present technique.