# Global phase diagram of a spin-orbit-coupled Kondo lattice model on the honeycomb lattice

## TL;DR

This paper explores the complex phase diagram of a spin-orbit-coupled Kondo lattice model on a honeycomb lattice, revealing various magnetic and topological phases driven by competing interactions.

## Contribution

It provides the first comprehensive phase diagram of this model, highlighting the emergence of topological insulators and magnetic phases influenced by spin-orbit coupling and Kondo interactions.

## Key findings

- Identification of a topological insulator with valence bond solid correlations.
- Discovery of antiferromagnetic phases with different magnetic moment orientations.
- Topologically nontrivial antiferromagnetic state at moderate to strong spin-orbit coupling.

## Abstract

Motivated by the growing interest in the novel quantum phases in materials with strong electron correlations and spin-orbit coupling, we study the interplay between the spin-orbit coupling, Kondo interaction, and magnetic frustration of a Kondo lattice model on a two-dimensional honeycomb lattice. We calculate the renormalized electronic structure and correlation functions at the saddle point based on a fermionic representation of the spin operators. We find a global phase diagram of the model at half-filling, which contains a variety of phases due to the competing interactions. In addition to a Kondo insulator, there is a topological insulator with valence bond solid correlations in the spin sector, and two antiferromagnetic phases. Due to a competition between the spin-orbit coupling and Kondo interaction, the direction of the magnetic moments in the antiferromagnetic phases can be either within or perpendicular to the lattice plane. The latter antiferromagnetic state is topologically nontrivial for moderate and strong spin-orbit couplings.