Global phase diagram, possible chiral spin liquid and topological superconductivity in the triangular Kitaev-Heisenberg model

TL;DR

This paper explores the phase diagram of the triangular Kitaev-Heisenberg model, revealing exotic spin liquids, magnetic orders, and topological superconductivity, with implications for experimental materials.

Contribution

It identifies a $Z_2$ chiral spin liquid and various topological superconducting phases in the model, advancing understanding of quantum spin liquids and topological states.

Findings

Discovery of a $Z_2$ chiral spin liquid with Chern number $oxed{ ext{±}2}$

Identification of topological $p$-wave superconductivity under doping

Mapping of magnetic and superconducting phases in the model

Abstract

The possible ground states of the undoped and doped Kitaev-Heisenberg model on a triangular lattice are studied. For the undoped system, a combination of the numerical exact diagonalization calculation and the four-sublattice transformation analysis suggests one possible exotic phase and four magnetically ordered phases including a collinear stripe pattern and a noncollinear spiral pattern in the global phase diagram. The exotic phase near the antiferromagnetic (AF) Kitaev point is further investigated by using the Schwinger-fermion mean-field method, and we obtain an energetically favorable $Z_2$ chiral spin liquid with a Chern number $\pm2$ as a promising candidate. At finite doping, we find that the AF Heisenberg coupling supports an $s$-wave or a $d_{x^2-y^2}+id_{xy}$-wave superconductivity (SC), while the AF and the ferromagnetic Kitaev interactions favor a $d_{x^2-y^2}+id_{xy}$-wave SC and a time-reversal invariant topological $p$-wave SC, respectively. Possible experimental realizations and related candidate materials are also discussed.