Phase diagram and thermal Hall conductivity of spin-liquid Kekul\'{e}-Kitaev model

TL;DR

This paper explores the phase diagram and thermal Hall conductivity of the Kekulé-Kitaev model on a honeycomb lattice, revealing topological and trivial spin-liquid phases and quantized thermal Hall effects relevant to experimental materials.

Contribution

It provides the first detailed phase diagram of the Kekulé-Kitaev model and calculates its thermal Hall conductivity, connecting theoretical predictions with experimental observations.

Findings

Identification of chiral topological and trivial spin-liquid phases.

Discovery of quantized thermal Hall conductivity over a wide temperature range.

Analysis of the impact of magnetic fields on the phase diagram.

Abstract

In this work we study the phase diagram of Kekul\'{e}-Kitaev model. The model is defined on a honeycomb lattice with bond dependent anisotropic exchange interactions making it exactly solvable in terms of Majorana representation of spins in close analogy to the Kitaev model. However, the energy spectrum of Majorana fermions has a multi-band structure characterized by Chern numbers 0, $\pm$1, and $\pm2$. We obtained the phase diagram of the model in the plane of exchange couplings and in the presence of a magnetic field and found chiral topological and trivial spin-liquid ground states. In the absence of magnetic field most part of the phase diagram is a trivial gapped phase continuously connected to an Abelian phase, while in the presence of the magnetic field a topological phase arises. Furthermore, motivated by recent thermal measurements on the spin-liquid candidate $\alpha$-RuCl$_{3}$, we calculated the thermal Hall conductivity at different regimes of parameters and temperatures and found the latter is quantized over a wide range of temperatures.