# Impact of off-diagonal exchange interactions on the Kitaev spin liquid state of $\alpha$-RuCl$_3$

## TL;DR

This paper studies how off-diagonal exchange interactions influence the gapped chiral spin liquid state in $ ext{α-RuCl}_3$, explaining experimental thermal Hall effects and suggesting possible coexistence with Fermi surfaces of Majorana fermions.

## Contribution

It reveals the significant role of off-diagonal exchange interactions in enhancing the Majorana fermion gap and inducing Fermi surfaces, advancing understanding of the Kitaev spin liquid in real materials.

## Key findings

- Off-diagonal interactions increase the Majorana fermion mass gap.
- These interactions can explain the robust thermal Hall quantization.
- They can induce Fermi surfaces when coexistence with zigzag order occurs.

## Abstract

Motivated by the recent experimental observation of the half-quantized thermal Hall conductivity for the candidate material of the Kitaev spin liquid, $\alpha$-RuCl$_3$[ Y. Kasahara et al., Nature 559, 227 (2018)], we investigate effects of non-Kitaev exchange interactions, which exist in the real material, on the gapped chiral spin liquid state realized in the case with an applied magnetic field. It is found that off-diagonal exchange interactions enhance significantly the mass gap of Majorana fermions. This result provides a possible explanation for robust quantization of the thermal Hall conductivity observed in the above-mentioned experiment. Furthermore, we demonstrate that if the Kitaev spin liquid state and the zigzag antiferromagnetic order coexist around the border of these two phases, off-diagonal exchange interactions can induce Fermi surfaces of Majorana fermions, leading to a state similar to the U(1) spin liquid.