Thermal Hall transport in Kitaev spin liquids

TL;DR

This study explores the thermal Hall effect in Kitaev spin liquids under magnetic fields, revealing quantum effects, the influence of additional interactions, and the topological nature of Majorana fermions, with implications for real materials like $$-RuCl$_{3}$.

Contribution

It provides a comprehensive theoretical analysis of thermal Hall transport in Kitaev models, incorporating quantum fluctuations and additional interactions, bridging theory and experiments.

Findings

Thermal Hall conductivity overshoots half-integer quantization and shows a hump at lower temperatures.

Field-direction dependence of $
$ is consistent with Majorana fermion Chern number sign.

Additional interactions $$ and $$ significantly modify the thermal Hall response.

Abstract

We investigate the thermal Hall conductivity in the Kitaev model with additional interactions under a magnetic field, employing a finite-temperature tensor network method benchmarked by a thermal pure quantum state technique. We find that the thermal Hall conductivity divided by temperature, $\kappa_{xy}/T$, significantly overshoots the value of the half-integer quantization and exhibits a pronounced hump while decreasing temperature. Moreover, we show that the field-direction dependence of $\kappa_{xy}/T$ is consistent with the sign of the Chern number associated with the Majorana fermions across a wide range of magnetic fields. We also demonstrate that the additional off-diagonal interactions, known as the $\Gamma$ and $\Gamma^{\prime}$ terms, considerably affect $\kappa_{xy}/T$. In particular, we show that positive $\Gamma$ and negative $\Gamma^{\prime}$ lead to a remarkable enhancement in the intermediate temperature region. From the comparison with the classical counterpart, we reveal that the effects of the $\Gamma$ term go beyond the classical picture, indicating significant quantum fluctuation effects, while those of the $\Gamma^\prime$ term are well captured at the classical level. These comprehensive analyses indicate that the enhanced thermal Hall response is consistently explained by dominant contributions from topological Majorana fermions, even within the polarized regime beyond the critical field. Our approach not only establishes a robust theoretical framework for understanding the thermal Hall transport in Kitaev materials such as $\alpha$-RuCl$_{3}$, but also offers a promising pathway to bridge the gap between theories and experiments across a wide range of strongly correlated materials.