Phononic-magnetic dichotomy of the thermal Hall effect in the Kitaev-Heisenberg candidate material Na$_2$Co$_2$TeO$_6$

TL;DR

This study investigates the thermal Hall effect in Na$_2$Co$_2$TeO$_6$, revealing a complex interplay of phononic and magnetic contributions, and emphasizes the importance of disentangling these to identify potential Majorana fermion signatures.

Contribution

It provides a detailed analysis of the thermal Hall effect in Na$_2$Co$_2$TeO$_6$, demonstrating the coexistence of phononic and magnetic signals and highlighting the challenges in detecting Majorana fermions.

Findings

Thermal Hall signal has both phononic and magnetic origins.

Sign change of $_{xy}$ occurs in the magnetically ordered phase.

Disentangling phonon and magnetic contributions is crucial for identifying Majorana fermions.

Abstract

Majorana fermions as emergent excitations of the Kitaev quantum spin liquid ground state constitute a promising concept in fault tolerant quantum computation. Experimentally, the recently reported topological half-quantized thermal Hall effect in the Kitaev material $\alpha$-RuCl$_3$ seems to confirm the Majorana nature of the material's magnetic excitations. It has been argued, however, that the thermal Hall signal in $\alpha$-RuCl$_3$ rather stems from phonons or topological magnons than from Majorana fermions. Here we investigate the thermal Hall effect of the closely related Kitaev quantum material Na$_2$Co$_2$TeO$_6$, and we show that the thermal Hall signal emerges from at least two components, phonons and magnetic excitations. This dichotomy results from our discovery that the transversal heat conductivity $\kappa_{xy}$ carries clear signatures of the phononic $\kappa_{xx}$, but changes sign upon entering the low-temperature, magnetically ordered phase. We systematically resolve the two components by considering the detailed temperature and field dependence of both $\kappa_{xy}$ and $\kappa_{xx}$. Our results demonstrate that uncovering a genuinely quantized magnetic thermal Hall effect in a Kitaev topological quantum spin liquid requires to disentangle phonon vs. magnetic contributions where the latter include potentially fractionalized excitations such as the expected Majorana fermions.