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For several years, the compound α-RuCl₃ is considered as one prime candidate material to host a Kitaev topological quantum spin liquid (TQSL). Such a TQSL has been predicted for the spin-1/2 Kitaev model on a honeycomb lattice in an external magnetic field [1]. The zero field ground state is a quantum spin liquid with itinerant Majorana fermions and immobile gauge fluxes as elementary excitations. An external magnetic field gaps out the Majorana bulk states and topological Majorana edge states emerge. Indeed, for α-RuCl₃ there is evidence for a significant Kitaev interaction acting between neighboring j_eff=1/2 moments. However, the ground state of α-RuCl₃ shows long-range antiferromagnetic order, indicative of additional Heisenberg-type and anistropy terms in the spin Hamiltonian. An in-plane field of about 8 T suppresses the magnetic order, which opens the question whether the field-induced ground state bears the main signatures of the Kitaev TQSL. In this talk, I will discuss our experimental efforts to probe the elementary magnetic excitations of α-RuCl₃ by thermal transport. After summarizing the main findings for the longitudinal heat conductivity κ_xx [2], and briefly discussing new data which extend our findings to very large magnetic fields and lower temperature, I will focus on the surprising and sizeable thermal Hall effect κ_xy with a field perpendicular to the RuCl_3-planes [3] as well as on our attemps to study this quantity for different field orientations.

[1] A. Kitaev, Annals of Physics 321, 2 (2006)
[2] R. Hentrich et al., Phys. Rev. Lett. 120, 117204 (2018)
[3] R. Hentrich et al., Phys. Rev. B 99, 085136 (2019)