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Thermal quantum Hall effect in the spin liquid RuCl_3: the role of phonons

The recent observation [1] of a half-integer quantized thermal Hall effect in α -RuCl 3   is interpreted as a unique signature of a chiral spin liquid with a Majorana edge mode. A similar quantized thermal Hall effect is expected in chiral topological superconductors. The unavoidable presence of gapless acoustic phonons, however, implies that, in contrast to the quantized electrical conductivity, the thermal Hall conductivity  is never exactly quantized in bulk materials.. The coupling to phonons destroys the ballistic thermal transport of the edge mode completely, as energy can leak into the bulk, thus drastically modifying the edge-picture of the thermal Hall effect. Nevertheless, the thermal Hall conductivity remains approximately quantized and we argue [2], that the coupling to phonons to the edge mode is a necessary condition for the observation of the quantized thermal Hall effect. The coupling of phonons to the spin liquid imprints a Berry phase onto the phonon system, which gives, however only a small correction
to the quantized Hall effect.

[1] Y. Kasahara, T. Ohnishi, N. Kurita, Tanaka H., J. Nasu, Y. Motome, T. Shibauchi, and Y. Matsuda, Nature 559, 227 (2018).
[2]  Yuval Vinkler-Aviv, Achim Rosch,  Phys. Rev. X 8, 031032 (2018).