Quantization of the thermal Hall conductivity at small Hall angles*

Recent experiments have described the measurement of a near-quantized thermal Hall conductance in α-RuCl₃ as direct evidence for the propagation of a chiral Majorana mode in this system and consequently as smoking gun evidence for an intermediate chiral spin liquid phase in this system. However, the large experimental longitudinal thermal conductivity, attributed to bulk phonons, begs for an investigation of the spin-lattice coupling, and its role on the quantization of the thermal Hall conductivity. We show that due to the bulk and edge mixing of energy propagation, the temperature gradient of the bulk phonons develops a transverse component which may contribute to a quantized effective thermal Hall conductance. We also discuss the situations where the quantization breaks down and predict notable experiments that test it.

Reference: Mengxing Ye, Gabor Halasz, Lucile Savary, and Leon Balents, Phys. Rev. Lett. 121, 147201(2018).