Approximately quantized thermal Hall effect of chiral liquids coupled to phonons

Understand

The recent observation of a half-integer quantized thermal Hall effect in $\alpha$-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 $\kappa_xy$ is never exactly quantized in real materials.
• Here, we investigate how phonons affect the quantization of the thermal conductivity focusing on the edge theory.