Quantum thermal Hall effect of chiral spinons on a kagome strip

We develop a theory for the thermal Hall coefficient in a spin-12 system on a strip of kagome lattice, where a chiral spin-interaction term is present. To this end, we model the kagome strip as a three-leg XXZ spin-ladder, and use bosonization to derive a low-energy theory for the spinons in this system. Introducing further a Dzyaloshinskii-Moriya interaction (D) and a tunable magnetic field (B), we identify three distinct B-dependent quantum phases: a valence-bond crystal (VBC), a "metallic" spin liquid (MSL), and a chiral spin liquid (CSL). In the presence of a temperature difference ΔT between the top and the bottom edges of the strip, we evaluate the net heat current Jh along the strip, and consequently the thermal Hall conductivity κxy. We find that the VBC-MSL-CSL transitions are accompanied by a pronounced qualitative change in the behavior of κxy as a function of B. In particular, analogously to the quantum Hall effect, κxy in the CSL phase exhibits a quantized plateau centered around a commensurate value of the spinon filling factor νs∝B/D.