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Thermal transport has been used to probe the nature of$\alpha\mbox{-}\mathrm{RuCl}_3$, an important candidate of Kitaev material. Tworemarkable observations were made under applied magnetic fields at lowtemperatures, and have stimulated extensive discussions. One is a sizablethermal Hall effect, and the other is an apparent "oscillation" of thelongitudinal thermal conductivity with the magnetic field. It has been proposedthat the former is due to a bosonic Chern band. Meanwhile, the origin of thelatter has largely remained obscure. This work aims to resolve this"oscillation" puzzle. By examining the thermal transport data as well as othermeasured properties of $\alpha\mbox{-}\mathrm{RuCl}_3$, we argue that the mostplausible scenario is that of phonons scattering with spin degrees of freedomacross multiple phases. We substantiate this picture into a phenomenologicaltheory, which reproduces the "oscillation" behavior in a simple manner andmakes predictions that can be examined by future experiments. Moreover, ourphenomenological theory and the aforementioned proposal for the thermal Halleffect support each other. We hope this work can thus help settle the physicalmechanism behind the thermal transport puzzles in$\alpha\mbox{-}\mathrm{RuCl}_3$.

On the Thermal Transport Puzzles in $\alpha\mbox{-}\mathrm{RuCl}_3$