Thermal Hall effect of optical phonons enhanced by discrete rotational symmetry

Motivated by the recent observations of giant thermal Hall signals in many materials, theoretical studies have explored various possible mechanisms for understanding the effect. However, the intrinsic contribution from optical phonons is widely believed to be negligible and largely ignored. In this study, we investigate the thermal Hall conductivity of optical phonons in systems with four-fold discrete rotational symmetry. We find that the discrete symmetry induces singularities in phonon bands and significantly enhance the thermal Hall conductivity, which has magnitudes comparable to that of the intrinsic contribution of acoustic phonons. Particularly, the thermal Hall conductivity is found to include a contribution proportional to $B\ln B$, thus logarithmatically enhanced in low measurement magnetic fields. Moreover, thermal Hall conductivity of optical phonons with finite bandwidths exhibits a non-monotonic temperature dependence which qualitatively aligns with experimental observations, although it is still too small by four orders of magnitude.