Phonons behave like electrons in the thermal Hall effect of cuprates

The thermal Hall effect, which arises when heat flows transversely to an applied thermal gradient, has become an important observable in the study of quantum materials. Recent experiments found a large thermal Hall conductivity kappa(xy )in many high-temperature cup rate superconductors, including deep inside the Mott insulator, but the underlying mechanism remains unknown. Here, we uncover a surprising linear temperature dependence for the inverse thermal Hall resistivity, 1/(sic)(H)=-kappa(2)(xx)/kappa(xy), in the Mott insulating cup rates La(2)CuO(4)and Sr2CuO2Cl2.We also find this linear scaling in the pseudo gap state of La1.6-xNd0.4SrxCuO4(Nd-LSCO) in the out-of-plane direction, highlighting the importance of phonons. On the electron-doped side, the linear inverse thermal Hall signal emerges in Nd2-xCexCuO4(NCCO) and Pr2-xCexCuO4(PCCO) at various dopings, including in the strange metal. Although such dependence arises in the simple Drude model for itinerant electrons, its origin is unclear in strongly correlated Mott insulating or pseudo gap states. We perform a Boltzmann analysis for phonons that incorporates skew scattering, and we are able to identify regimes where a linear Tinverse Hallresistivity appears. Finally, we suggest future experiments that would further our fundamental understanding of heat transport in the cup rates and other quantum materials