Microscopic Theory of the Phonon Thermal Hall Effect in Chiral Mott Insulators

The thermal Hall effect (THE) probes charge-neutral excitations in insulators, where the charge gap blocks electronic transport. Recently, phonons have been shown to induce a THE comparable in magnitude to the spin contribution, underscoring their critical role in thermal transport. Here, we develop a microscopic theory of the phonon thermal Hall effect (PTHE) in chiral Mott insulators. First, we derive the exact analytic form of the effective Raman interaction in half-filled Mott insulators, showing that its strength is directly proportional to the scalar spin chirality. Next, we demonstrate the intrinsic PTHE explicitly on the kagome lattice. Crucially, our formulation reveals a temperature-dependent crossover in the transport behavior under isotopic substitution. Using this result, we establish a scaling law that quantitatively separates the phonon contribution to the THE from other background signals. Our results not only provide the first fully microscopic derivation of the PTHE, but also establish a definitive experimental standard for isolating microscopic heat carriers in chiral Mott insulators.