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We present a systematic study of the nonlinear thermal Hall responses inbosonic systems using the quantum kinetic theory framework. We demonstrate theexistence of an intrinsic nonlinear boson thermal current, arising from thequantum metric which is a wavefunction dependent band geometric quantity. Incontrast to the nonlinear Drude and nonlinear anomalous Hall contributions, theintrinsic nonlinear thermal conductivity is independent of the scatteringtimescale. We demonstrate the dominance of this intrinsic thermal Hall responsein topological magnons in a two-dimensional ferromagnetic honeycomb latticewithout Dzyaloshinskii-Moriya interaction. Our findings highlight thesignificance of band geometry induced nonlinear thermal transport and motivateexperimental probe of the intrinsic nonlinear thermal Hall response withimplications for quantum magnonics.

Intrinsic nonlinear thermal Hall transport of magnons: A Quantum kinetic theory approach