Berry phase and thermal transport coefficients in magnon systems

Abstract

We theoretically calculate transverse thermal transport coefficients of the magnon system in the clean limit by the linear response theory in analogy with the electron. We find that there are additional correction terms to what are calculated by the usual Kubo formula. These correction terms arise because external fields change not only the distribution function but also the current operators in thermal transport. We show that the total thermal transport coefficients are expressed by the Berry curvature in momentum space; therefore the thermal Hall effect of magnon is totally due to the property of the magnon band structure.