A mechanism for thermal Hall effect in Mott insulating spin liquid

We study the origin of thermal Hall effect from the spinon transport in a U(1) spinon metal. The external magnetic field, that polarizes the spins, effectively generates an internal U(1) gauge flux for the spinons and twists the spinon motion through the antisymmetric interaction. Such a mechanism for Lorentz force generation differs fundamentally from the induction of the internal U(1) gauge flux in the weak Mott insulating regime from the charge fluctuations. We apply this understanding to the specific cases of spinon metals in Kagome lattice and hyperkagome lattice. We carry out a numerical calculation of the thermal Hall conductivity within the linear response theory and discuss the relevance with the thermal transport measurement in Kagome materials volborthite and kapellasite.