Unquantized thermal Hall effect in quantum spin liquids with spinon fermi surfaces

Quantum spin liquids are of great interest because of their remarkable properties, including hosting fractionalized excitations and topological order. Recent theoretical studies have found quantum spin liquid states with spinon Fermi surfaces upon the application of a magnetic field on a gapped state with topological order. We investigate the thermal Hall conductivity across this transition, describing how the quantized thermal Hall conductivity of the gapped state changes to an unquantized thermal Hall conductivity in the gapless spinon Fermi surface state. We consider two cases, both of potential experimental interest: the state with non-Abelian Ising topological order on the honeycomb lattice, and the state with Abelian chiral spin liquid topological order on the triangular lattice. The thermal Hall conductivity is a powerful probe of the unconventional, charge-neutral excitations in these spin liquids, and our results bear direct relevance to recent experimental observations in the candidate Kitaev material, alpha-RuCl3.