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Motivated by the recent surge of field-driven phenomena discussed for Kitaevmaterials, in particular the experimental observation of a finite thermal Halleffect and theoretical proposals for the emergence of additional spin liquidphases beyond the conventional Kitaev spin liquid, we develop a theoreticalunderstanding of the thermal Hall effect in honeycomb Kitaev materials inmagnetic fields. Our focus is on gapless U(1) spin liquids with a spinon Fermisurface, which have been shown to arise as field-induced phases. We demonstratethat in the presence of symmetry-allowed, second-neighbor Dzyaloshinskii-Moriyainteractions these spin liquids give rise to a finite, non-quantized, thermalHall conductance in a magnetic field. The microscopic origin of this thermalHall effect can be traced back to an interplay of Dzyaloshinskii-Moriyainteraction and Zeeman coupling, which generates an internal U(1) gauge fluxthat twists the motion of the emergent spinons. We argue that such anon-quantized thermal Hall effect is a generic response in Kitaev models for arange of couplings.

Thermal Hall signatures of non-Kitaev spin liquids in honeycomb Kitaev materials