  We study the origin of Lorentz force on the spinons in a U(1) spin liquid. We
are inspired by the previous observation of gauge field correlation in the
pairwise spin correlation using the neutron scattering measurement when the
Dzyaloshinskii-Moriya interaction intertwines with the lattice geometry. We
extend this observation to the Lorentz force that exerts on the (neutral)
spinons. 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 Dzyaloshinskii-Moriya interaction. Such a mechanism for the
emergent Lorentz force 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 case of spinon metals
on the kagome lattice. Our suggestion of emergent Lorentz force generation and
the resulting topological thermal Hall effect may apply broadly to other
non-centrosymmetric spin liquids with Dzyaloshinskii-Moriya interaction. We
discuss the relevance with the thermal Hall transport in kagome materials
volborthite and kapellasite.
