Quantized thermal transport in the fractional quantum Hall effect

We analyze thermal transport in the fractional quantum Hall effect (FQHE), employing a Luttinger liquid model of edge states. Impurity mediated interchannel scattering events are incorporated in a hydrodynamic description of heat and charge transport. The thermal Hall conductance ${\mathrm{K}}_{\mathrm{H}}$ is shown to provide universal characterization of the FQHE state, and reveals nontrivial information about the edge structure. The Lorenz ratio between thermal and electrical Hall conductances violates the free-electron Wiedemann-Franz law, and for some fractional states is predicted to be negative. We argue that thermal transport may provide a unique way to detect the presence of the elusive upstream propagating modes, predicted for fractions such as ν=2/3 and ν=3/5.