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Quantized Thermal Transport in the Fractional Quantum Hall Effect

C. L. Kane·Matthew P. A. Fisher
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Abstract

We analyze thermal transport in the fractional quantum Hall effect (FQHE), employing a Luttinger liquid model of edge states. Impurity mediated inter-channel scattering events are incorporated in a hydrodynamic description of heat and charge transport. The thermal Hall conductance, $K_H$, is shown to provide a new and universal characterization of the FQHE state, and reveals non-trivial information about the edge structure. The Lorenz ratio between thermal and electrical Hall conductances {\it violates} the free-electron Wiedemann-Franz law, and for some fractional states is predicted to be {\it 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 $ν=3/5$.

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C. L. Kane, Matthew P. A. Fisher. 1996-03-15. Quantized Thermal Transport in the Fractional Quantum Hall Effect. https://doi.org/10.1103/physrevb.55.15832

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