In most electrical conductors, we expect charge and heat to be transported in the same direction. However, in certain two-dimensional electron systems, fractional quantum Hall states can cause charge and heat to flow in opposite directions.
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Heun, S. Charge down and heat up. Nature Phys 8, 640–641 (2012). https://doi.org/10.1038/nphys2407
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DOI: https://doi.org/10.1038/nphys2407
