Topological and disorder corrections to the transverse Wiedemann-Franz law and Mott relation in kagome magnets

The Wiedemann-Franz law and Mott relation are textbook paradigms on the ratios of the thermal and thermoelectric conductivities to electrical conductivity, respectively. Deviations from them usually reveal insights for intriguing phases of matter. The recent topological kagome magnets TbMn$_6$Sn$_6$ and Mn$_3$Ge show confusingly opposite derivations in the Hall measurement. We calculate the topological and disorder corrections to the Wiedemann-Franz law and Mott relation for the Hall responses in topological kagome magnets. The calculation indicates the dominance of the topological correction in the experiments. More importantly, we derive analytic correction formulas, which can universally capture the two opposite experiments with the chemical potential as the only parameter and will be a powerful guidance for future explorations on the magnetic topological matter.