Finite-temperature violation of the anomalous transverse Wiedemann-Franz law in absence of inelastic scattering.

The Wiedemann-Franz law links the ratio of electronic charge and heat conductivity to fundamental constants. It has been tested in numerous solids, but the extent of its relevance to the anomalous transverse transport, which represents the topological nature of the wave function, remains an open question. Here we present a study of anomalous transverse response in the noncollinear antiferromagnet Mn$_{3}$Ge extended from room temperature down to sub-Kelvin temperatures and find that the anomalous Lorenz ratio remains close to the Sommerfeld value up to 100 K, but not above. The finite-temperature violation of the Wiedemann-Franz correlation is caused by a mismatch between the thermal and electrical summations of the Berry curvature, rather than the inelastic scattering as observed in ordinary metals. It reveals a 10 meV energy scale in the Berry spectrum of Mn$_3$Ge, in agreement with the theoretical calculations. Furthermore, we verify the Bridgman relation by directly measuring the anomalous Ettingshausen and Nernst effects. Our results demonstrate a new route to violating the Wiedemann-Franz law in the topological transport.