Intrinsic anomalous Nernst effect amplified by disorder in a half-metallic semimetal

Intrinsic anomalous Nernst effect (ANE), like its Hall counterpart, is generated by Berry curvature of electrons in solids. Little is known about its response to disorder. In contrast, the link between the amplitude of the ordinary Nernst coefficient and the mean-free-path is extensively documented. Here, by studying Co$_3$Sn$_2$S$_2$, a topological half-metallic semimetal hosting sizable and recognizable ordinary and anomalous Nernst responses, we demonstrate an anti-correlation between the amplitude of ANE and carrier mobility. We argue that the observation, paradoxically, establishes the intrinsic origin of the ANE in this system. We conclude that various intrinsic off-diagonal coefficients are set by the way the Berry curvature is averaged on a grid involving the mean-free-path, the Fermi wavelength and the de Broglie thermal length.