Enhancement of the transverse thermoelectric conductivity originating from stationary points in nodal lines

Abstract

Motivated by the recent discovery of a large anomalous Nernst effect in ${\mathrm{Co}}_{2}\mathrm{Mn}\mathrm{Ga}$, ${\mathrm{Fe}}_{3}X$ ($X$=Al, Ga) and ${\mathrm{Co}}_{3}{\mathrm{Sn}}_{2}{\mathrm{S}}_{2}$, we performed a first-principles study to clarify the origin of the enhancement of the transverse thermoelectric conductivity ${\ensuremath{\alpha}}_{ij}$ in these ferromagnets. The intrinsic contribution to ${\ensuremath{\alpha}}_{ij}$ can be understood in terms of the Berry curvature $\mathrm{\ensuremath{\Omega}}$ around the Fermi level, and $\mathrm{\ensuremath{\Omega}}$ is singularly large along nodal lines (which are gapless in the absence of the spin-orbit coupling) in the Brillouin zone. We find that not only the Weyl points but also stationary points in the energy dispersion of the nodal lines play a crucial role. The stationary points make sharp peaks in the density of states projected onto the nodal line, clearly identifying the characteristic Fermi energies at which ${\ensuremath{\alpha}}_{ij}$ is most dramatically enhanced. We also find that ${\ensuremath{\alpha}}_{ij}/T$ breaks the Mott relation and show a peculiar temperature dependence at these energies. The present results suggest that the stationary points will give us a useful guiding principle to design magnets showing a large anomalous Nernst effect.