Characterization of topological band structures away from the Fermi level by the anomalous Nernst effect

Resolving the structure of energy bands in transport experiments is a major\nchallenge in condensed matter physics and material science. Sometimes, however,\ntraditional electrical conductance or resistance measurements only provide very\nsmall signals, and thus limit the ability to obtain direct band structure\ninformation. In this case, it has been proven beneficial to employ\nthermoelectric measurements which are sensitive to the first derivative of the\ndensity of states with respect to energy, rather than to its value itself. Due\nto the large interest in topological effects these days, it is important to\nidentify a similar concept for detecting the Berry curvature in a band\nstructure. Nowadays, the common way to access the Berry curvature directly via\nmeasurements is the anomalous Hall effect, but the corresponding signal can be\ntoo small to be detected when the topological features of the band structure\nlie too far off the Fermi level. In this work we propose to investigate\ntopological band structure features utilizing the anomalous Nernst effect which\nis tied to the derivative of the anomalous Hall effect with respect to energy.\nThereby, also signatures become resolvable, which are elusive in anomalous Hall\nmeasurements. We demonstrate the underlying mechanisms for a minimal effective\nfour-band model and exemplary for the real Heusler compounds Co$_2$Fe$X$\n($X$=Ge,Sn), which host topological nodal lines about 100 meV above the Fermi\nlevel. This work demonstrates that anomalous Nernst measurements can be an\neffective tool for the characterization of topological band structures, both at\nroom temperature and in the quantum transport regime at cryogenic temperatures.\n