Anomalous transport effects from the Berry curvature point of view: symmetries and different mechanisms

Jonathan NOKY

The discovery of topological states in condensed matter has opened up a new perspective to understand materials. Due to special band structures and enlarged Berry curvature, there can be a strong enhancement and even quantized responses. By combining these features with a broken time-reversal symmetry, e.g. via magnetism, more exotic linear response effects such as the anomalous Hall effect and the anomalous Nernst effect can be observed. The intrinsic contributions of these effects only depend on the Berry curvature, therefore they can be strongly enhanced by designing the band structure in a suitable way.
There are different mechanisms that can induce a large Berry curvature into the band structure. On the one hand, the property of Weyl points to act as its monopoles can be utilized. This leads to a strong concentration of the Berry curvature at these points, enhancing the overall value. On the other hand, it is possible to start from nodal lines, which are closed loops in momentum space that are usually protected by a mirror symmetry. If this mirror symmetry can be broken, e.g. via the orientation of magnetic moments, the protection of the gapless nodal line is lifted and it can create an inverted band gap, which also hosts strong Berry curvature.
However, it is not only important to have these topological features in the band structure, it is also necessary to find them close to the Fermi level. The exact position strongly influences the strength of the anomalous Hall and Nernst effects, which react differently to this localized Berry curvature. While the anomalous Hall conductivity reaches its maximum at the energetic position of the topological feature, the anomalous Nernst conductivity is more sensible to features in a certain energetic distance. Therefore, the thermoelectric effect can detect topological features that are not visible in the electrical measurements.
All the above described mechanisms and effects can be analyzed in both effective models and real materials. Here, Heusler compounds are employed because they are a very versatile class of compounds and a lot of properties can be tuned by varying compositions.