Anomalous transport effects in the Berry curvature vector field perspective



The concept of Berry phase and Berry curvature has become ubiquitous in solid state physics as it relates to variety of phenomena, such as topological insulators, polarization, and various Hall effects. It is well known that large Berry curvatures arise from close proximity of hybridizing bands. However, the vectorial nature of the Berry curvature vector field is not utilized in current research despite its rich structure with its own topological features. We present Berry curvature monopoles and higher dimensional flows in real materials and relate them to anomalous transport effects. They can also provide a novel unique view on the electronic structure in all three dimensions which covers for several weaknesses of conventional visualisations.