Berry connection polarizability tensor and third-order Hall effect

One big achievement in modern condensed matter physics is the recognition of the importance of various band geometric quantities in physical effects. As prominent examples, Berry curvature and the Berry curvature dipole are connected to the linear and the second-order Hall effects, respectively. Here, we show that the Berry connection polarizability (BCP) tensor, as another intrinsic band geometric quantity, plays a key role in the third-order Hall effect. Based on the extended semiclassical formalism, we develop a theory for the third-order charge transport and derive explicit formulas for the third-order conductivity. Our theory is applied to the two-dimensional (2D) Dirac model to investigate the essential features of the BCP and the third-order Hall response. We further demonstrate the combination of our theory with the first-principles calculations to study a concrete material system, the monolayer FeSe. Our work establishes a foundation for the study of third-order transport effects, and reveals the third-order Hall effect as a tool for characterizing a large class of materials and for probing the BCP in band structure.

Automated summary

The text discusses the importance of band geometric quantities in physical effects in modern condensed matter physics, using examples of Berry curvature and Berry curvature dipole connected to Hall effects. Furthermore, it introduces the role of the Berry connection polarizability (BCP) tensor in the third-order Hall effect and presents a theory for the third-order charge transport. The study applies this theory to the Dirac model in two dimensions and demonstrates its application in studying materials like monolayer FeSe.