Berry connection polarizability tensor and third-order Hall effect

TL;DR

This paper introduces the Berry connection polarizability tensor as a key factor in the third-order Hall effect, developing a theoretical framework and applying it to 2D models and real materials like monolayer FeSe.

Contribution

It establishes a new theoretical approach linking Berry connection polarizability to third-order Hall effects, expanding understanding of band geometric quantities in transport phenomena.

Findings

Derived explicit formulas for third-order conductivity.

Applied theory to 2D Dirac model and monolayer FeSe.

Revealed third-order Hall effect as a tool for material characterization.

Abstract

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.