Nonlinear Hall effect in Rashba systems with hexagonal warping

TL;DR

This paper investigates the second- and third-order nonlinear Hall effects in Rashba systems with hexagonal warping, providing analytical models and predictions for experimental realization of Berry curvature multipole phenomena.

Contribution

It introduces a comprehensive analysis of nonlinear Hall responses in Rashba systems with hexagonal warping, including analytical expressions and the prediction of a third-order Hall effect.

Findings

Discovery of a unique dipole profile in Rashba systems with hexagonal warping.

Prediction of a third-order Hall effect in these systems.

Analytical calculation of Berry connection polarizability tensor.

Abstract

Rashba spin-orbit coupled systems are an important class of materials noted for diverse fundamental and applied phenomena. Recently, the emergence of non-linear Hall effect under conditions of time-reversal symmetry has been discovered in materials with broken inversion symmetry. In this work, we study the second- and third-order Hall response in Rashba systems with hexagonal warping. Starting with a low-energy model, we obtain the analytic expressions and discover the unique dipole profile in Rashba systems with hexagonal warping. Furthermore, we extend the analysis using a realistic tight-binding model. Next, we predict the existence of a third-order Hall effect in these systems, and calculate the Berry connection polarizability tensor analytically. We also show how the model parameters affect the third-order conductivity. Our predictions can help in the experimental realization of Berry curvature multipole physics in Rashba materials with hexagonal warping, and provide a new platform for engineering the non-linear Hall effects.