Nonlinear Hall effect in Rashba systems with hexagonal warping

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.

Hexagonal warping effects on Bloch oscillations in proximitized Rashba systems

“…Hence, the low energy physics of the surface states remains unaffected by the bulk, which is a reasonable approximation. The two-band Hamiltonian of the Rashba system in proximity to a substrate within the tight-binding model obtained from the low energy Hamiltonian can be described as [36][37][38][39]…”

“…2m * is the quadratic term that generates particle-hole asymmetry, the second term represents the Rashba-type spinorbit coupling, the third term shows the hexagonal warping effect which remains invariant under threefold rotation and therefore is solely responsible for the hexagonal distortion fulfilling the symmetry properties elaborated in [36,40] with k ± = k x ± ik y , whereas the final term in equation ( 5) characterizes the proximity-induced band gap in the energy spectrum of the proximitized Rashba system with hexagonal warping.…”

Chirality-Tunable Nonlinear Hall Effect

“…In typical experimental arrangements, as illustrated in refs., , the relaxation time, τ, usually falls within the picosecond range, while the alternating current frequency is adjustable across the spectrum of 10 to 1000 Hz. Hence, we can neglect the frequency dependence in the denominator, as the product of ω and τ is significantly smaller than 1, ωτ ≪ 1. , With this approximation, we can utilize the tensor representation of the BCD provided in eqs and to obtain the following current density components .25ex2ex j x = 3 e 3 τ 2 ℏ 2 ( 2 D x x ) scriptE z scriptE y j y = prefix− 3 e 3 τ 2 ℏ 2 ( 2 D x x ) scriptE z scriptE x j z = 0 …”