Nonlinear optical Hall effect of few-layered NbSe2

TL;DR

This study investigates the nonlinear optical Hall effect in few-layer NbSe2, revealing layer-dependent behaviors and potential for opto-spintronics applications through second harmonic generation.

Contribution

It provides a detailed numerical analysis of nonlinear optical Hall conductivities in NbSe2, highlighting the layer-dependent effects and polarization dependencies, and proposes mechanisms for generating Hall currents in even layers.

Findings

Nonlinear optical Hall conductivity is nonzero in odd-layered NbSe2.

Polarization dependence of nonlinear optical responses is characterized.

Electric fields can induce Hall currents in even-layered NbSe2 by breaking inversion symmetry.

Abstract

NbSe$_2$ is one of metallic two-dimensional (2D) transition-metal dichalcogenide (TMDC) materials. Because of broken crystal inversion symmetry, large spin splitting is induced by Ising-type spin-orbit coupling in odd-number-layered NbSe$_2$, but absent for even-number-layered NbSe$_2$ with the inversion symmetry. In this paper, we numerically calculate nonlinear optical charge and spin Hall conductivities of few-layered NbSe$_2$ based on an effective tight-binding model which includes $d_{z^2}$, $d_{x^2-y^2}$ and $d_{xy}$ orbitals of Nb atom. We show that the nonlinear optical Hall conductivity for second harmonic generation (SHG) process has nonvanishing value in odd-number-layered NbSe$_2$. Also, we provide nonlinear optical selection rule in few-layered NbSe$_2$ and their polarization dependences. In further, for even-number-layered case, the nonlinear optical Hall currents can be generated by applying electric fields which break inversion symmetry. We also discuss that the nonlinear optical Hall effect is expected to occur in TMDC materials in general. Thus, our results will serve to design potential opt-spintronics devices based on 2D materials to generate the spin Hall current by SHG.