Optical-vortex-pulse induced nonequilibrium spin textures in spin-orbit coupled electrons

TL;DR

This work addresses how optical vortex beams carrying orbital angular momentum $m\hbar$ per photon can induce nonequilibrium spin textures in a spin-orbit-coupled two-dimensional electron gas. By applying linear response theory to a 2DEG with Rashba and Dresselhaus SOIs and modeling Laguerre-Gaussian vortex pulses in the THz range, the authors demonstrate that the OAM of light is encoded into in-plane spin textures, with the imprint depending on the SOI regime. In the Rashba-dominated case, spins polarize in a pattern that tracks the doughnut-shaped intensity and winds with the beam OAM $m$, while at the ${\rm SU}(2)$ symmetric point ($\alpha_R=\beta_D$) spins align along a fixed in-plane direction and the total spin remains zero despite local textures; the maximal local polarization grows with increasing $|m|$. These findings highlight a route to ultrafast spin manipulation using structured light and suggest that higher-frequency vortex beams could probe similar physics in metals with larger Fermi energies, with potential detection via magneto-optical Kerr effects.

Abstract

Optical vortex beams are a type of topological light characterized by their inherent orbital angular momentum, leading to the propagation of a spiral-shaped wavefront. In this study, we focus on two-dimensional electrons with Rashba and Dresselhaus spin-orbit interactions and examine how they respond to pulsed vortex beams in the terahertz frequency band. Spin-orbital interactions play a vital role in transferring the orbital angular momentum of light to electron systems and generating spatiotemporal spin textures. We show that the spatiotemporal spin polarization of electrons reflects orbital angular momentum carried by optical vortex pulses. These findings demonstrate how optical vortices facilitate ultrafast spin manipulation in spin-orbit-coupled electrons. Our results can be straightforwardly extended to the case of higher-frequency vortex beams for other two-dimensional metals with a larger Fermi energy.

Figures (7)

• Figure 1: (a) Schematic image of our setup. A pulsed vortex beam is irradiated to a 2DEG formed in the quantum well of the GaAs/AlGaAs heterostructure. (b) The spatial profile of the electric field generated by the vortex beam along the propagation ($z$) axis, $|{\bm E}(x,y=0,z)|$ (the upper panel) and $|{\bm E}(\rho_{\rm max},z)|$ (the lower pannel), where $(\rho,z)$ is the cylindrical coordinate and $\rho_{\rm max}$ is defined so that $E_0\equiv \max|{\bm E}(\rho,z=0)|$ at $\rho=\rho_{\rm max}$. The electric field sharply peaks within the Rayleigh range, $z_{\rm R}=O(100~\mu{\rm m})$. The inset is the electric field at the focal plane ($z=0$), where $x/w_0,~y/w_0\in [-3,3]$. Here we consider the vortex beam carrying the orbital angular momentum, $m=2$. For the further details, see Sec. \ref{['sec:vortex']}. (c,d) Fermi surfaces (thick curves) and spin polarization (arrows) of spin-orbit-coupled electrons on the Fermi surfaces: (c) $\beta_{\rm D}/\alpha_{\rm R}=0$ and (d) $\beta_{\rm D}/\alpha_{\rm R}=1$.
• Figure 2: Linear response of the spin density, ${\bm S}({\bm x},t)/S_0$, induced by monochromatic vortex beams with $(\lambda,m)=(1,0)$ (a1), $(1,1)$ (a2), $(1,2)$ (a3), $(-1,0)$ (c1), $(-1,1)$ (c2), and $(-1,2)$ (c3), where $\lambda$ and $m$ are the SAM and OAM of light, respectively. The scaled quantity, $S({\bm x},t)/S_0$, with $S_0\equiv \hbar /2$ represents the spin density per $1~\mu{\rm m}^2$. We also plot the intensity of the electric field induced by the vortex beams with $(\lambda,m)=(1,0)$ (b1), $(1,1)$ (b2), $(1,2)$ (b3), $(-1,0)$ (d1), $(-1,1)$ (d2), and $(-1,2)$ (d3). Here we set $\alpha_{\rm D}k_{\rm F}=0.1~{\rm meV}$ and $\beta_{\rm D}=0$. The arrows in (a*) and (c*) correspond to the local spins $(S_x,S_y)/S_0$, and the color represents the amplitude of the local spin, $|{\bm S}(x,y)|/S_0$. The thick arrows in (b*) and (d*) show the direction of the electric field, ${\bm E}({\bm x})/|{\bm E}({\bm x})|$.
• Figure 3: Snapshots of the local spin density in 2DEGs with $\alpha_{\rm R}k_{\rm F}= 0.1~{\rm meV}$ and $\beta_{\rm D}=0$ after the optical vortex pulse is irradiated. The OAM of light is set to be $m=1$ (a) and $m=2$ (b), where the SAM of light is fixed to $\lambda = 1$.
• Figure 4: Local spin density in 2DEGs with the ${\rm SU}(2)$ symmetric SOI, $\alpha_{\rm R}k_{\rm F}=\beta_{\rm D}k_{\rm F}=0.1~{\rm meV}$ after the vortex beams with $(m,\lambda)=(1,1)$ and $(2,1)$ are irradiated.
• Figure 5: Snapshots of the local spin density in 2DEGs with $\alpha_{\rm R}k_{\rm F}=\beta_{\rm D}= 0.1~{\rm meV}$ after the irradiation of pulsed vortex beams with $(m,\lambda)=(1,1)$ (a) and $(2,1) (b)$.