Linearly Polarized Light-Induced Anomalous Hall Effect and Topological Phase Transitions in an Altermagnetic Topological Insulator

Abstract

A recently identified class of collinear magnetic order, characterized by vanishing net magnetization yet unconventional spin splitting, known as altermagnets (AMs), has attracted significant research interest. Controlling the unconventional spin splitting and the associated band topology in AMs offers opportunities for realizing novel spin and topological transport phenomena. In this work, using Floquet engineering with periodically driven linearly polarized light (LPL), we explore light-induced control of an AM topological insulator. Remarkably, we find that AMs and conventional antiferromagnets (AFMs) exhibit distinct responses under LPL irradiation. Specifically, since LPL breaks neither time-reversal ($\mathcal{T}$) symmetry nor parity-time-reversal ($\mathcal{PT}$) symmetry, it is incapable of generating spin splitting or inducing an anomalous Hall effect (AHE) in conventional AFMs. In contrast, AMs intrinsically lack both $\mathcal{T}$ and $\mathcal{PT}$ symmetries. Their spin-up and spin-down bands are related by the combined symmetry of time reversal $\mathcal{T}$ and a crystal rotation. We show that LPL readily breaks these symmetries, thereby triggering a finite AHE exclusively in AMs. Furthermore, LPL can drive the AM topological insulator into a fully spin-polarized Chern insulating phase. Our findings not only provide a robust experimental scheme to distinguish AMs from conventional AFMs, but also establish a promising pathway toward dissipationless spintronic applications.

Figures (5)

• Figure 1: Schematic illustrations of the optical setup and the magnetic lattice models. (a) Top view of the linearly polarized light configuration, where $\theta$ denotes the polarization angle relative to the $x$ axis. (b) Lattice model of the two-dimensional $d$-wave altermagnet. (c) Lattice model of the two-dimensional antiferromagnet. In (b) and (c), red and blue solid circles represent atoms with spin-up and spin-down moments, respectively, while gray circles represent non-magnetic atoms.
• Figure 2: Calculated band structures and Fermi surfaces of altermagnets (AMs) and antiferromagnets (AFMs). Band structures (first and third columns) and Fermi surfaces at $E_{F}=2v$ (second and fourth columns) are shown for the AM [panels (a), (b), (e), and (f)] and AFM [panels (c), (d), (g), and (h)]. The rows correspond to different light intensity. (a)-(d) the equilibrium state without light irradiation ($A_0=0$); (e)-(h) under irradiation by linearly polarized light (LPL) with light intensity at $A_0=1.0$ and polarization direction at $\theta=0$. Red solid lines and blue dashed lines represent the spin-up and spin-down bands, respectively. The parameters are set as: $m = 4.2v$, $b = -v$ and $t_a = \sqrt{3}$ for the AM; and $m = 4.2v$, $b = -2v$, and $t_a = 1$ for the AFM.
• Figure 3: Light-induced anomalous Hall effect (AHE). (a) The anomalous Hall conductivity (AHC) as a function of the Fermi energy for $A_{0}=0$ (black line), $A_{0}=0.3$ (blue line), $A_{0}=0.6$ (red line) and $A_{0}=0.9$ (green line), with $\theta=0$. (b) Comparison between the AHC calculated using the high-frequency approximation (red line) and accounting for the occupation of Floquet states (blue line) at $\omega = 10$, with $A_0 = 0.6$ and $\theta = 0$. (c) The AHC as a function of $\theta$ at a fixed Fermi energy $E_{F} = 2v$. (d) Schematic polar plot sign of $\sigma_{xy}$ for AMs. Red (blue) regions indicate positive (negative). The parameters are $m = 4.2v$, $b = -v$, and $t_a = \sqrt{3}$.
• Figure 4: Light-induced evolution of the spin-resolved band gap and the associated topological phase transitions under linearly polarized light (LPL). The evolution of the spin-up and spin-down band gaps under LPL irradiation for (a) a trivial altermagnet (AM), (b) a trivial antiferromagnet (AFM), (c) quantum spin Hall (QSH) AM, (d) QSH AFM. The red solid lines and blue dashed lines represent the band gaps for the spin-up and spin-down bands, respectively. Yellow, light blue, and white regions denote the QSH, Chern insulator ($C=-1$), and topologically trivial phases, respectively. The parameters for a trivial AM are $m=4.2v, b=-v, t_a= \sqrt{3}$, for a trivial AFM are $m=4.2v, b=-2v, t_a= 1$, for a AM QSH insulator are $m=3.8v, b=-v, t_a= \sqrt{3}$, for a AFM QSH insulator are $m=3.8v, b=-2v, t_a= 1$. The polarization direction $\theta=0$.
• Figure 5: Phase diagrams under linearly polarized light irradiation as a function of the light intensity $A_{0}$ and the polarization direction $\theta$. (a) The phase diagram for the $d$-wave quantum spin Hall (QSH) altermagnets, the parameters are $m=3.8v, b=-1v, t_a= \sqrt{3}$. (b) The phase diagram for the QSH antiferromagnet, the parameters are $m=3.8v, b=-2v, t_a= 1$.