Quantization of spin circular photogalvanic effect in altermagnetic Weyl semimetals

Abstract

We theoretically predict a spin-current analog of the quantized circular photogalvanic effect in Weyl semimetals. This phenomenon is forbidden in antiferromagnets by symmetry but uniquely allowed in altermagnets, highlighting a novel and intrinsic characteristic of altermagnetism. To systematically explore second-order spin current responses, we classify all symmetry-allowed responses based on spin point groups. Furthermore, we provide a comprehensive classification of altermagnetic Weyl semimetals by identifying spin space groups that host symmetry-enforced Weyl points. Utilizing this classification, we construct a symmetry-guided tight-binding model and confirm our predictions. Finally, we identify Weyl crossings in a material candidate via first-principle calculations. Our work unveils a distinctive optical response of altermagnets, paving the way for a new frontier in altermagnetism.

Figures (4)

• Figure 1: Schematic illustration of quantization of spin CPGE. Spin-polarized Weyl points in altermagnetic Weyl semimetals create quantized spin-polarized photocurrent. Oppositely polarized currents flow in the opposite direction by crystal symmetry and produce quantized pure spin currents.
• Figure 2: Comparison of spin CPGE in antiferromagnets and altermagnets. (a-1) Band structure of $\mathcal{PT}$-symmetric antiferromagnetic Weyl semimetals with a mirror plane. (a-2) The vanished trace of the spin conductivities $\mathrm{tr}[\beta^{\uparrow,\downarrow}]$. The red curve shows $\mathrm{tr}[\beta^{\uparrow}]$ and the blue for the spin down, respectively. (b-1) Spin-split energy bands of an altermagnet with $[C_2||\bar{C}_4]$ symmetry as an example. The Weyl points lie along $\Gamma\textrm{-} X$ and $\Gamma\textrm{-} Y$, and also along $\Gamma\textrm{-}\bar{X}$ and $\Gamma\textrm{-}\bar{Y}$ (not shown). (b-2) The quantized trace of the spin conductivity for altermagnetic case. The value is $+2$ reflecting the sum of monopole charges along $\Gamma\textrm{-} Y$ and $\Gamma\textrm{-}\bar{Y}$ lines for the spin-up sector.
• Figure 3: Calculation of the conductivity tensor for a tight-binding model of SSG $R\prescript{1}{}{3}^2c$. (a) Band structure of the model. Red solid lines indicate spin-up bands and blue dashed lines indicate spin-down bands. (b) The high-symmetry points and the path are shown in the top view of the reciprocal space. The points $\Gamma=\vb{0},\,L_1=\vb{b}_1/2,\,L_2=\vb{b}_2/2,$ and $T'=T-\vb{b}_3=(\vb{b}_1+\vb{b}_2-\vb{b}_3)/2$ lie on the glide plane, where the bands are spin-degenerate. Here, reciprocal vectors are $\vb{b}_1=2\pi\qty(1/a,1/(\sqrt{3}a),1/c),\vb{b}_2=2\pi\qty(-1/a,1/(\sqrt{3}a),1/c)$, and $\vb{b}_3=2\pi\qty(0,-2/(\sqrt{3}a),1/c)$. Hopping parameters are $(c_1,c_2,c_3,c_4)=(1+1.5i,1.9+1.6i,1.3+0.53i,0.83+0.67i)$, the lattice constants are $a=1,\,c=6$, and the Fermi energy is $E_F=-2.5$, ensuring that the Weyl point at $T'$ is close to the Fermi energy. (c) Plots of the spin-polarized traces of the conductivity tensors $\mathrm{tr}[\beta^{\uparrow,\downarrow}]$, in units of $i\beta_0=ie^3\pi/h^2$ as functions of the light frequency $\omega$. The insets show schematic photo-excitation around a Weyl point.
• Figure 4: DFT calculation of $\mathrm{MnTiO_3}$ without spin-orbit coupling. Red and blue lines (surfaces) show spin-up and spin-down bands, respectively. (a) Constant-energy isosurface at $E = E_F - 0.49~\mathrm{eV}$. Highlighted are the topmost valence bands, converging to the quadratic Weyl point $T$. Time-reversal symmetry is broken and spin-splitting with even-parity wave (g-wave) anisotropy is visible. (b) Conventional (hexagonal) unit cell of $\mathrm{MnTiO_3}$. Spin space group generators are shown: mirror $\mathrm{[C_2||M_y|t(0, 0, \frac{1}{2})]}$ connects sites with opposite spins, 3-fold rotation $\mathrm{[E||C_3]}$ connects same-spin sites. (c,d) Band structures of 4 topmost valence bands. Altermagnetic spin splitting of roughly 50 meV is visible. (c) Path equal to the model band structure. (d) Path along 3 lines around $T = (1/2, 1/2, 1/2)$. Horizontal line shows the energy level of the isosurface in (a).