Spin-selective elliptic optical dichroism and perfectly spin-polarized third-order nonlinear photocurrent in altermagnets

Abstract

It is shown that the low-energy theory of a $d$-wave altermagnet is characterized by anisotropic Dirac cones with up and down spins based on a recently proposed tight-binding model. Spin-selective perfect elliptic dichroism occurs in this system, where only up-spin or down-spin electrons are excited by elliptically polarized light. Then, we derive a formula for the third-order photocurrent induced by applying both elliptically polarized light and static electric field, which is described in terms of quantum metric and the Berry curvature. Based on it, we predict only up-spin polarized current is induced. It is the leading order of photocurrent because the second-order photocurrent such as the injection current and the shift current are prohibited due to inversion symmetry inherent to altermagnets. It is intriguing that nonzero photocurrent is induced only by the anisotropy of the Dirac cones. Our results will be useful for future photo-excited spintronics based on altermagnets.

Figures (3)

• Figure 1: (a) Illustration of the Lieb lattice model. Red (cyan) disks represent sites with up (down) spin. Small yellow disks represent non-magnetic sites. The tight-binding model is constructed only with the use of red and blue disks, where the hopping terms are modified in the presence of yellow disks. Red (cyan) arrows represent hoppings between the next-nearest neighbor up(down)-spin sites. Green arrows represent hoppings between the nearest-neighbor sites between opposite spins. We have set $A=t_{1}+t_{2}$, $B=t_{1}-t_{2}$, $C=\lambda _{1}+\lambda _{2}$ and $D=\lambda _{1}-\lambda _{2}$ in the Hamiltonian (\ref{['H1']}). (b) Bird's eye's view of the band structure containing two anisotropic Dirac cones. (c) Top view of the band structure. Red (blue) color represents the up-spin (down-spin) band structure.
• Figure 2: (a) Optical absorption as a function of $\omega$. Red (blue) curve corresponds to the spin up (down) polarization. We have set $\vartheta =\vartheta ^{\text{Y}}$, where only electrons with up spin is excited. (b) Optical absorption as a function of $\vartheta$ at the optical band edge $\hbar \omega =2\left\vert \Delta \right\vert$. We have set $t=4;\lambda =0.5;B=-1$ and $u=-2.2$.
• Figure 3: (a) Jerk current as a function of $\omega$ dependence Red (blue) curve corresponds to the spin up (down) polarization. We have set $\vartheta =\vartheta ^{\text{Y}}$, where only electrons with up spin is excited. (b) Jerk current as a function of $\vartheta$ at the optical band edge $\hbar \omega =2\left\vert \Delta \right\vert$.