Antiparallel spin polarizations as quadratic response in chiral systems

Abstract

Chirality-dependent spin generation has attracted considerable attention in condensed matter physics. In this paper, we theoretically investigate antiparallel spin polarization as a chirality-dependent quadratic response, by using a finite chiral system composed of triangular prisms. Based on the nonlinear Kubo formalism and real-time simulations, we demonstrate that spatially inhomogeneous antiparallel spin polarizations are induced as a dissipative quadratic DC response to a homogeneous AC electric field. In particular, we elucidate role of microscopic parameters characterizing the handedness of chirality, and naive expectation of spin polarization as a consequence of spin accumulation of spin current.

Figures (7)

• Figure 1: Schematic of chirality-dependent spin $\bm{s}$ generation as (a) linear and (b) quadratic responses to an electric field $\bm{E}$. Blue and light-blue arrows represent spins and the spin-current flow, respectively. See also in yoshimi2025.
• Figure 2: (a) Structure of the finite $N$-layer triangular-prism system along the $z$ axis under the point group $D_{\rm 3h}$. (b) In-plane and (c) out-of-plane ETM degrees of freedom belonging to the $A_1"$ irreducible representation in $D_{\rm 3h}$. Red arrows represent imaginary hoppings with polar property and $\sigma_\nu$ for $\nu=x,y,z$ denote the Pauli matrix in spin space.
• Figure 3: (a) Layer dependence of the electric monopole (onsite potential) $\braket{Q_{0}}_{l}$ and (b) the ETMs (spin-dependent imaginary hoppings) $\braket{G_{0\perp}}_{l}$ and $\braket{G_{0\parallel}}_{l, l+1}$ for the equilibrium state. The model parameters are $t'_{\perp}=2$, $t'_{\parallel}=1$, $t"_{\perp}=0.5$, $t"_{\parallel}=0.3$, and $T=0.01$.
• Figure 4: Layer dependence of (a) $\chi^{(l)}_{M_zE_zE_z}(\Omega, -\Omega)$ and (b) $\chi^{(l,l+1)}_{G_{0\parallel}E_zE_z}(\Omega, -\Omega)$ for $\Omega = 1$. The other parameters are the same as those of Fig. \ref{['f:Q0_G0xy_G0z']}, and the handedness of the blue and red lines is opposite to each other. Black line in (b) represents $\partial_z \chi^{(l,l+1)}_{G_{0\parallel} E_zE_z}(\Omega, -\Omega)$ for $(t"_{\perp}, t"_{\parallel})= (0.5, 0.3)$.
• Figure 5: Layer dependence of $\chi^{(l)}_{M_zE_zE_z}(\Omega, -\Omega)$ for $(t"_{\perp}, t"_{\parallel})=(0.5, 0.3)$, $(0.5, -0.3)$, $(-0.5, 0.3)$, and $(-0.5, -0.3)$. The other parameters are the same as those of Fig. \ref{['f:chi_G0zEzEz_chi_szEzEz']}.