Symmetry-isolated magnetoelectric electro-optic effects in noncentrosymmetric metals

We classify the symmetry-constrained forms of the Berry curvature dipole $\mathbf{D}$, gyrotropic magnetic tensor $\mathbf{K}$, and magnetoelectric electro-optic (EO) tensor $\mathbf{G}$, which describe metallic optical and EO effects in time-reversal symmetric, noncentrosymmetric metals. We identify 11 space groups (SGs) in which $\mathbf{D}$ and $\mathbf{K}$ vanish by symmetry while $\mathbf{G}$ remains allowed, thereby providing a more direct route to observing the recently predicted magnetoelectric EO effects associated with $\mathbf{G}$. First-principles based calculations confirm that $\mathbf{D}$ and $\mathbf{K}$ vanish for representative materials, while $\mathbf{G}$ remains allowed and tunable via Fermi level shifting. We further show that the choices of SG and experimental configuration provide complementary paths for isolating $\mathbf{G}$-driven EO effects, including cases where $\mathbf{D}$ and $\mathbf{K}$ are also symmetry-allowed. In an oblique-incidence geometry, the $\mathbf{D}$-driven response produces a helicity-even absorption or gain correction, whereas the $\mathbf{G}$-driven response couples the $s$ and $p$ optical sectors and produces a bias-induced circular dichroism with a characteristic $\sin\theta\cos\theta$ angular dependence. This provides a direct experimental route for separating the $\mathbf{D}$- and $\mathbf{G}$-driven EO signatures in noncentrosymmetric metals.