Kerr-like effect induced by quantum-metric nematicity

Abstract

The magneto-optic Kerr effect (MOKE), which describes the rotation and ellipticity of linearly polarized light upon reflection, typically occurs in magnetic materials that break time-reversal ($\mathcal{T}$) symmetry. Here we theoretically demonstrate that a similar effect can emerge even in two-dimensional nonmagnetic systems with $\mathcal{T}$ symmetry, owing to the nontrivial quantum geometry of electrons. We reveal that the nematicity of the quantum metric, which corresponds to electric quadrupole moment of electron wave packets, gives rise to a Kerr-like effect (KLE) depending on the incident polarization angle. Notably, neither magnetic order nor spin-orbit coupling, which are conventionally considered essential for the MOKE, is required for its emergence. The KLE is demonstrated by using both a minimal tight-binding model and a model for strained MoS$_2$ with parameters determined by first-principle calculations. This work reveals a quantum-geometric origin for polarization rotation effects beyond the MOKE and offers a distinct approach to probe quantum geometry and multipole moments of electrons.

Figures (5)

• Figure 1: Schmatic figure of the (a) MOKE and (b) KLE. The incident light is affected by (a) the Berry curvature and (b) the quantum-metric nematicity and reflected as an elliptically-polarized light, and experiences a polarization rotation $\theta_K$ (red arrow) and gains an ellipticity $\zeta_K$, which depends on the incident polarization angle $\phi$ (blue arrow) only for the KLE.
• Figure 2: The optical conductivity (in units of $e^2/h$) and quantum metric nematicity in the nonmagnetic minimal model. The optical conductivity (a) $\text{tr} \sigma$, (b) $\bar{\sigma}_{x^2-y^2}$, (c) $\bar{\sigma}_{xy}$ and corresponding JDOS with the smearing parameter $\eta=0.01$. The distribution of quantum metric (d) $\text{tr} g$, (e) $\bar{g}_{x^2-y^2}$, and (f) $\bar{g}_{xy}$ in the first Brillouin zone, with $"\times"$ denoting the position of two valleys K and $\text{K}^\prime$. The dashed curve shows the equal energy contour for the optical transition with different photon energy.
• Figure 3: KLE in nonmagnetic minimal model. The rotation angle $\theta_K$ and ellipticity $\zeta_K$ (a) versus photon energy $\hbar \omega$ ($\phi=0$), and (b) versus polarization angle $\phi$ ($\hbar \omega=4$ eV).
• Figure 4: KLE in strained MoS$_2$ with and without SOC. The $\theta_K$ and $\zeta_K$ (a) versus photon energy $\hbar \omega$ ($\phi=0$), and (b) versus polarization angle $\phi$ ($\hbar \omega=3.4 eV$).
• Figure 5: The quantum metric nematicity and optical conductivity (in units of $e^2/h$) in strained MoS$_2$. (a) The band structure along the high symmetry lines. The distribution of the logarithm of the quantum metric (b) $\text{tr} g$, (c) $\bar{g}_{x^2-y^2}$, and (d) $\bar{g}_{xy}$ in the first Brillouin zone. The optical conductivity (e) $\text{tr} \sigma$, (f) $\bar{\sigma}_{x^2-y^2}$, (g) $\bar{\sigma}_{xy}$ and corresponding JDOS.