Metallic Electro-Optic Effect in Twisted Double-Bilayer Graphene

Abstract

Recent theoretical advances have highlighted the role of Bloch state intrinsic properties in enabling unconventional electro-optic (EO) phenomena in bulk metals, offering novel strategies for dynamic optical control in quantum materials. Here, we identify an alternative EO mechanism in bulk metallic systems that arises from the interplay between Berry curvature and the orbital magnetic moment of Bloch electrons. Focusing on twisted double-bilayer graphene (TDBG), we show that the enhanced intrinsic properties of moiré Bloch bands give rise to a sizable linear magnetoelectric EO response, a first-order, electric-field-induced non-Hermitian correction to the gyrotropic magnetic susceptibility. This mechanism dominates in $C_{3z}$-symmetric TDBG, where EO contributions originating from the Berry curvature dipole (BCD) are symmetry-forbidden. Our calculations reveal giant, gate-tunable linear and circular dichroism in the terahertz regime, establishing a robust and tunable platform for ultrafast EO modulation in two-dimensional materials beyond the BCD paradigm.

Figures (4)

• Figure 1: (a) In bias-free twisted graphene systems, circular dichroism (CD) has been attributed to the interaction between in-plane magnetic moments $\mathbf{M}$ and the optical fields $\mathbf{E}_\omega$, $\mathbf{B}_\omega$. These in-plane moments arise from chiral interlayer moiré coupling at finite twist angles $\theta$. (b) In contrast, the metallic magnetoelectric electro-optic effect generates out-of-plane magnetic moments in twisted graphene under static electric fields $\mathbf{E}_0$, which couple with the optical fields to produce a distinct dichroic response. (c) Schematic setup for modeling the vertical displacement field in twisted double bilayer graphene. Following Ref. Slot2023, we neglect screening effects and assume a vertical bias difference of $U/3$ between adjacent graphene layers.
• Figure 2: (a) and (b) display the electronic structure of double-bilayer graphene twisted by $\theta = 1.75^{\circ}$, under vertical bias $U = 0$ meV and $U = 27.5$ meV, respectively, for the K valley Bistritzer-MacDonald model. (c) Shows the associated momentum-resolved Berry curvature, orbital magnetic moment and the bias-induced magnetoelectric coupling of Bloch electrons of the top most valance states. Results for the K' valley Bistritzer-MacDonald model are obtained by means of a time-reversal operation, i.e., by means of the prescription $\Omega^z_{n\textbf{k}} (\textrm{K-valley}) \rightarrow -\Omega^z_{n\textbf{k}} (\textrm{K'-valley})$, $m^z_{n\textbf{k}} (\textrm{K-valley}) \rightarrow -m^z_{n\textbf{k}} (\textrm{K'-valley})$ and $\chi^{zz}_{n\textbf{k}} (\textrm{K-valley}) \rightarrow \chi^{zz}_{n\textbf{k}} (\textrm{K'-valley})$, where, $\chi^{zz}_{n\textbf{k}} = \Omega^z_{n\textbf{k}}m^z_{n\textbf{k}}$.
• Figure 3: The general metallic optical response of $C_{3z}$ symmetric twisted double bilayer graphene, given in Eq. \ref{['eq:constitutive']}, depends on two parameters, $\sigma_E$ and $\alpha$, capturing the Drude conductivity and the bias induced metallic magnetoelectric EO response. Panels (a) and (b) display the $\sigma_E = e^2V$ and $\alpha$ as a function of the Fermi energy at distinct twist angles, as obtained from the Bistritzer-MaDonald model. We have set, $\tau = 10$ ps and $E_0^y = 10^4$ V/m. Panels (c) and (d) show the evolution of the maximum attainable bias-induced magnetoelectric coupdling $\alpha_{\textrm{max}}$ as a fuction of the vertical bias $U$ and twist angle $\theta$, respectively.
• Figure 4: (a) Schematic of the system with the twisted double bilayer graphene at $z=0$, in between dielectrics with relative permittivities $\epsilon_1$ ($z < 0$) and $\epsilon_2$ ($z > 0$). The incidence plane is depicted and the incidence angle is $\rho$ (b) Ellipticity with respect to frequency and incidence angle $\rho$ at $\theta = 1.750^{\circ}$ twisting; (c) with respect to frequency at $\rho = 45^{\circ}$; and (d) with respect to $\rho$ at $\omega = 0.3$ THz (See Fig. \ref{['fig3']} for corresponding $\sigma_\textrm{E}$ and $\alpha$). In panels (b)-(d), $\gamma = 10^{11}$ rad$\cdot$s$^{-1}$, $\epsilon_1 = \epsilon_2 = 1$, $E_0 = 10^5$ V$\cdot$m$^{-1}$, $\phi = 90^{\circ}$.