Manipulating Charge Distribution in Moiré Superlattices by Light

Abstract

In ordinary solids, nonlinear optical responses are typically studied in terms of unit-cell averages due to the angström-scale lattice constants. In contrast, moiré superlattices, characterized by a large length scale, unlock an often-overlooked degree of freedom: intra-supercell spatial variations of local observables. Here, we formulate the second-order direct current (DC) charge response in a spatially resolved manner, showing that even uniform optical illumination can drive a static, spatially non-uniform charge redistribution within a supercell. This effect is ubiquitous and cannot be forbidden by any crystalline symmetries. Furthermore, we identify a dominant contribution arising from diverging analytical response coefficients, which leads to linear-in-time growth of the redistribution in the absence of relaxation. This growth is driven by the convergence or divergence of local DC photocurrents. Applying our theory to twisted bilayer MoTe$_2$, we demonstrate strong, highly tunable charge modulation controlled by light intensity and frequency, opening a route to in situ, all-optical control of moiré-periodic electrostatic potentials. Our work underscores the importance of intra-cell degrees of freedom, which enable a qualitatively richer class of nonlinear optical responses in moiré superlattices.

Figures (4)

• Figure 1: Illustration of a moiré supercell under uniform optical illumination, showing in-plane, non-uniform DC photocurrents (green arrows) converging toward the cell center. Red and blue colors mark regions of positive and negative charge accumulation resulting from photocurrent convergence and divergence.
• Figure 2: (a) Band structure of $\text{tMoTe}_{\text{2}}$ at twist angle $\theta=1.0^\circ$. The $\pm \mathbf{K}$ valley degrees of freedom, inherited from monolayer $\text{MoTe}_{\text{2}}$, remain decoupled. Blue solid and red dashed lines are bands from the $+\mathbf{K}$ and $-\mathbf{K}$ valleys, respectively. The band gap is $1.057$ eV. (b) Brillouin zones of the top (solid gray), bottom (dashed gray) monolayer MoTe$_2$, and the moiré Brillouin zone of tMoTe$_2$ (black). (c) Enlarged moiré Brillouin zone, showing high-symmetry points and six reciprocal lattice vectors ($\mathbf{G}_{1-6}$) with the smallest magnitude.
• Figure 3: Frequency dependence of $\zeta^{xx}(\mathbf{G}_2; \omega_0)$. Real and imaginary parts are shown in the top and bottom subplots, respectively. Here, $\zeta_0 \approx 1.602\times 10^{-19} \, \mathrm{C}^3/\mathrm{J}^2$. The full charge response [Eq. (\ref{['eq:zeta']})] is shown as solid green lines; the accumulation-only contribution [Eq. (\ref{['eq:zeta_inj']})] is indicated by dashed orange lines. Vertical dotted lines mark the band gap energy at $\hbar \omega_0 \approx 1.057~\text{eV}$
• Figure 4: Real-space charge redistribution in $\text{tMoTe}_{\text{2}}$ under linearly polarized illumination. (a,b) Photoinduced charge density $\Delta\rho(\mathbf{r})$ under $x$-polarized light at photon energies $\hbar \omega_0 = 1.104 \, \mathrm{eV}$ and $1.122 \, \mathrm{eV}$, respectively, with fixed intensity $1.0\times 10^{11} \, \mathrm{W/m^2}$. The dashed parallelogram in (a) outlines a moiré supercell, with high-symmetry stacking sites MM, XM, and MX marked by black, blue, and green dots. (c,d) Moiré-periodic electrostatic potentials $U(\mathbf{r})$ induced in a nearby layered material, computed from the charge distributions in (a,b), respectively. (e) Comparison between the charge response coefficient $2\eta\,\zeta^{xx}(\mathbf{G}_2; \omega_0)$ computed directly (solid pink) and inferred from the continuity equation [Eq. (\ref{['eq:CE_coef']})] via the corresponding photocurrent (cyan dots). (f) Spatial distribution of the DC photocurrent (black arrows) and time derivative $\partial_t \Delta\rho$ (color map) under the same conditions as in (b), within a single moiré supercell.