Manipulating Charge Distribution in Moir\'e Superlattices by Light

Abstract

In ordinary solids, nonlinear optical responses are typically studied in terms of unit-cell averages due to the angstr\"om-scale lattice constants. In contrast, moir\'e 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 moir\'e-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 moir\'e superlattices.