  We show that interlayer charge transfer in 2D materials can be driven by an
in-plane electric field, giving rise to electrical multipole generation in
linear and second order of in-plane field. The linear and nonlinear effects
have quantum geometric origins in the Berry curvature and quantum metric
respectively, defined in extended parameter spaces characteristic of layered
materials. We elucidate their symmetry characters, and demonstrate sizable
dipole and quadrupole polarizations respectively in twisted bilayers and
trilayers of transition metal dichalcogenides. Furthermore, we show that the
effect is strongly enhanced during the topological phase transition tuned by
interlayer translation. The effects point to a new electric control on layer
quantum degree of freedom.
