Interlayer electric multipoles induced by in-plane field from quantum geometric origins

In two-dimensional layered materials, we show that interlayer charge transfer 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 respectively novel quantum geometric origins in the Berry curvature and quantum metric defined in extended parameter spaces characteristic of layered materials. We elucidate the symmetry characters of the phenomena, and demonstrate sizable dipole and quadrupole polarizations respectively in twisted bilayers and trilayers of transition metal dichalcogenides. The effects point to a new electric control on layer quantum degree of freedom, constituting a building block of layertronics.