Ultrahigh-Density Polar Vortex Lattice in Square-Shaped Moiré Bilayers of Lead Chalcogenides

Nanoscale exotic polar topological structures, such as vortices and skyrmions, hold promise for next-generation electronic devices, yet their spontaneous formation in 2D van der Waals (vdW) materials remains quite challenging. Herein, we demonstrate from first-principles that ultrahigh-density polar vortices emerge in the square moiré bilayer formed by twisting two layers of centrosymmetric PbS with the D₄ point group. The emerged ferroelectricity arises from the inherent complex strain associated with the twisted structures, and the resulting electron polarization is much greater than that obtained in sliding ferroelectricity. Notably, the engineered strain patterns are characterized by peculiar inhomogeneous in-plane fields with a checkerboard distribution of uniaxial tension. This nanoscale nonuniform strain produces an ultrahigh-density vortex polarization lattice. The results from our study not only reveals a new mechanism for electric polarization and polar topologies in moiré bilayers but also provides opportunities for designing 2D ultrahigh-density electric devices.