Symmetry Breakdown in Franckeite: Spontaneous Strain, Rippling, and Interlayer Moiré

Franckeite is a naturally occurring layered mineral with a structure composed of alternating stacks of SnS₂-like and PbS-like layers. Although this superlattice is composed of a sequence of isotropic two-dimensional layers, it exhibits a spontaneous rippling that makes the material structurally anisotropic. We demonstrate that this rippling comes hand in hand with an inhomogeneous in-plane strain profile and anisotropic electrical, vibrational, and optical properties. We argue that this symmetry breakdown results from a spatial modulation of the van der Waals interaction between layers due to the SnS₂-like and PbS-like lattices incommensurability.