Van der Waals induced rippling and anisotropy in the natural superlattice Franckeite*

Franckeite, a naturally occurring van-der-Waals hetereostructure, is composed of alternating pseudohexagonal and pseudotetragonal two-dimensional layers. While both types of layers are in principle mechanically and electrically isotropic in the plane, Franckeite, like its cousin Cylindrite, exhibits a characteristic rippling pattern, the origin or which has remained unclear. Here we show, using continuum elasticity theory, that rippling is ultimately the result of a mechanical instability produced by a one-dimensional moiré superlattice forming in Franckeite's interlayer alignment. We also show that the ripples give rise to marked anisotropies in the electrical and optical sectors, as measured by differential reflectance, polarised Raman spectroscopy and electrical transport measurements. This picture connects the properties of bulk Franckeite to the basic mechanisms governing low-angle moiré multilayers, such as twisted graphene bilayers.