Ab-initio study of heterostructures of vertically stacked and rotationally aligned incommensurate 2D-films*

Heterostructures obtained through vertical stacking of atomically-thin films are expected to provide a new generation of materials platforms for fundamental science investigations as well as applications. We discuss how one Bi$_2$Se$_3$ quintuple-layer (QL) deposited on an MoS$_2$ trilayer (TL) can stack aligned rotationally with long-range crystallographic order, despite the incommensurability of their lattices to form a new type of well-defined $heterocrystal$. Surprisingly, interaction between the Bi$_2$Se$_3$ and MoS$_2$ layers leads to electronic properties of the heterocrystal that are quite distinct from those of the parent films. We discuss our experimental findings in terms of first-principles computations of electronic and spin-structures, as well as charge densities for heterostructures of Bi$_2$Se$_3$ stacked layer-by-layer on MoSe$_2$ and WS$_2$ films.