New approach for the molecular beam epitaxy growth of scalable single-crystalline WSe$_2$ monolayers.

The search for high-quality transition metal dichalcogenides mono- and multi-layers grown on large areas is still a very active field of investigation nowadays. Here, we use molecular beam epitaxy to grow 15$\times$15 mm large WSe$_2$ on mica in the van der Waals regime. By screening one-step growth conditions, we find that very high temperature ($>$900$^{\circ}$C) and very low deposition rate ($<$0.015 nm/min) are necessary to obtain high quality WSe$_2$ films. The domain size can be larger than 1 $\mu$m and the in-plane rotational misorientation less than $\pm$0.5$^{\circ}$. The WSe$_2$ monolayer is also robust against air exposure, can be easily transferred over 1 cm$^2$ on SiN/SiO$_2$ and exhibits strong photoluminescence signal. Moreover, by combining grazing incidence x-ray diffraction and transmission electron microscopy, we could detect the presence of few misoriented grains. A two-dimensional model based on atomic coincidences between the WSe$_2$ and mica crystals allows us to explain the formation of these misoriented grains and gives suggestion to remove them and further improve the crystalline quality of WSe$_2$.