Spin splitting and strain in epitaxial monolayer WSe$_2$ on graphene

We present the electronic and structural properties of monolayer ${\mathrm{WSe}}_{2}$ grown by pulsed-laser deposition on monolayer graphene (MLG) on SiC. The spin splitting in the ${\mathrm{WSe}}_{2}$ valence band at $\overline{\mathrm{K}}$ was ${\mathrm{\ensuremath{\Delta}}}_{\mathrm{SO}}=0.469\ifmmode\pm\else\textpm\fi{}0.008$ eV, as determined by angle-resolved photoemission spectroscopy. Synchrotron-based grazing-incidence in-plane x-ray diffraction (XRD) revealed the in-plane lattice constant of monolayer ${\mathrm{WSe}}_{2}$ to be ${a}_{{\mathrm{WSe}}_{2}}=3.2757\ifmmode\pm\else\textpm\fi{}0.0008$ \AA{}. This indicates a lattice compression of $\ensuremath{-}0.19$% relative to bulk ${\mathrm{WSe}}_{2}$. By using the experimentally determined graphene lattice constant (${a}_{\mathrm{MLG}}=2.4575\ifmmode\pm\else\textpm\fi{}0.0007$ \AA{}), we found that a $3\ifmmode\times\else\texttimes\fi{}3$ unit cell of the slightly compressed ${\mathrm{WSe}}_{2}$ is perfectly commensurate with a $4\ifmmode\times\else\texttimes\fi{}4$ graphene lattice with a mismatch below 0.03%, which could explain why the monolayer ${\mathrm{WSe}}_{2}$ is compressed on MLG. From XRD and first-principles calculations, we conclude that the observed size of strain will affect ${\mathrm{\ensuremath{\Delta}}}_{\mathrm{SO}}$ only on the order of a few meV. In addition, angle-resolved, ultraviolet, and x-ray photoelectron spectroscopies shed light on the band alignment between ${\mathrm{WSe}}_{2}$ and MLG/SiC and indicate electron transfer from graphene to the ${\mathrm{WSe}}_{2}$ monolayer. As further revealed by atomic force microscopy, the ${\mathrm{WSe}}_{2}$ island size depends on the number of carbon layers on top of the SiC substrate. This suggests that the epitaxy of ${\mathrm{WSe}}_{2}$ favors the weak van der Waals interactions with graphene, while it is perturbed by the influence of the SiC substrate and its carbon buffer layer.