  Besides its predicted promising high electron mobilities at room temperature,
PtSe2 bandgap sensitively depends on the number of monolayers combined by van
der Waals interaction according to our calculations. We understand this by
using bandstructure calculations based on the density functional theory. It was
found that the front orbitals of VBM and CBM are contributed mainly from pz and
px+y orbitals of Se which are sensitive to the out-plane and in-plane lattice
constants, respectively. The van der Waals force enhances the bonding
out-of-plane, which in-turn influences the bonding in-plane. We found that the
thickness dependent bandgap has the same origin as the strain dependent
bandgap, which is from the change of the front orbital interactions. The work
shows the flexibilities of tuning the electronic and optical properties of this
compound in a wide range.
