Fig. 3: Strain distribution and band alignment in various high-symmetry regions of the MoSe₂/WS₂ moiré supercell at a 60° twist angle.

a Moiré lattice for 60° twist angle MoSe₂/WS₂ (top)_. \({{{{\rm{H}}}}}_{{{{\rm{X}}}}}^{{{{\rm{M}}}}}\), \({{{{\rm{H}}}}}_{{{{\rm{X}}}}}^{{{{\rm{X}}}}}\), and \({{{{\rm{H}}}}}_{{{{\rm{M}}}}}^{{{{\rm{M}}}}}\) (where M is the transition metal atom and X is the chalcogen atom) are three high-symmetry regions in the unit cell. Their stacking configurations are shown in the black dashed box (bottom). b Strain distribution in the same moiré lattice plotted as a variation in local lattice constants from equilibrium. Red (positive) indicates compressive strain; blue (negative) indicates tensile strain. In the \({{{{\rm{H}}}}}_{{{{\rm{X}}}}}^{{{{\rm{M}}}}}\) region, MoSe₂ is under compressive strain while WS₂ is under tensile strain. The \({{{{\rm{H}}}}}_{{{{\rm{X}}}}}^{{{{\rm{X}}}}}\) region shows the opposite. c GW band edges (conduction band minimum (CBM) and valence band maximum (VBM)) of strained monolayer MoSe₂ and WS₂ with bilayer screening. All energies are aligned relative to the vacuum level. In each region, WS₂ and MoSe₂ are strained in opposite directions, so MoSe₂ is plotted with increasing strain, and WS₂ is plotted with decreasing strain. Circles are unstrained lattice constant in \({{{{\rm{H}}}}}_{{{{\rm{M}}}}}^{{{{\rm{M}}}}}\). Squares are average length of the lattice constants in high-symmetry regions \({{{{\rm{H}}}}}_{{{{\rm{X}}}}}^{{{{\rm{M}}}}}\) and \({{{{\rm{H}}}}}_{{{{\rm{X}}}}}^{{{{\rm{X}}}}}\). Triangles are maximum or minimum length of the lattice constant, appearing at the boundary of regions \({{{{\rm{H}}}}}_{{{{\rm{X}}}}}^{{{{\rm{M}}}}}\) and \({{{{\rm{H}}}}}_{{{{\rm{X}}}}}^{{{{\rm{X}}}}}\). Results indicate type Ⅰ band alignment in the \({{{{\rm{H}}}}}_{{{{\rm{X}}}}}^{{{{\rm{X}}}}}\) region and type Ⅱ band alignment in the \({{{{\rm{H}}}}}_{{{{\rm{X}}}}}^{{{{\rm{M}}}}}\) region.