Fig. 1. (Color online) Schematic procedure to calculate the valence band offsets for heterostructured CsPbBr₃/MoSe₂. (a) Step I, calculating the energy difference between the VBM and core level in γ-CsPbBr₃ and monolayer MoSe₂, respectively. (b) Step II, calculating the core levels of each layer in CsPbBr₃/MoSe₂ superlattice and doing core-level alignment. A superlattice of CsPbBr₃/MoSe₂ is constructed in (b) to do the core-level alignment.

Fig. 2. (Color online) Band structures of (a) γ-CsPbBr₃ and (b) MoSe₂ monolayer by using PBE (brown lines) and HSE06 (blue lines) functionals. Band structures with and without SOC are both calculated to explore the influence of SOC on the electronic structures. The VBMs are taken as the reference in all the band structures. All of the band gaps are labeled.

Fig. 3. (Color online) Band alignment of CsPbBr₃ and MoSe₂ is calculated by using PBE and HSE06 functionals. Conduction and valence band offsets are labeled in black. Red-dashed lines in (d) are the corrected band edges of CsPbBr₃ and MoSe₂ monolayer with Hatree-Fock exchange percentage of 15% for MoSe₂ monolayer and 45% for CsPbBr₃. The corrected band gaps are labeled in blue. The conduction and valence band offsets are 0.26 and –0.13 eV, respectively.

Fig. 4. (Color online) The charge difference at the interfaces between MoSe₂ monolayer and (a) CsBr-terminated, (b) PbBr-terminated CsPbBr₃ slab.

Fig. 5. (Color online) The projected band structures of CsPbBr₃/MoSe₂ heterostructures. (a) Interface between MoSe₂ and CsBr-terminated CsPbBr₃. (b) Interface between MoSe₂ and PbBr-terminated CsPbBr₃. The red and blue dots represent the bands dominated by MoSe₂ layer and CsPbBr₃, respectively.