1：Experimental Design and Method Selection:

First-principles density functional theory (DFT) calculations were performed using the Vienna ab initio simulation package (VASP) with a plane-wave basis set and Perdew-Burke-Ernzerhofer (PBE) projected augmented wave pseudopotential. The hybrid Heyd-Scuseria-Ernzerhof (HSE06) functional method was used to correct the underestimated bandgaps. The weak vdW interaction was described by the DFT-D2 correction of Grimme.

2：Sample Selection and Data Sources:

The study focused on the GaTe/C2N vdW heterostructure, constructed by combining a 2 × 2 supercell of GaTe sheet and a 1 × 1 unit cell of C2N layer.

3：List of Experimental Equipment and Materials:

Computational simulations were conducted without physical equipment, utilizing software packages for electronic structure calculations.

4：Experimental Procedures and Operational Workflow:

Atomic positions were fully relaxed until energy and forces were converged. A vacuum space in the z-direction more than 25 ? was used to avoid interactions between adjacent heterobilayers. A 21 × 21 × 1 (11 × 11 × 1) k-mesh for the PBE (HSE06) calculations was utilized to sample the Brillouin zone.

5：Data Analysis Methods:

The electronic and optical properties were analyzed based on the HSE06 results. The band structures, density of states, and optical absorption spectra were calculated to understand the properties of the heterostructure.