1：Experimental Design and Method Selection:

The study used the full-potential linearized augmented plane wave (FP-LAPW) method within the framework of density functional theory (DFT) as implemented in the Wien2k code. The generalized gradient approximation (GGA) with PBE functional was used for structural parameters, and the Tran-Blaha modified Becke-Johnson (TB-mBJ) potential approximation was used for electronic and optical properties.

2：Sample Selection and Data Sources:

The study focused on Bi2Te3-xSex alloys with compositions x = 0, 1, 2, and 3 of Se.

3：List of Experimental Equipment and Materials:

The Wien2k computational package was used for calculations.

4：Experimental Procedures and Operational Workflow:

The muffin-tin radii (MT) for each atom (Bi, Te, and Se) were selected to be 2.50 atomic units (a.u.). The Kmax = 8 (RMT)?1, the Fourier expanded charge density was truncated at Gmax=12(Ryd)1/2, and the l-expansion of the non-spherical potential and charge density was carried out up to lmax = 10. The cut-off energy was set to ?6 Ryd to isolate core from valence states.

5：50 atomic units (a.u.). The Kmax = 8 (RMT)?1, the Fourier expanded charge density was truncated at Gmax=12(Ryd)1/2, and the l-expansion of the non-spherical potential and charge density was carried out up to lmax = The cut-off energy was set to ?6 Ryd to isolate core from valence states. Data Analysis Methods:

5. Data Analysis Methods: The total energies were calculated for different volumes about the equilibrium cell volume V0 and adapted to the Murnaghan's equation of state to find the ground state properties.