Bi-S network origin of cation-disorder stability and dispersive band edges in AgBiS2
Cation-disordered AgBiS2 is a promising lead-free optoelectronic material, but both its ordered structure and the microscopic origin of its favorable electronic properties remain debated. Theory has proposed a mixed-coordination tendency with tetrahedral AgS4 and octahedral BiS6 units, whereas experiments mainly report octahedrally coordinated ordered and cation-disordered phases, together with local cation off-centering. Here, we combine a machine-learning interatomic potential with a deep-learning Hamiltonian to resolve the coupled structural and electronic evolution of AgBiS2 at large length scales. We identify the three-dimensional Bi-S network as the central structural motif governing both disorder stability and band-edge electronic states. At weak disorder, Ag/Bi exchange competes with the off-centering tendency of the Ag sublattice, producing strongly distorted local environments and convoluted diffraction signatures that hinder the identification of the ordered phase. With increasing disorder, BiS6-like units connect into a continuous Bi-S network, which stabilizes the rocksalt-like disordered phase. Despite strong cation disorder, AgBiS2 retains clear semiconductor-like band dispersion and develops a direct band gap. The connected Bi:p-S:p states supported by the Bi-S network preserve a dispersive conduction-band edge and a small electron effective mass. In contrast, mobile Ag disrupts the long-range periodicity of Ag-S bonding, leading to strongly localized valence states. These results clarify the structural controversy in ordered AgBiS2 and establish a unified physical picture of disorder stability and optoelectronic response in nonisovalent semiconductor alloys.