Resolving the Topological and Optical Inconsistencies of Bismuth through Extended Hubbard Corrections

Bismuth (Bi) is well known for its strong spin–orbit coupling (SOC) and distinctive electronic properties, yet its topological nature has remained a subject of debate. Previous experimental and theoretical studies have reported conflicting results, suggesting that Bi could be either topologically trivial or nontrivial. In this work, we apply an extended Hubbard model that includes both on-site (U) and intersite (V) Coulomb interactions to address these inconsistencies. This approach successfully reproduces key experimental observations, such as the lattice constants, band gap, and SOC-induced band inversion at the L point, thereby resolving the long-standing mismatch between theory and experiment. Moreover, our optical conductivity analysis reveals that the two peaks observed below 1 eV originate from transitions between flat bands near the T and W points, rather than from Γ-point transitions as previously assumed. These results provide a more consistent understanding of Bi's electronic and topological properties and establish a unified theoretical framework that can guide the design of Bi-based quantum and spintronic devices.