High-fidelity electronic structure and properties of InSb: $G_0W_0$ and Bayesian-optimized hybrid functionals and DFT+$U$ approaches

This study presents a refined approach to computing the electronic structure of indium antimonide (InSb) using advanced \textit{ab initio} techniques with the In and Sb $4d^{10}$ semicore electrons included in the valence states. These states are modeled using fully relativistic projector augmented waves (PAW) and optimized norm-conserving Vanderbilt (ONCV) pseudopotentials. However, standard Kohn-Sham density-functional theory (DFT) calculations with these pseudopotentials often produce non-physical band inversions and incorrect band gaps at the $\Gamma$-point due to $5p$-$4d$ repulsion and self-interaction errors (SIE). To resolve these issues, we apply a combination of hybrid Heyd-Scuseria-Ernzerhof (HSE) exchange-correlation (XC) functionals, many-body perturbation theory (MBPT) via quasiparticle $G_0W_0$, and DFT+$U$, significantly improving the accuracy of the band structure over previous studies. A Bayesian optimization framework is used to refine key parameters, including the inverse screening length ($\mu$) and Hartree-Fock (HF) exchange fraction ($\alpha$) in HSE-based XC functionals, as well as the Hubbard $U$ parameters in DFT+$U$, leading to significantly improved band structure predictions. This approach yields highly precise band gaps, bulk moduli, effective masses, Luttinger parameters, valence bandwidth, and $4d$ band positions, achieving unprecedented agreement with experimental data. The resulting model resolves the long-standing incomplete description of InSb's electronic band structure and provides a transferable computational framework for accurate electronic structure predictions across diverse material systems, offering valuable insights for future electronic, optoelectronic, energy, and quantum applications.