Origin of superconductivity in hole doped SrBiO₃ bismuth oxide perovskite from parameter-free first-principles simulations

Superconductivity, characterized by zero resistance and magnetic flux expulsion, arises from the formation of Cooper pairs. While well-understood in simple elements via phonon exchange, the mechanism in high-temperature oxide superconductors remains complex, often attributed to strong electronic correlations. The recent discovery of superconductivity in nickel-based oxides has renewed interest in first-principles simulations for understanding these materials. Sr1-xKxBiO3 and Ba1-xKxBiO3 offer ideal systems for testing these simulations due to their structural similarity to nickelates and the presence of several complexities exhibited by oxide superconductors. In their bulk form, SrBiO3 and BaBiO3 are insulators with a band gap resulting from a breathing distortion (Boc) and charge disproportionation of Bi4+ into Bi3+/Bi5+. Upon hole doping with K, these materials become superconducting. Previous theoretical studies often struggled to capture these features using standard density functional theory (DFT) methods. This study aims to determine the minimum level of theory required to accurately model these complex superconductors and elucidate the underlying pairing mechanism.

Several theoretical studies have attempted to explain the behavior of bismuthates and their superconducting phases, often concluding that standard DFT (using LDA or GGA) fails to reproduce the insulating character and breathing mode (Boc) in BaBiO3. These methods also underestimate the electron-phonon coupling constant (λ). More sophisticated methods like hybrid DFT and GW calculations yield better results but are computationally expensive, limiting their applicability to large supercells necessary to model doping effects and symmetry lowering. Recent work has shown that the SCAN meta-GGA functional accurately predicts the band gaps in ABO3 perovskites through mechanisms such as octahedral crystal field splitting, symmetry lowering, Jahn-Teller effects, and disproportionation. This suggests that SCAN-DFT might be sufficient for studying doping effects in complex oxide superconductors.

This research employed DFT simulations using the SCAN meta-GGA functional, known for its improved accuracy in describing self-interaction errors and predicting lattice distortions. Hole doping was modeled by substituting Sr2+ with K+ ions, using the Special Quasi-random Structure (SQS) technique to represent cation disorder in a 32-formula unit supercell. The low-temperature P21/n phase of SrBiO3 was used as the starting structure. Potential energy surfaces for lattice distortions were generated by applying finite amplitudes of distortions to a perfect cubic Pm-3m cell. Phonon frequencies were determined by fitting the potential energy surfaces of frozen displacements. Superconducting properties were calculated using a simplified approach based on the breathing mode (Boc), estimating the reduced electron-phonon matrix element (REPME), the electron-phonon coupling constant (λ), and the critical temperature (Tc). The VASP DFT code was used for all calculations, with specific parameters outlined in the original paper.

The SCAN-DFT simulations accurately reproduced the experimental structural and electronic properties of SrBiO3, including its insulating nature and the amplitude of lattice distortions. Analysis of the potential energy surface demonstrated that octahedral rotations enhance the breathing mode (Boc) amplitude. At low K doping, holes are trapped on the lattice, forming polaronic states leading to semiconducting behavior. Intermediate doping leads to a metallic state with residual Boc distortion, whereas at higher doping (x ≥ 0.4375), similar to the experimentally observed superconducting region (x = 0.45–0.6), the Boc distortion vanishes. The calculated electron-phonon coupling constant (λ) of 1.22 and Boc frequency of 66 meV are in close agreement with experimental values. The disappearance of the breathing mode and the appearance of a single parabolic band structure are strongly correlated with the onset of superconductivity. The study also found limited miscibility of K in SrBiO3, consistent with experimental observations. The role of K doping is attributed primarily to steric effects, reducing octahedral rotations and suppressing Boc stabilization, rather than inducing complex electronic interactions. The study found that increasing K-doping hardens the breathing mode.

These findings strongly suggest that the proximity of a charge and bond-ordered phase, characterized by the breathing mode distortion (Boc), is a crucial prerequisite for superconductivity in bismuthates. The calculated electron-phonon coupling constant and critical temperature are in excellent agreement with experimental data, validating the use of SCAN-DFT for understanding these materials. The observed behavior suggests that the phonon mode associated with the breathing distortion plays a dominant role in the superconducting mechanism, potentially through the creation of Cooper pairs. The indirect effect of K doping, primarily through steric influences on lattice distortions, highlights a simpler explanation for superconductivity than solely strong correlation effects.

This study demonstrates that parameter-free SCAN-DFT simulations are capable of accurately predicting the key features of superconductivity in hole-doped SrBiO3. The results highlight the importance of lattice distortions, specifically the breathing mode, in the superconducting mechanism and suggest that the proximity of a disproportionated phase is a prerequisite for superconductivity in these bismuthates. Future research could investigate other oxide superconductors to determine the universality of the identified mechanism and could explore further the role of lattice dynamics beyond the breathing mode in these materials.

The study employed a simplified approach for calculating superconducting properties, focusing on the breathing mode contribution. A complete electron-phonon calculation including all phonon modes would be computationally expensive for the large supercell used. The accuracy of the calculated critical temperature (Tc) relies on the chosen screened Coulomb potential (μ*), which introduces some uncertainty. The study also limits its investigation to K doping contents up to x = 0.625 due to the limited miscibility of K in SrBiO3.