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

The study addresses how superconductivity emerges in hole-doped bismuthate perovskites Sr1−xKxBiO3 and identifies the minimal first-principles framework required to capture their superconducting behavior. Superconductivity, arising from Cooper pairing, is phonon-mediated in simple elements but is often linked to proximity to magnetic or charge-ordered states in complex oxides. There is a common belief that strong electronic correlations are essential for high-Tc oxides, potentially limiting standard DFT. Bismuthates (SrBiO3, BaBiO3) are ideal testbeds: they are perovskites exhibiting octahedral rotations and a bond-disproportionation (breathing) distortion leading to Bi3+/Bi5+ differentiation and a negative charge-transfer insulating state. Upon K-induced hole doping, they become superconducting with Tc ~5–30 K over specific x ranges, and experiments indicate strong electron-phonon coupling (λ ~1.3). However, standard LDA/GGA often fail to reproduce the insulating state and breathing mode, and underestimate EPC, while hybrid/GW methods are too costly for realistic doped supercells including disorder and symmetry lowering. The research question is whether a parameter-free semilocal functional (SCAN) can capture doping trends, the insulator-metal transition, and superconducting quantities, and to elucidate the mechanism—particularly the role of the breathing mode and its coupling to octahedral rotations—in forming Cooper pairs.

Prior theoretical work reported that LDA/GGA do not stabilize the breathing distortion or the insulating state in BaBiO3 and underestimate EPC (λ ~0.3–0.4 vs experimental ~1.3). Hybrid functionals and GW improve band gaps and EPC but are computationally prohibitive for large, disordered supercells and full structural relaxations. Octahedral rotations have been proposed to enhance EPC. Polaronic hole trapping and bipolaron formation at low doping have been predicted in BaBiO3. Beyond bismuthates, band gap opening mechanisms in perovskites can arise from crystal-field splitting, symmetry-lowering (rotations), Jahn-Teller, or disproportionation without invoking strong dynamical correlations; SCAN has successfully captured trends in correlated oxides (nickelates, cuprates). Open issues include mapping global trends vs x in Sr1−xKxBiO3 and clarifying the superconducting transition mechanism and prerequisites.

DFT calculations employ the parameter-free meta-GGA SCAN functional (VASP, PAW; energy cutoff 650 eV). Hole doping is modeled by substituting Sr2+ with K+ using Special Quasirandom Structures (SQS) in a 32-formula-unit supercell (2×2×4 of the primitive Pm-3m cell), enabling alloy disorder and all relevant lattice distortions (octahedral rotations and breathing) and allowing polaron formation. Geometry optimizations include atomic positions and lattice parameters until forces <0.05 eV/Å, with Γ-centered k-meshes (4×4×3 for relaxations; 5×5×3 for DOS and energy surfaces). Starting structures are based on the low-temperature P21/n phase of SrBiO3. Potential energy surfaces (PES) are computed by freezing distortion mode amplitudes (rotations, breathing Boc) in a cubic reference or in the doped ground states; phonon frequencies for Boc are extracted by fitting the PES to a harmonic-plus-anharmonic form E=aQ2+bQ3 and identifying ω=√(a/M). Superconducting quantities are estimated by freezing Boc displacements u in the relaxed doped ground state to induce a bandgap opening ΔE, yielding the reduced electron-phonon matrix element D=ΔE/(2u). The EPC constant λ is evaluated via λ=N(EF)(ħ2/2Mω2)D2 using the computed ωBoc and N(EF). The critical temperature Tc is estimated with the Allen-Dynes modified McMillan equation using ωlog corrected following SCAN-DFT adjustments to LDA-based values and μ* in the 0.1–0.15 range (μ*=0.15 used for reported Tc). Symmetry analyses use FINDSYM and ISODISTORT.

- SCAN-DFT accurately reproduces insulating SrBiO3 with Eg ≈ 0.48 eV and structural parameters close to experiment; the breathing mode Boc amplitude is underestimated by ~10% relative to experiment. - In the undistorted cubic reference, both octahedral rotations and the breathing mode exhibit double-well PES, indicating intrinsic instabilities; rotations enhance and stabilize Boc via trilinear-like couplings, increasing its amplitude and energy gain. - Low hole doping (x=0.0625–0.125): a semiconducting state forms with intermediate acceptor states in the gap (Eg ~0.25 eV at x=0.0625); holes localize as a bipolaron on a Bi site, shortening local Bi–O bonds to ~2.16 Å vs ~2.30 Å elsewhere, akin to Bi5+. - Miscibility: Calculations predict limited K miscibility in the SrBiO3 P21/n framework; a biphasic SrBiO3+KBiO3 solution is more stable than single-phase Sr1−xKxBiO3 for 0.65 ≤ x < 1, consistent with experimental synthesis limits (x ≲ 0.6). A strong stability window exists for 0.4 < x < 0.6. - Insulator–metal transition: For x=0.1875–0.375 the system is metallic but retains electronic asymmetry and small band gaps due to residual Boc; for x ≥ 0.4375 (up to 0.625) Boc vanishes, Bi sites become equivalent, and the band structure shows a single broad parabola centered at Γ with no residual gaps. - Doping suppresses the intrinsic disproportionation instability (Boc shows single-well PES with increasing stiffness as x increases). However, coupling to rotations can temporarily stabilize Boc up to x≈0.375; beyond x≥0.4375 rotations are too small, and Boc remains unstable only at zero amplitude. - Superconductivity prerequisite: The superconducting composition range (experimentally x≈0.45–0.6) coincides with the regime where Boc is on the verge of stabilization (soft mode, a_eff ≈ 0) but has zero equilibrium amplitude; proximity to the disproportionated phase is essential. - Superconducting quantities at x≈0.4375: ωBoc ≈ 66 meV (experiment: ~62 meV in BaBiO3); REPME D ≈ 11.7 eV/Å (improved over GGA ~7.8 eV/Å; comparable to HSE06 ~11 eV/Å and GW ~13.7 eV/Å). D increases linearly with x. - EPC and Tc: Using computed N(EF), ωBoc, and D, λ ≈ 1.03–1.24 for 0.4375 < x < 0.625, matching experimental λ ≈ 1.3 ± 0.2. Estimated Tc ≈ 25–33 K for μ* = 0.15, in line with observed Tc up to ~34 K. With increasing x, ωBoc hardens and N(EF) decreases, but rising D compensates, keeping Tc roughly constant. - Mechanism: K doping primarily tunes steric tolerance factor, reducing octahedral rotations and thereby suppressing Boc stabilization; BaBiO3 (larger tolerance factor) requires smaller K content to reach superconductivity, consistent with experiments.

The simulations show that SCAN-DFT, without adjustable correlation parameters, captures the evolution from an insulating, bond-disproportionated state to a metallic and superconducting regime upon K doping in SrBiO3. The key finding is that superconductivity emerges when the breathing distortion is softened and near instability but has zero equilibrium amplitude; its vibrations, enhanced by coupling with octahedral rotation modes, can generate spin-paired electron–hole states (Cooper pairs). This resolves the mechanism in terms of strong electron–phonon coupling dominated by the Boc mode rather than invoking universally strong electron correlations. The calculated EPC (λ ~1.0–1.24), Boc frequency (~66 meV), density of states, and Tc (25–33 K) align with experimental data, validating the approach. The work highlights that structural mode couplings govern electronic instabilities and pairing strength, and that steric tuning via A-site substitution controls the proximity to the disproportionated phase, setting the superconducting dome boundaries. The near-constant Tc across the superconducting region arises from compensating trends: D increases with x while N(EF) and 1/ω contributions decrease, underscoring the need to evaluate superconducting parameters at each doping rather than extrapolating from a single composition.

This study demonstrates that parameter-free SCAN-DFT accurately reproduces structural, electronic, and superconducting properties of hole-doped SrBiO3 across doping, including the insulator-to-metal transition, polaronic states at low x, limited K miscibility, and superconducting EPC and Tc in the optimal doping range. The mechanism centers on the breathing-mode (Boc) lattice instability and its coupling to octahedral rotations: superconductivity appears when the system lies near, but not within, the disproportionated phase. These insights suggest a general paradigm for oxide superconductors where proximity to charge/bond order and specific lattice mode couplings are prerequisites for strong EPC and pairing. Future work should pursue full electron–phonon calculations including all phonon branches in disordered supercells when computationally feasible, and investigate analogous disproportionation-driven mechanisms in nickelates and other complex oxides to test the universality of this scenario.

- Full first-principles electron–phonon calculations including all phonon modes are not feasible for the large, disordered 32-formula-unit supercells; superconducting parameters are estimated from the dominant Boc mode and model corrections to ωlog. - The Boc amplitude in the SCAN-DFT bulk is underestimated by ~10% relative to experiment, potentially shifting the predicted superconducting onset to slightly lower x than measured. - Approximations include treating Bi d states as core in PAW potentials, finite k-point sampling, and reliance on frozen-phonon PES fits for frequencies. - Only the low-temperature P21/n-derived structures are considered as starting points; potential alternative phases or local motifs at high doping may be missed. - Tc estimates depend on assumed μ* (here 0.15) and on mapping SCAN corrections onto LDA-derived ωlog. - Alloy disorder is represented by SQS within a finite supercell, which may not capture all long-range configurational effects.