【DFT】超导性背后的机制：SCAN泛函揭示

超导电性是材料对直流电电阻为零、并能排除磁通量的一种状态。目前对于超导体形成背后的微观机制尚未得到澄清和统一，但镍基氧化物R_1-xSr_xNiO₂的发现为复杂氧化物中的超导理论提供了新的测试平台。Sr_1-xK_xBiO₃和Ba_1-xK_xBiO₃是理想的化合物，可用于测试第一性原理模拟技术，它们表现出氧化物的复杂性，并且是采用钙钛矿结构的氧化物超导体之一。

由法国诺曼底大学CRISMAT实验室的Julien Varignon博士研究表明，SCAN泛函足以捕捉在空穴掺杂时SrBiO₃从绝缘态到金属态的特性转变过程，并揭示超导现象背后的机制和先决条件。

Fig. 2 Ground state properties of SrBiO3.

作者通过将第一性原理DFT结果映射到涉及相关晶格畸变的Landau模型上，证明了产生绝缘相的根源是在块体基态中本征不稳定的Bi⁴⁺阳离子歧化成了Bi³⁺和Bi⁵⁺阳离子。该过程伴随产生B_oc这种呼吸模式的扭曲，其振幅被八面体旋转进一步增强。

在弱掺杂含量（x=0.0625~0.125）下，空穴被困在晶格上，中间态被局域在带隙中，最终材料形成了半导体。在中等掺杂含量（x = 0.1875~0.375）时，材料形成了金属相，然而由于呼吸模式与八面体旋转耦合，呼吸模式仍然存在于基态，尽管这种结构畸变本身并不愿意在材料中自发产生。这种模式的存在使费米能级附近的能带产生了一些小的带隙。而当掺杂量x=0.4375时，能带结构中不再有这些带隙，这个掺杂含量让人联想到实验报告的超导相（x=0.45-0.6）。在x≥0.4375附近，由于八面体旋转，呼吸模式在材料中趋于稳定，其振动可在材料中形成自旋配对的电子和空穴，即库珀对。

Fig. 4 Miscibility of K within the SrBiO3 structure.

因此，作者的结果表明，接近产生自旋电子和空穴的晶格不稳定性是铋酸盐超导性的先决条件，与实验观察到的超导相有界掺杂含量完全一致。在x=0.4375的超导相内，从模拟中提取了与呼吸模式B_oc相关的电子–声子耦合常数λ为1.22，B_oc频率为66 meV，与实验值（λ=1.3±0.2和ω=62 meV）非常一致。当掺杂量较大时，费米能级的态密度减小，呼吸模的频率升高；然而随着x的增加（上限为0.625），略为增加的还原电子–声子矩阵元中仍保留有非零Tc。

Fig. 5 Trends in electronic and structural properties upon hole doping SrBiO3.

因此，这项研究（i）验证了使用SCAN-DFT研究复杂氧化物超导体中的掺杂效应；（ii）要求检查超导镍酸盐和其他氧化物超导体中的歧化效应，以确定铋酸盐中已确定的机制是否也与这些新发现的氧化物超导体相关。该文近期发表于npj Computational Materials  9: 30 (2022)。

Editorial Summary

Superconductivity is a state in which a material has zero resistance to direct current and can discharge magnetic flux. The microscopic mechanism behind superconductor formation has not yet been clarified and unified, but the discovery of nickel-based oxides R_1-xSr_xNiO₂provides a new testbed for the theory of superconductivity in complex oxides.Sr_1-xK_xBiO₃and Ba_1-xK_xBiO₃ are ideal compounds for testing first-principles simulation techniques, they exhibit the complexity of oxides, and are one of the oxide superconductors using a chalcogenide structure. 

Dr. Julien Varignon from Laboratoire CRISMAT, Normandie Université, France, showed that the SCAN functional is sufficient to capture the trends in insulating to the metal character of SrBiO₃ upon hole doping and to reveal the mechanism and prerequisites behind the appearance of superconductivity. By mapping the first-principles DFT results on a Landau model involving the relevant lattice distortions, the insulating phase is shown to be reached by disproportionation effects associated with an intrinsic instability of Bi⁴⁺ cations to disproportionation to Bi³⁺/Bi⁵⁺cations in the bulk ground state. This is accompanied by a breathing mode distortion B_oc whose amplitude is further enhanced by the octahedra rotations. At weak doping content (x = 0.0625 to 0.125), holes are trapped on the lattice and intermediate states are localized in the band gap, ultimately resulting in a semiconducting behavior. At intermediate doping content (x = 0.1875 to 0.375), a metallic phase is reached but the breathing mode is still present in the ground state due to its coupling with octahedral rotations, despite the fact that the structural distortion alone is not willing to spontaneously pop up in the material. The presence of this mode induces small gaps in the bands dispersing around the Fermi level. No gaps are anymore identified in the band structure at x = 0.4375, a doping content reminiscent of the superconducting phase reported experimentally (x = 0.45–0.6). Around x ≥ 0.4375, the breathing mode is found on the verge of becoming stable in the material due to octahedral rotations and thus its vibration can form spin-paired electrons and holes in the material, i.e., Cooper pairs. These results thus suggest that the proximity of a lattice instability producing spin-paired electrons and holes is a prerequisite for superconductivity in the bismuthates, in sharp agreement with the bounded doping content observed experimentally for the superconducting phase. Within the superconducting phase at x = 0.4375, an electron-phonon coupling constant λ associated with the breathing mode B_oc of 1.22 and a B_oc frequency of 66 meV are extracted from the simulations, in sharp agreement with the experimental values (λ = 1.3 ± 0.2 and ω = 62 meV, respectively). At larger doping content, the breathing mode frequency becomes harder and the density of states at the Fermi level decreases but a slightly increased reduced electron-phonon matrix element with increasing x preserves a non-zero T_c up to x = 0.625. 

Their study thus (i) validates the use of SCAN-DFT for studying doping effects in complex oxide superconductors and (ii) calls for inspection of disproportionation effects in superconducting nickelates and other oxide superconductors to see if the identified mechanism in bismuthates is also relevant for these newly identified oxide superconductors. This article was recently published in npj Computational Materials 9: 30 (2022).

原文Abstract及其翻译

Origin of superconductivity in hole doped SrBiO₃bismuth oxide perovskite from parameter-free first-principles simulations (无参数第一性原理研究空穴掺杂SrBiO₃氧化铋钙钛矿超导性的起源)

Julien Varignon 

Abstract The recent discovery of nickel oxide superconductors have highlighted the importance of first-principles simulations for understanding the formation of the bound electrons at the core of superconductivity. Nevertheless, superconductivity in oxides is often ascribed to strong electronic correlation effects that density functional theory (DFT) cannot properly take into account, thereby disqualifying this technique. Being isostructural to nickel oxides, Sr_1-xK_xBiO₃ superconductors form an ideal testbed for unveiling the lowest theory level needed to model complex superconductors and the underlying pairing mechanism yielding superconductivity. Here I show that parameter-free DFT simulations capture all the experimental features and related quantities of Sr_1-xK_xBiO₃ superconductors, encompassing the prediction of an insulating to metal phase transition upon increasing the K doping content and of an electron-phonon coupling constant of 1.22 in sharp agreement with the experimental value of 1.3 ± 0.2. The proximity of a disproportionated phase is further demonstrated to be a prerequisite for superconductivity in bismuthates.

摘要最近发现的镍氧化物超导体凸显了第一原理模拟对于理解超导核心的束缚电子的形成的重要性。然而，氧化物中的超导性通常归因于强电子相关效应，而这种效应通常无法在密度泛函理论(DFT)的框架中准确模拟。Sr_1-xK_xBiO₃超导体与镍氧化物具有等结构，为揭示复杂超导体模型所需的最低理论水平以及产生超导性的潜在配对机制提供了理想的试验台。在这里，我展示了无参数DFT模拟捕获了Sr_1-xK_xBiO₃超导体的实验特性和相关量，包括在增加K含量时绝缘态到金属态的相变预测，以及与实验值为1.3±0.2完全一致的电子–声子耦合常数1.22。本工作还进一步证明了接近歧化相是形成铋酸盐超导性的先决条件。