Recently, using X-ray free-electron laser radiation, the first direct experimental evidence of the existence of a real-space paired state of charge carriers was obtained in the parent compound BaBiO₃ of the bismuthate family of high-temperature superconductors (HTSCs), whose perovskite-like structure is similar to that of cuprate HTSCs. This confirmed the fundamental premises of our previously formulated model of a spatially separated Fermi—Bose mixture, implying a new, original mechanism for high-temperature superconductivity in bismuthates. In this review, we discuss the progress achieved with this model based on results obtained with an X-ray free-electron laser and go through details of the complete phase diagram of the superconducting and normal states in Ba_1-xK_xBiO₃ bismuth oxides at various potassium doping concentrations. We also discuss new, unique quantum states of matter in the form of a bosonic insulator (semiconductor) with initially paired charge carriers and two energy gaps, and a bosonic metal shunted by a fermionic component. We also provide experimental evidence that local pairing of electrons and holes is responsible for the set of the main anomalous properties of the bismuthate family. Given the numerous similarities in the behavioral patterns of various families of perovskite superconductors, we believe that our work will provide new impetus to understanding the nature of high-temperature superconductivity in bismuth oxides and other families, including cuprate HTSCs.

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Keywords: high-temperature superconductivity, perovskite structure, Fermi—Bose mixture, real-space pairing PACS: 41.60.Cr, 61.05.cj, 61.10.Ht, 71.45.Lr, 74.20.Mn, 74.25.Dw, 74.70.−b, 74.72.Cj, 78.47.+p (all) DOI: 10.3367/UFNe.2025.09.040028 URL: https://ufn.ru/en/articles/2026/1/c/ Citation: Menushenkov A P, Kagan M Yu "Real-space pairing and formation of Fermi—Bose mixture in BaBiO3-based family of superconducting oxides" Phys. Usp. 69 (1) (2026) Received: 8th, April 2025, revised: 5th, September 2025, accepted: 10th, September 2025 Оригинал: Менушенков А П, Каган М Ю «Спаривание в реальном пространстве и образование ферми-бозе смеси в семействе сверхпроводящих оксидов на основе BaBiO3» УФН 196 28–47 (2026); DOI: 10.3367/UFNr.2025.09.040028