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Real-space pairing and formation of Fermi—Bose mixture in BaBiO3-based family of superconducting oxides

Aleksei P. Menushenkov, M. Yu. Kagan

Published Sep 1, 2025• 0 citations
Publisher

Abstract

Recently, using X-ray free-electron laser radiation, the first direct experimental evidence of the existence of a realspace paired state of charge carriers was obtained in the parent compound BaBiO 3 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 1Àx K x BiO 3 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.

DOI
10.3367/ufne.2025.09.040028

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Real-space pairing and formation of Fermi—Bose mixture in BaBiO3-based family of superconducting oxides

Aleksei P. Menushenkov, M. Yu. Kagan

³ÑÆÇÓÉÂÐËÇ 1. £ÄÇÆÇÐËÇ (28).2. ¡ÐÑÏÂÎßÐÞÇ ÔÄÑÌÔÕÄ ÔÇÏÇÌÔÕÄ ÄÞÔÑÍÑÕÇÏÒÇÓÂÕÖÓÐÞØ ÔÄÇÓØÒÓÑ-ÄÑÆÐËÍÑÄ Ð ÑÔÐÑÄÇ BaBiO 3 (30).3. °ÔÑÃÇÐÐÑÔÕË ÎÑÍÂÎßÐÑÌ àÎÇÍÕÓÑÐÐÑÌ Ë ÍÓËÔÕÂÎÎËÚÇÔÍÑÌ ÔÕÓÖÍÕÖ-ÓÞ Ba 1Àx K x BiO 3 (32).4. ±ÓâÏÑÇ àÍÔÒÇÓËÏÇÐÕÂÎßÐÑÇ ÆÑÍÂÊÂÕÇÎßÔÕÄÑ ËÔØÑÆÐÑ ÔÒÂÓÇÐÐÑÅÑ ÔÑÔÕÑâÐËâ ÐÑÔËÕÇÎÇÌ ÊÂÓâÆÂ Ä BaBiO 3 (33).5. ®ÇØÂÐËÊÏ ÆËÔÒÓÑÒÑÓÙËÑÐËÓÑÄÂÐËâ Bi6sëO2p-ÔÄâÊË Ë ÒÓËÓÑÆ ÔÒÂ-ÓËÄÂÐËâ Ä BaBiO 3 (38).6. °ÃÓÂÊÑÄÂÐËÇ ×ÇÓÏË-ÃÑÊÇ ÔÏÇÔË Ä Ba 1Àx K x BiO 3 (41).7. ®ÇØÂÐËÊÏ ÔÄÇÓØÒÓÑÄÑÆËÏÑÔÕË Ä Ba 1Àx K x BiO 3 РÑÔÐÑÄÇ ÏÑÆÇÎË ÒÓÑÔÕÓÂÐÔÕÄÇÐÐÑ ÓÂÊÆÇÎÈÐÐÑÌ ×ÇÓÏË-ÃÑÊÇ ÔÏÇÔË (42).8. ³ÓÂÄÐÇÐËÇ Ô ÍÖÒÓÂÕÂÏË (44).9. ©ÂÍÎáÚÇÐËÇ (45).³ÒËÔÑÍ ÎËÕÇÓÂÕÖÓÞ (45).ÜÇÎâÏË Ë ÃÑÊÑÐÐÑÅÑ ÏÇÕÂÎÎÂ, ÛÖÐÕËÓÑÄÂÐÐÑÅÑ ×ÇÓÏËÑÐÐÑÌ ÍÑÏÒÑÐÇÐÕÑÌ, Ë ÒÓËÄÑÆâÕÔâ àÍÔÒÇÓËÏÇÐÕÂÎßÐÞÇ ÆÑÍÂÊÂÕÇÎßÔÕÄ ÕÑÅÑ, ÚÕÑ ËÏÇÐÐÑ ÎÑÍÂÎßÐÑÇ ÔÒÂÓËÄÂÐËÇ àÎÇÍÕÓÑÐÑÄ Ë ÆÞÓÑÍ ÑÕÄÇÕÔÕÄÇÐÐÑ Ê ÔÑÄÑÍÖÒÐÑÔÕß ÑÔÐÑÄÐÞØ ÂÐÑÏÂÎßÐÞØ ÔÄÑÌÔÕÄ ÔÇÏÇÌÔÕÄ ÄËÔÏÖÕÂÕÑÄ.µÚËÕÞÄÂâ ÃÑÎßÛÑÇ ÍÑÎËÚÇÔÕÄÑ ÂÐÂÎÑÅËÌ Ä ÑÔÑÃÇÐÐÑÔÕâØ ÒÑÄÇÆÇÐËâ ÓÂÊÎËÚÐÞØ ÔÇÏÇÌÔÕÄ ÒÇÓÑÄÔÍËÕÐÞØ ÔÄÇÓØÒÓÑÄÑÆÐËÍÑÄ, ÏÞ ÒÑÎÂÅÂÇÏ, ÚÕÑ ÐÂÛ ÓÂÃÑÕ ÆÂÔÕ ÐÑÄÞÌ ËÏÒÖÎßÔ Í ÒÑÐËÏÂÐËá ÒÓËÓÑÆÞ ÄÞÔÑÍÑÕÇÏÒÇÓÂÕÖÓÐÑÌ ÔÄÇÓØÒÓÑÄÑÆËÏÑÔÕË Ä ÑÍÔËÆÂØ ÄËÔÏÖÕÂ Ë ÆÓÖÅËØ ÔÇÏÇÌÔÕÄÂØ, ÄÍÎáÚÂâ ÍÖÒÓÂÕÐÞÇ £´³±.

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The studies of a number of systems treated in terms of an inhomogeneous (spatially separated) Fermi–Bose mixture with superconducting clusters or droplets of the order parameter in a host medium with unpaired normal states are reviewed. A spatially separated Fermi–Bose mixture is relevant to superconducting Ba-KBiO3 bismuth oxides. Droplets of the order parameter can occur in thin films of a dirty metal, described in the framework of the strongly attractive two-dimensional Hubbard model at a low electron density with a clearly pronounced diagonal disorder. The Bose–Einstein condensate droplets are formed in mixtures and dipole gases with an imbalance in the densities of the Fermi and Bose components. The Bose–Einstein condensate clusters also arise at the center or at the periphery of a magnetic trap involving spin-polarized Fermi gases. Exciton and plasmon collapsing droplets can emerge in the presence of the exciton–exciton or plasmon–plasmon interaction. The plasmon contribution to the charge screening in MgB2 leads to the formation of spatially modulated inhomogeneous structures. In metallic hydrogen and metal hydrides, droplets can be formed in shock-wave experiments at the boundary of the first-order phase transition between the metallic and molecular phases. In a spatially separated Fermi–Bose mixture arising in an Aharonov–Bohm interference ring with a superconducting bridge in a topologically nontrivial state, additional Fano resonances may appear and collapse due to the presence of edge Majorana modes in the system.

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The studies of a number of systems treated in terms of an inhomogeneous (spatially separated) Fermi–Bose mixture with superconducting clusters or droplets of the order parameter in a host medium with unpaired normal states are reviewed. A spatially separated Fermi–Bose mixture is relevant to superconducting Ba-KBiO3 bismuth oxides. Droplets of the order parameter can occur in thin films of a dirty metal, described in the framework of the strongly attractive two-dimensional Hubbard model at a low electron density with a clearly pronounced diagonal disorder. The Bose–Einstein condensate droplets are formed in mixtures and dipole gases with an imbalance in the densities of the Fermi and Bose components. The Bose–Einstein condensate clusters also arise at the center or at the periphery of a magnetic trap involving spin-polarized Fermi gases. Exciton and plasmon collapsing droplets can emerge in the presence of the exciton–exciton or plasmon–plasmon interaction. The plasmon contribution to the charge screening in MgB2 leads to the formation of spatially modulated inhomogeneous structures. In metallic hydrogen and metal hydrides, droplets can be formed in shock-wave experiments at the boundary of the first-order phase transition between the metallic and molecular phases. In a spatially separated Fermi–Bose mixture arising in an Aharonov–Bohm interference ring with a superconducting bridge in a topologically nontrivial state, additional Fano resonances may appear and collapse due to the presence of edge Majorana modes in the system.

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Various BCS-like pairing theories are still invariably used to describe the unusual superconducting/superfluid states and properties of condensed matters without clarifying the fermionic or bosonic nature of Cooper pairs and the relevant mechanisms of superconductivity and superfluidity. We show that the bosonization of Cooper pairs and the novel superconductivity and superfluidity resulting from the condensation of an attractive Bose gas of Cooper pairs into a superfluid state in high-Tc cuprates and other exotic systems occur under the condition εF≲2εA (where εF is the Fermi energy, εA is the energy of the effective attraction between fermions). We argue that the simple BCS criterion (i.e. formation of an energy gap on the Fermi surface) is insufficient for the occurrence of unconventional superconductivity (superfluidity) and the superconducting/superfluid transition in attractive Bose systems is more λ-like than the usual Bose–Einstein condensation. The new and specific criteria for unconventional superconductivity and superfluidity are formulated. Mean-field theory of the three- and two-dimensional superfluid Bose condensates of Cooper pairs describes reasonably well the novel superconducting states (i.e., two distinct superconducting phases below the bulk superconducting transition temperature Tc and a vortex-like state above Tc) and properties (such as λ-like transition at Tc, first-order phase transition and gapless bosonic excitations somewhat below Tc or even far below Tc) of high-Tc cuprates in full agreement with the experimental findings. The unusual superconducting/superfluid states and properties of heavy-fermion and organic compounds, Sr2RuO4, 3He, 4He and atomic Fermi gases are explained more clearly by this theory.

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Electromagnetic properties of local pair superconductors

S. Robaszkiewicz, R. Micnas, T. Kostyrko

Recent experimental findings concerning the temperature-dependence of the penetration depth and strong empirical evidence for a universal 3D X – Y critical behaviour in several classes of high- T c superconductors suggest that Bose condensation of ‘weakly charged’ bosons can be a driving mechanism for the phase transition in extreme type II superconductors. We explore the occurence of analogous behaviour in a simple model of local electron pairs, which is that of hard-core charged bosons on a lattice. We examine the electromagnetic properties of the model in the superfiuid phase as a function of boson concentration and density–density interaction. In the low-density limit, with the use of the exact scattering length, we present new results for the ground state characteristics. The relevance of the obtained results to interpretation of experimental data on high- T c oxides is discussed. Introduction Some recent experimental results concerning temperature-dependence of the London penetration depth and empirical evidence for a universal 3D X – Y critical behaviour in several families of high- T c superconductors indicate that Bose condensation can be a driving mechanism for the phase transition in these extreme type II superconductors [1–3]. Motivated by these experimentally established universal trends, we examine the electromagnetic properties of the effective pseudo-spin model of the local pair superconductor, equivalent to a hard-core charged Bose gas on a lattice, for the case of arbitrary electron concentration n . From linear response theory, the current response is obtained and expressions for the paramagnetic and diamagnetic kernels are evaluated in the RPA (random phase approximation) and SWA (spin-wave approximation).

Cambridge University Press eBooks•Sep 7, 1995•0 citations
Recently, using X-ray free-electron laser radiation, the first direct experimental evidence of the existence of a realspace paired state of charge carriers was obtained in the parent compound BaBiO 3 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 1Àx K x BiO 3 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.
³ÑÆÇÓÉÂÐËÇ 1. £ÄÇÆÇÐËÇ (28).2. ¡ÐÑÏÂÎßÐÞÇ ÔÄÑÌÔÕÄ ÔÇÏÇÌÔÕÄ ÄÞÔÑÍÑÕÇÏÒÇÓÂÕÖÓÐÞØ ÔÄÇÓØÒÓÑ-ÄÑÆÐËÍÑÄ Ð ÑÔÐÑÄÇ BaBiO 3 (30).3. °ÔÑÃÇÐÐÑÔÕË ÎÑÍÂÎßÐÑÌ àÎÇÍÕÓÑÐÐÑÌ Ë ÍÓËÔÕÂÎÎËÚÇÔÍÑÌ ÔÕÓÖÍÕÖ-ÓÞ Ba 1Àx K x BiO 3 (32).4. ±ÓâÏÑÇ àÍÔÒÇÓËÏÇÐÕÂÎßÐÑÇ ÆÑÍÂÊÂÕÇÎßÔÕÄÑ ËÔØÑÆÐÑ ÔÒÂÓÇÐÐÑÅÑ ÔÑÔÕÑâÐËâ ÐÑÔËÕÇÎÇÌ ÊÂÓâÆÂ Ä BaBiO 3 (33).5. ®ÇØÂÐËÊÏ ÆËÔÒÓÑÒÑÓÙËÑÐËÓÑÄÂÐËâ Bi6sëO2p-ÔÄâÊË Ë ÒÓËÓÑÆ ÔÒÂ-ÓËÄÂÐËâ Ä BaBiO 3 (38).6. °ÃÓÂÊÑÄÂÐËÇ ×ÇÓÏË-ÃÑÊÇ ÔÏÇÔË Ä Ba 1Àx K x BiO 3 (41).7. ®ÇØÂÐËÊÏ ÔÄÇÓØÒÓÑÄÑÆËÏÑÔÕË Ä Ba 1Àx K x BiO 3 РÑÔÐÑÄÇ ÏÑÆÇÎË ÒÓÑÔÕÓÂÐÔÕÄÇÐÐÑ ÓÂÊÆÇÎÈÐÐÑÌ ×ÇÓÏË-ÃÑÊÇ ÔÏÇÔË (42).8. ³ÓÂÄÐÇÐËÇ Ô ÍÖÒÓÂÕÂÏË (44).9. ©ÂÍÎáÚÇÐËÇ (45).³ÒËÔÑÍ ÎËÕÇÓÂÕÖÓÞ (45).ÜÇÎâÏË Ë ÃÑÊÑÐÐÑÅÑ ÏÇÕÂÎÎÂ, ÛÖÐÕËÓÑÄÂÐÐÑÅÑ ×ÇÓÏËÑÐÐÑÌ ÍÑÏÒÑÐÇÐÕÑÌ, Ë ÒÓËÄÑÆâÕÔâ àÍÔÒÇÓËÏÇÐÕÂÎßÐÞÇ ÆÑÍÂÊÂÕÇÎßÔÕÄ ÕÑÅÑ, ÚÕÑ ËÏÇÐÐÑ ÎÑÍÂÎßÐÑÇ ÔÒÂÓËÄÂÐËÇ àÎÇÍÕÓÑÐÑÄ Ë ÆÞÓÑÍ ÑÕÄÇÕÔÕÄÇÐÐÑ Ê ÔÑÄÑÍÖÒÐÑÔÕß ÑÔÐÑÄÐÞØ ÂÐÑÏÂÎßÐÞØ ÔÄÑÌÔÕÄ ÔÇÏÇÌÔÕÄ ÄËÔÏÖÕÂÕÑÄ.µÚËÕÞÄÂâ ÃÑÎßÛÑÇ ÍÑÎËÚÇÔÕÄÑ ÂÐÂÎÑÅËÌ Ä ÑÔÑÃÇÐÐÑÔÕâØ ÒÑÄÇÆÇÐËâ ÓÂÊÎËÚÐÞØ ÔÇÏÇÌÔÕÄ ÒÇÓÑÄÔÍËÕÐÞØ ÔÄÇÓØÒÓÑÄÑÆÐËÍÑÄ, ÏÞ ÒÑÎÂÅÂÇÏ, ÚÕÑ ÐÂÛ ÓÂÃÑÕ ÆÂÔÕ ÐÑÄÞÌ ËÏÒÖÎßÔ Í ÒÑÐËÏÂÐËá ÒÓËÓÑÆÞ ÄÞÔÑÍÑÕÇÏÒÇÓÂÕÖÓÐÑÌ ÔÄÇÓØÒÓÑÄÑÆËÏÑÔÕË Ä ÑÍÔËÆÂØ ÄËÔÏÖÕÂ Ë ÆÓÖÅËØ ÔÇÏÇÌÔÕÄÂØ, ÄÍÎáÚÂâ ÍÖÒÓÂÕÐÞÇ £´³±.
In this review article we consider theoretically and give experimental support to the models of the Fermi-Bose mixtures and the BCS-BEC (Bardeen Cooper Schrieffer–Bose Einstein) crossover compared with the strong-coupling approach, which can serve as the cornerstones on the way from high-temperature to room-temperature superconductivity in pressurized metallic hydrides. We discuss some key theoretical ideas and mechanisms proposed for unconventional superconductors (cuprates, pnictides, chalcogenides, bismuthates, diborides, heavy-fermions, organics, bilayer graphene, twisted graphene, oxide hetero-structures), superfluids and balanced or imbalanced ultracold Fermi gases in magnetic traps. We build a bridge between unconventional superconductors and recently discovered pressurized hydrides superconductors H3S and LaH10 with the critical temperature close to room temperature. We discuss systems with a line of nodal Dirac points close to the Fermi surface and superconducting shape resonances, and hyperbolic superconducting networks which are very important for the development of novel topological superconductors, for the energetics, for the applications in nano-electronics and quantum computations.
The studies of a number of systems treated in terms of an inhomogeneous (spatially separated) Fermi–Bose mixture with superconducting clusters or droplets of the order parameter in a host medium with unpaired normal states are reviewed. A spatially separated Fermi–Bose mixture is relevant to superconducting Ba-KBiO3 bismuth oxides. Droplets of the order parameter can occur in thin films of a dirty metal, described in the framework of the strongly attractive two-dimensional Hubbard model at a low electron density with a clearly pronounced diagonal disorder. The Bose–Einstein condensate droplets are formed in mixtures and dipole gases with an imbalance in the densities of the Fermi and Bose components. The Bose–Einstein condensate clusters also arise at the center or at the periphery of a magnetic trap involving spin-polarized Fermi gases. Exciton and plasmon collapsing droplets can emerge in the presence of the exciton–exciton or plasmon–plasmon interaction. The plasmon contribution to the charge screening in MgB2 leads to the formation of spatially modulated inhomogeneous structures. In metallic hydrogen and metal hydrides, droplets can be formed in shock-wave experiments at the boundary of the first-order phase transition between the metallic and molecular phases. In a spatially separated Fermi–Bose mixture arising in an Aharonov–Bohm interference ring with a superconducting bridge in a topologically nontrivial state, additional Fano resonances may appear and collapse due to the presence of edge Majorana modes in the system.
The studies of a number of systems treated in terms of an inhomogeneous (spatially separated) Fermi–Bose mixture with superconducting clusters or droplets of the order parameter in a host medium with unpaired normal states are reviewed. A spatially separated Fermi–Bose mixture is relevant to superconducting Ba-KBiO3 bismuth oxides. Droplets of the order parameter can occur in thin films of a dirty metal, described in the framework of the strongly attractive two-dimensional Hubbard model at a low electron density with a clearly pronounced diagonal disorder. The Bose–Einstein condensate droplets are formed in mixtures and dipole gases with an imbalance in the densities of the Fermi and Bose components. The Bose–Einstein condensate clusters also arise at the center or at the periphery of a magnetic trap involving spin-polarized Fermi gases. Exciton and plasmon collapsing droplets can emerge in the presence of the exciton–exciton or plasmon–plasmon interaction. The plasmon contribution to the charge screening in MgB2 leads to the formation of spatially modulated inhomogeneous structures. In metallic hydrogen and metal hydrides, droplets can be formed in shock-wave experiments at the boundary of the first-order phase transition between the metallic and molecular phases. In a spatially separated Fermi–Bose mixture arising in an Aharonov–Bohm interference ring with a superconducting bridge in a topologically nontrivial state, additional Fano resonances may appear and collapse due to the presence of edge Majorana modes in the system.
Various BCS-like pairing theories are still invariably used to describe the unusual superconducting/superfluid states and properties of condensed matters without clarifying the fermionic or bosonic nature of Cooper pairs and the relevant mechanisms of superconductivity and superfluidity. We show that the bosonization of Cooper pairs and the novel superconductivity and superfluidity resulting from the condensation of an attractive Bose gas of Cooper pairs into a superfluid state in high-Tc cuprates and other exotic systems occur under the condition εF≲2εA (where εF is the Fermi energy, εA is the energy of the effective attraction between fermions). We argue that the simple BCS criterion (i.e. formation of an energy gap on the Fermi surface) is insufficient for the occurrence of unconventional superconductivity (superfluidity) and the superconducting/superfluid transition in attractive Bose systems is more λ-like than the usual Bose–Einstein condensation. The new and specific criteria for unconventional superconductivity and superfluidity are formulated. Mean-field theory of the three- and two-dimensional superfluid Bose condensates of Cooper pairs describes reasonably well the novel superconducting states (i.e., two distinct superconducting phases below the bulk superconducting transition temperature Tc and a vortex-like state above Tc) and properties (such as λ-like transition at Tc, first-order phase transition and gapless bosonic excitations somewhat below Tc or even far below Tc) of high-Tc cuprates in full agreement with the experimental findings. The unusual superconducting/superfluid states and properties of heavy-fermion and organic compounds, Sr2RuO4, 3He, 4He and atomic Fermi gases are explained more clearly by this theory.
Recent experimental findings concerning the temperature-dependence of the penetration depth and strong empirical evidence for a universal 3D X – Y critical behaviour in several classes of high- T c superconductors suggest that Bose condensation of ‘weakly charged’ bosons can be a driving mechanism for the phase transition in extreme type II superconductors. We explore the occurence of analogous behaviour in a simple model of local electron pairs, which is that of hard-core charged bosons on a lattice. We examine the electromagnetic properties of the model in the superfiuid phase as a function of boson concentration and density–density interaction. In the low-density limit, with the use of the exact scattering length, we present new results for the ground state characteristics. The relevance of the obtained results to interpretation of experimental data on high- T c oxides is discussed. Introduction Some recent experimental results concerning temperature-dependence of the London penetration depth and empirical evidence for a universal 3D X – Y critical behaviour in several families of high- T c superconductors indicate that Bose condensation can be a driving mechanism for the phase transition in these extreme type II superconductors [1–3]. Motivated by these experimentally established universal trends, we examine the electromagnetic properties of the effective pseudo-spin model of the local pair superconductor, equivalent to a hard-core charged Bose gas on a lattice, for the case of arbitrary electron concentration n . From linear response theory, the current response is obtained and expressions for the paramagnetic and diamagnetic kernels are evaluated in the RPA (random phase approximation) and SWA (spin-wave approximation).