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arXiv:2508.17487 · Journal of Superconductivity and Novel Magnetism

Mechanisms of Superconductivity and Inhomogeneous States in Metallic Hydrogen and Electron Systems with Attraction

M. Yu. Kagan, A. V. Krasavin, R. Sh. Ikhsanov, E. A. Mazur, A. P. Menushenkov

Published Nov 24, 2025• 0 citations
arXivHTMLPDF
DOI
10.1007/s10948-025-07087-3

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In this short review, we first discuss the results, which are mainly devoted to the generalizations of the famous Kohn–Luttinger mechanism of superconductivity in purely repulsive fermion systems at low electron densities. In the context of repulsive-U Hubbard model and Shubin–Vonsovsky model we consider briefly the superconducting phase diagrams and the symmetries of the order parameter in novel strongly correlated electron systems including idealized monolayer and bilayer graphene. We stress that purely repulsive fermion systems are mainly the subject of unconventional low-temperature superconductivity. To get the high temperature superconductivity in cuprates (with T C of the order of 100 K) we should proceed to the t–J model with the van der Waals interaction potential and the competition between short-range repulsion and long-range attraction. Finally we note that to describe superconductivity in metallic hydrogen alloys under pressure (with T C of the order of 200 K) it is reasonable to reexamine more conventional mechanisms connected with electron–phonon interaction. These mechanisms arise in the attractive-U Hubbard model with static onsite or intersite attractive potential or in more realistic theories (which include retardation effects) such as Migdal–Eliashberg strong coupling theory or even Fermi–Bose mixture theory of Ranninger et al. and its generalizations.
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.