Fermi-Bose mixtures and BCS-BEC crossover in high-Tc superconductors

Abstract

In this review article we consider theoretically and give experimental support to the models of the Fermi-Bose mixtures and the BCS-BEC 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 line of nodal Dirac points close to the Fermi surface, 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.

19 pages, 7 figures

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• Collective flow of fermionic impurities immersed in a Bose-Einstein Condensate
• Room temperature superconductivity dome at a Fano resonance in superlattices of wires
• High-Tc superconducting dome in artificial heterostructures made of nanoscale quantum building blocks
• High-$T$${}_{\text{C}}$ Superconductivity in Hydrogen Clathrates Mediated by Coulomb Interactions between Hydrogen and Central-Atom Electrons
• Formation of droplets of the order parameter and superconductivity in inhomogeneous Fermi-Bose mixtures (Brief review)
• Evaluating Superconductors through Current Induced Depairing
• Superconductivity in Quantum Complex Matter: the Superstripes Landscape
• Accelerating analysis of Boltzmann equations using Gaussian mixture models: Application to quantum Bose-Fermi mixtures