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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.
The effect of particle-hole fluctuations for the BCS-BEC crossover is investigated by use of functional renormalization. We compute the critical temperature for the whole range in the scattering length $a$. On the BCS side for small negative $a$ we r
The recent observation of quantum oscillations in underdoped high-Tc superconductors, combined with their negative Hall coefficient at low temperature, reveals that the Fermi surface of hole-doped cuprates includes a small electron pocket. This stron
We theoretically investigate the ground state of trapped neutral fermions with population imbalance in the BCS-BEC crossover regime. On the basis of the single-channel Hamiltonian, we perform full numerical calculations of the Bogoliubov-de Gennes eq
We study dynamic ground state properties in the crossover from weak (BCS) to strong coupling (BEC) superfluidity. Our approach is based on the attractive Hubbard model which is analyzed by the dynamical mean field theory (DMFT) combined with the nume
We present a theory of superconducting p-n junctions. We consider a 2-band model of doped bulk semiconductors with attractive interactions between the charge carriers and derive the superconducting order parameter, the quasiparticle density of states