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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…
Using a functional renormalization group approach we study the zero temperature phase diagram of two-dimensional Bose-Fermi mixtures of ultra-cold atoms in optical lattices, in the limit when the velocity of bosonic condensate fluctuations…
Some materials can have the dispersionless parts in their electronic spectra. These parts are usually called flat bands and generate the corps of unusual physical properties of such materials. These flat bands are induced by the…
We study the superfluid phase of the one-band attractive Hubbard model of fermions as a prototype of a strongly correlated s-wave fermion superfluid on a lattice. We show that the collective mode spectrum of this superfluid exhibits, in…
We theoretically study the proximity effect and the inverse proximity effect in a topological insulator/iron-based superconductor heterostructure based on the microscopic model. The superconducting order parameter is self-consistently…
Effects of superconducting fluctuations on the Fulde-Ferrell (FF) state are discussed in a spatially isotropic three-dimensional superconductor under a magnetic field. For this system, Shimahara recently showed that within the…
We theoretically investigate strong-coupling properties of an ultracold Fermi gas in the BCS-BEC crossover regime in the non-equilibrium steady state, being coupled with two fermion baths. By developing a non-equilibrium strong-coupling…
We investigate the zero-temperature properties of a superfluid Bose-Fermi mixture by introducing a set of coupled Galilei-invariant nonlinear Schr\"odinger equations valid from weak-coupling to unitarity. The Bose dynamics is described by a…
Order parameters represent a fundamental resource to characterize quantum matter. We show that pair superfluids can be rigorously defined in terms of a nonlocal order parameter, named odd parity, which derivation is experimentally…
Multi-band superconductivity in topological semimetals are the paradigms of unconventional superconductors. Their exotic gap structures and topological properties have fascinated searching for material realizations and applications. In this…
Pair density waves and exotic superconductivity have long been of strong interest, and have attracted much recent attention. We present a joint theoretical and experimental exploration of possible signatures of fermion pairing with finite…
We investigate the finite-temperature superfluid behavior of ultracold atomic Fermi gases in quasi-two-dimensional Lieb lattices with a short-range attractive interaction, using a pairing fluctuation theory within the BCS-BEC crossover…
Most theoretical treatments of inhomogeneous superconductivity/fermionic superfluidity have been based on the Bogoliubov-deGennes equations (or, else, on their various simplified forms), which implement a standard mean-field decoupling in…
We demonstrate how solutions to quantum few-fermion scattering problems can be the point-of-departure of a new treatment of a generalized many-body wave function. Our focus is on a particular ansatz for the ground state wave function of a…
We investigate the effect exerted by spin-polarized fermions on the interaction between superfluid bosons for a Bose-Fermi mixture residing on an optical lattice, with particular emphasis on the possibility of an induced phase-separation.…
We study the two-dimensional Bose-Fermi mixture on square lattice at finite temperature by using the determinant quantum Monte Carlo method within the weakly interacting regime. Here we consider the attractive Bose-Hubbard model and free…
We study the phase fluctuations in the normal state of generic two-dimensional superconducting systems with s-wave pairing. The effect of phase fluctuations of the pairing fields can be dealt with perturbatively using disorder averaging,…
We study s-wave superconductivity in the two dimensional attractive Hubbard model in an applied magnetic field, assume the extreme Pauli limit, and examine the role of spatial fluctuations in the coupling regime corresponding to BCS-BEC…
Topological superconductors give rise to unconventional superconductivity, which is mainly characterized by the symmetry of the superconducting pairing amplitude. However, since the symmetry of the superconducting pairing amplitude is not…
In this article we review recent progress in the understanding of multiband superconductivity and its relationship to odd-frequency pairing. We begin our discussion by reviewing the emergence of odd-frequency pairing in a simple two-band…