We investigate the dynamical effects of pairing interaction on superconductivity in BCS-BEC crossover by studying the Holstein model at half filling where the electron-phonon coupling
g controls the crossover. The dynamical mean-field theory was employed in combination with the numerical renormalization group technique to study the frequency dependence of phonon mediated interaction between electrons in a superconductive state. The frequency dependence induces distinct features such as the absence of the dispersion back bending of Bogoliubov quasiparticles, nonmonotonous coupling dependence of the pairing gap, and the critical temperature
Tc being maximum at
gc1, the lower critical coupling of the normal state insulator to metal transition. Some of these features have intriguing similarities with the recent observations in the ${\mathrm{FeSe}}_{1\ensuremath{-}x}{\mathrm{S}}_{x}$ and ${\mathrm{Fe}}_{1+y}{\mathrm{Se}}_{x}{\mathrm{Te}}_{1\ensuremath{-}x}$ iron chalcogenides in the BCS-BEC crossover.
We investigate the emergence of the collective mode in the phonon spectra of the superconducting state within the Holstein model by varying the electron-phonon coupling. Using dynamical mean field theory combined with the numerical renormalization group technique, we calculate the phonon spectra. In the superconducting state with a pairing gap ( Δ P ), the peak position of the collective mode ( ω col ) evolves from the Bardeen-Cooper-Schrieffer (BCS) regime, manifesting near 2 Δ P and increasing with coupling, to the Bose-Einstein condensation (BEC) regime, where ω col decreases with increasing coupling. The decrease of ω col matches well with the reduction of superfluid stiffness, which originates from the increasing phase fluctuations of local pairs with coupling strength. In the crossover regime with intermediate coupling, ω col aligns with the soft phonon mode ( ω s ) of the normal state and decreases with increasing coupling when ω s < 2 Δ P . Additionally, comparing the collective mode weight to Δ P suggests that the collective mode predominantly stems from U(1) gauge symmetry breaking across all coupling strengths. Published by the American Physical Society 2024
We review the BCS–BEC crossover in relativistic Fermi systems, including the QCD matter at finite density. In the first part, we study the BCS–BEC crossover in a relativistic four-fermion interaction model and show how the relativistic effect affects the BCS–BEC crossover. In the second part, we investigate both two-color QCD at finite baryon density and pion superfluid at finite isospin density, by using an effective Nambu–Jona–Lasinio model. We will show how the model describes the weakly interacting diquark and pion condensates at low density and the BEC–BCS crossover at high density.