Superconducting properties of some strongly correlated fermionic systems

Abstract

Throughout this thesis, we investigate the properties of some strongly correlated fermionic systems, focusing on the superconducting phase transitions and Charge ordering. In view of recent experiments with ultracold fermionic atoms in optical lattices, which have renewed interest in the study of the attractive Hubbard model (AHM), we have performed an extensive minus-sign–free Determinant Quantum Monte Carlo (DQMC) studies of this model on a square lattice. We have obtained a detailed phase diagram for the critical superconducting temperature, Tc, in terms of the band filling, ⟨n⟩, and interaction strength, U, from which we pinpoint a somewhat wide region |U|/t ≈ 5±1 (t is the hopping amplitude) and ⟨n⟩ ≈ 0.79±0.09 leading to a maximum Tc ≈ 0.16t. Two additional temperature scales, namely pairing, Tp, and degeneracy, Td, have been highlighted: the former sets the scale for pair formation (believed to be closely related to the scale for the gap of spin excitations in cuprates), while the latter sets the scale for dominant quantum effects. Our DQMC data for the distribution of doubly occupied sites, for the momentum distribution function, and for the quasiparticle weight show distinctive features on both sides of the BCS-BEC crossover, being also suggestive of an underlying crossover between Fermi- and non-Fermi liquid behaviors. However, the superconducting (superfluid) critical temperatures Tc’s are still somewhat smaller than the lowest temperatures achieved in experiments. We then analyze how superconductivity can be enhanced by layering, studying bilayer and three-dimensional cubic lattice geometries to identify conditions under which Tc increases. We have found that by a judicious choice of fillings and intensity of on-site attraction, a bilayer can exhibit Tc’s between 1.5 and 1.7 times those of the single layer; for the simple-cubic lattice the enhancement can be 30% larger than the maximum for the single layer. We also check the accuracy of both a BCS-like estimate for Tc in the attractive Hubbard model as well as of an upper bound for Tc based on the superfluid density. Additionally, we assess the role of next-nearest neighbor hopping, t′, in tuning the density of states at the Fermi level, which affects superconducting properties. Our results show that a judicious choice of t′ can increase Tc by up to 50% compared to the case with only nearest-neighbor hopping. In contrast, Tp decreases with increasing |t′/t|, which should represent a reduction of the pseudogap region, favoring a more BCS-like behavior at intermediate coupling. We further analyze the interacting density of states to characterize the transition from a pseudogap regime to a fully gapped superconducting state. These findings suggest that NNN hopping could be a viable route to increase Tc to values closer to experimentally accessible temperature scales. Finally, we investigate the impact of Rashba spin-orbit coupling on charge-ordered phases in a Holstein-like model on a square lattice at half-filling band, within a mean-field, cluster perturbation theory and DQMC approach. As result, we show that the ground state charge density wave phase is not destroyed when the Rashba spin-orbit coupling parameter α is increasing. In addition, in a pure Rasbha spin-orbit coupling regime, where the hopping parameter is absent, we found a rich phase diagram with semimetal for low values of electron-phonon coupling and consequent transition to change density wave states for high intensities of electron-phonon coupling. Furthermore, there is a coexistence of superconducting and charge density wave states for a high phonon frequency and electron-phonon coupling.