D-wave pairing in the two-dimensional Hubbard model with low filling

The superconductivity of Sr2RuO4 under c-axis uniaxial stress

Applying in-plane uniaxial pressure to strongly correlated low-dimensional systems has been shown to tune the electronic structure dramatically. For example, the unconventional superconductor Sr₂RuO₄ can be tuned through a single Van Hove point, resulting in strong enhancement of both T_c and H_c2. Out-of-plane (c axis) uniaxial pressure is expected to tune the quasi-two-dimensional structure even more strongly, by pushing it towards two Van Hove points simultaneously. Here, we achieve a record uniaxial stress of 3.2 GPa along the c axis of Sr₂RuO₄. H_c2 increases, as expected for increasing density of states, but unexpectedly T_c falls. As a first attempt to explain this result, we present three-dimensional calculations in the weak interaction limit. We find that within the weak-coupling framework there is no single order parameter that can account for the contrasting effects of in-plane versus c-axis uniaxial stress, which makes this new result a strong constraint on theories of the superconductivity of Sr₂RuO₄.

In the superconductor Sr2RuO4, in-plane strain is known to enhance both the superconducting transition temperature Tc and upper critical field Hc2, but the effect of out-of-plane strain has not been studied. Here, the authors find that Hc2 is enhanced under out-of-plane strain, but Tc unexpectedly decreases.

Fermi-Bose Mixtures and BCS-BEC Crossover in High-Tc Superconductors

In this review article we consider theoretically and give experimental support to the models of the Fermi-Bose mixtures and the BCS-BEC (Bardeen Cooper Schrieffer–Bose Einstein) 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 a line of nodal Dirac points close to the Fermi surface and 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.

Superconducting fluctuations in the normal state of the two-dimensional Hubbard model

We compute the two-particle quantities relevant for superconducting correlations in the two-dimensional Hubbard model within the dynamical cluster approximation. In the normal state we identify the parameter regime in density, interaction, and second-nearest-neighbor hopping strength that maximizes the d_{x^{2}-y^{2}} superconducting transition temperature. We find in all cases that the optimal transition temperature occurs at intermediate coupling strength, and is suppressed at strong and weak interaction strengths. Similarly, superconducting fluctuations are strongest at intermediate doping and suppressed towards large doping and half filling. We find a change in sign of the vertex contributions to d_{xy} superconductivity from repulsive near half filling to attractive at large doping. p-wave superconductivity is not found at the parameters we study, and s-wave contributions are always repulsive. For negative second-nearest-neighbor hopping the optimal transition temperature shifts towards the electron-doped side in opposition to the van Hove singularity, which moves towards hole doping. We surmise that an increase of the local interaction of the electron-doped compounds would increase T_{c}.

Evaluation of the two-particle propagator for the Hubbard model with the help of the Hubbard-I approximation

The Hubbard-I approximation is generalized to allow for direct evaluation of the equal-time anomalous two-electron propagator for the Hubbard model on a two-dimensional square lattice. This propagator is compared against the quantum Monte Carlo data obtained by Aimi and Imada (2007 J. Phys. Soc. Japan 76 113708) in the limit of strong electron-electron interaction. The Hubbard-I predictions are in good qualitative agreement with the Monte Carlo results. In particular, d-wave correlations decay as cr( - 3) ('free-electron' behaviour) if the separation r exceeds 2-3 lattice constants. However, the Hubbard-I approximation underestimates the coefficient c by a factor of about 3. We conclude that the Hubbard-I approximation, despite its simplicity and artefacts, captures the qualitative behaviour of the two-particle propagator for the Hubbard model, at least for moderate values of r.