Abstract:
It has been argued that inhomogeneity generally can enhance superconductivity in the cuprate high-Tc materials. To check the validity of this claim, we study d-wave superconductivity on the checkerboard Hubbard model on a square lattice using the Cellular Dynamical Mean Field theory method with an exact diagonalization solver at zero temperature. The d-wave order parameter is computed for various inhomogeneity levels over the entire doping range of interest in both strong and weak coupling regimes. At a given doping, the size of the d-wave order parameter manifests itself directly in the height of the coherence peaks and hence is an appropriate measure of the strength of superconductivity. The weak coupling results reveal a suppression of the order parameter in the presence of inhomogeneity for small to intermediate hole dopings, while it is enhanced for large dopings. In contrast, for strong coupling there is a monotonic decrease in the maximum amplitude of the superconducting order parameter with inhomogeneity over the entire doping range of interest. Furthermore, at moderately high inhomogeneity, the system undergoes a first-order transition from the superconducting to the normal state in the underdoped regime. In the overdoped regime, the change in the value of the superconducting order parameter correlates with the height of the lowest energy peak in the spectral weight of antiferromagnetic spin fluctuations, confirming the connection between antiferromagnetic fluctuations and d-wave superconductivity found in earlier studies on the homogeneous case. Our results are benchmarked by comparisons with numerically exact results on the checkerboard Hubbard ladder.

Abstract:
Many theoretical approaches find d-wave superconductivity in the prototypical one-band Hubbard model for high-temperature superconductors. At strong-coupling (U > W, where U is the on-site repulsion and W=8t the bandwidth) pairing is controlled by the exchange energy J=4t^2/U. One may then surmise, ignoring retardation effects, that near-neighbor Coulomb repulsion V will destroy superconductivity when it becomes larger than J, a condition that is easily satisfied in cuprates for example. Using Cellular Dynamical Mean-Field theory with an exact diagonalization solver for the extended Hubbard model, we show that pairing, at strong coupling, is preserved even when V>>J, as long as V

Abstract:
A phenomenological strong coupling model that has been used to analyze superconducting- insulator-superconducting (SIS) break junction experiments on optimal to overdoped Bi-2212 is modified to include a pseudogap. The calculated density of states and SIS conductances are compared with experimental data on the underdoped phase of Bi-2212

Abstract:
The Hubbard model on a square lattice is one of the most studied condensed-matter quantum problems.Here we find evidence that for intermediate $U/4t$ values and a hole-concentration range $x\in (x_c,x_*)$ the ground state of the Hubbard model on the square lattice perturbed by weak three-dimensional (3D) uniaxial anisotropy has long-range d-wave superconducting order. Here $t$ is the effective nearest-neighbor transfer integral and $U$ the effective on-site repulsion. The lower critical concentration $x_c$ involves the Ginzburg number Gi and is approximately given by $x_c\approx {\rm Gi}+x_0\approx 0.05$. Here $x_0<{\rm Gi}$ is a small critical hole concentration that marks a sharp quantum phase transition from a Mott-Hubbard insulator with long-range antiferromagnetic order for $x

Abstract:
It is expected that at weak to intermediate coupling, d-wave superconductivity can be induced by antiferromagnetic fluctuations. However, one needs to clarify the role of Fermi surface topology, density of states, pseudogap, and wave vector of the magnetic fluctuations on the nature and strength of the induced d-wave state. To this end, we study the generalized phase diagram of the two-dimensional half-filled Hubbard model as a function of interaction strength $U/t$, frustration induced by second-order hopping $t^{\prime}/t$, and temperature $T/t$. In experiment, $U/t$ and $t^{\prime}/t$ can be controlled by pressure. We use the two-particle self-consistent approach (TPSC), valid from weak to intermediate coupling. We first calculate as a function of $t^{\prime}/t$ and $U/t$ the temperature and wave vector at which the spin response function begins to grow exponentially.D-wave superconductivity in a half-filled band can be induced by such magnetic fluctuations at weak to intermediate coupling, but only if they are near commensurate wave vectors and not too close to perfect nesting conditions where the pseudogap becomes detrimental to superconductivity. For given $U/t$ there is thus an optimal value of frustration $t^{\prime}/t$ where the superconducting $T_c$ is maximum. The non-interacting density of states plays little role. The symmetry d$_{x^{2}-y^{2}}$ vs d$_{xy}$ of the superconducting order parameter depends on the wave vector of the underlying magnetic fluctuations in a way that can be understood qualitatively from simple arguments.

Abstract:
A century on from its discovery, a complete fundamental understanding of superconductivity is still missing. Considerable research efforts are currently devoted to elucidating mechanisms by which pairs of electrons can bind together through the mediation of a boson field different than the one associated to the vibrations of a crystal lattice. PuCoGa_5, a 5f-electron heavy-fermion superconductor with a record critical temperature T_c=18.5 K, is one of the many compounds for which the short-range, isotropic attraction provided by simple electron-phonon coupling does not appear as an adequate glue for electron pairing. Here, we report the results of point-contact spectroscopy measurements in single crystals of PuCoGa_5. Andreev reflection structures are clearly observed in the low-temperature spectra, and unambiguously prove that the paired superconducting electrons have wavefunction with the d-wave symmetry of a four-leaf clover. A straightforward analysis of the spectra provide the amplitude of the gap and its temperature dependence, \Delta(T). We obtain \Delta(T -> 0) = 5.1 \pm 0.3 meV and a gap ratio, 2\Delta/k_B T_c = 6.5 \pm 0.3, indicating that the compound is in the regime of strong electron-boson coupling. The gap value and its temperature dependence can be well reproduced within the Eliashberg theory for superconductivity if the spectral function of the mediating bosons has a spin-fluctuations-like shape, with a peak energy of 6.5 meV. Electronic structure calculations, combining the local density approximation with an exact diagonalization of the Anderson impurity model, provide a hint about the possible origin of the fluctuations.

Abstract:
We investigate the superfluid properties of d-wave pairing symmetry within the Extended Hubbard Model (EHM) in a magnetic field. We analyze the temperature and magnetic field dependencies of the order parameter. We find that in the two-dimensional case, the spatially homogeneous spin polarized superfluidity ($SC(P\neq0)$) is stable in the weak coupling limit, at T=0, as opposed to the s-wave pairing symmetry case in 2D. We construct the ground state phase diagrams both for fixed chemical potential ($\mu$) and electron concentration ($n$). Furthermore, we obtain the temperature vs. magnetic field and temperature vs. spin polarization phase diagrams.

Abstract:
We show that, at weak to intermediate coupling, antiferromagnetic fluctuations enhance d-wave pairing correlations until, as one moves closer to half-filling, the antiferromagnetically-induced pseudogap begins to suppress the tendency to superconductivity. The accuracy of our approach is gauged by detailed comparisons with Quantum Monte Carlo simulations. The negative pressure dependence of Tc and the existence of photoemission hot spots in electron-doped cuprate superconductors find their natural explanation within this approach.

Abstract:
We analyze the pairing instabilities for fermions on hexagonal lattices (both honeycomb and triangular ones) in a wide range of fermionic densities. We argue that for a generic doping in this range, superconductivity at weak coupling is of Kohn-Luttinger type, and, due to the presence of electronic interactions beyond on-site repulsion, is a threshold phenomenon, with superconductivity emerging only if the attraction generated by the Kohn-Luttinger mechanism exceeds the bare repulsion in some channel. For disconnected Fermi pockets, we predict that Kohn-Luttinger superconductivity, if it occurs, is likely to be $f$-wave. While the Kohn-Luttinger analysis is adequate over most of the doping range, a more sophisticated analysis is needed near Van Hove doping. We treat Van Hove doping using a parquet renormalization group, the equations for which we derive and analyze. Near this doping level, superconductivity is a universal phenomenon, arising from any choice of bare repulsive interactions. The strongest pairing instability is into a chiral $d-$wave state ($d+id$). At a truly weak coupling, the strongest competitor is a spin-density-wave instability, however, $d-$wave superconductivity still wins. Moreover, the feedback of the spin density fluctuations into the Cooper channel significantly enhances the critical temperature over the estimates of the Kohn Luttinger theory. We analyze renormalization group equations at stronger couplings and find that the main competitor to $d-$wave supoerconductivity away from weak coupling is actually ferromagnetism. We also discuss the effect of the edge fermions and show that they are unimportant in the asymptotic weak coupling limit, but may give rise to, e.g., a charge-density-wave order at moderate coupling strengths.