Superconducting phase diagram of itinerant antiferromagnets

We study the phase diagram of the Hubbard model in the weak-coupling limit for coexisting spin-density-wave order and spin-fluctuation-mediated superconductivity. Both longitudinal and transverse spin fluctuations contribute significantly to the effective interaction potential, which creates Cooper pairs of the quasi-particles of the antiferromagnetic metallic state. We find a dominant $d_{x^2-y^2}$-wave solution in both electron- and hole-doped cases. In the quasi-spin triplet channel, the longitudinal fluctuations give rise to an effective attraction supporting a $p$-wave gap, but are overcome by repulsive contributions from the transverse fluctuations which disfavor $p$-wave pairing compared to $d_{x^2-y^2}$. The sub-leading pair instability is found to be in the $g$-wave channel, but complex admixtures of $d$ and $g$ are not energetically favored since their nodal structures coincide. Inclusion of interband pairing, in which each fermion in the Cooper pair belongs to a different spin-density-wave band, is considered for a range of electron dopings in the regime of well-developed magnetic order. We demonstrate that these interband pairing gaps, which are non-zero in the magnetic state, must have the same parity under inversion as the normal intraband gaps. The self-consistent solution to the full system of five coupled gap equations give intraband and interband pairing gaps of $d_{x^2-y^2}$ structure and similar gap magnitude. In conclusion, the $d_{x^2-y^2}$ gap dominates for both hole and electron doping inside the spin-density-wave phase.Comment: 14 pages, 9 figure

Local modulations of the spin-fluctuation mediated pairing interaction by impurities in d-wave superconductors

We present a self-consistent real space formulation of spin-fluctuation mediated d-wave pairing. By calculating all relevant inhomogeneous spin and charge susceptibilities in real space within the random phase approximation (RPA), we obtain the effective pairing interaction and study its spatial dependence near both local potential and hopping impurities. A remarkably large enhancement of the pairing interaction may be obtained near the impurity site. We discuss the relevance of our result to inhomogeneities observed by scanning tunneling spectroscopy on the surface of cuprate superconductors.Comment: 8 pages, 7 figure

Interpretation of scanning tunneling quasiparticle interference and impurity states in cuprates

We apply a recently developed method combining first principles based Wannier functions with solutions to the Bogoliubov-de Gennes equations to the problem of interpreting STM data in cuprate superconductors. We show that the observed images of Zn on the surface of Bi$_2$Sr$_2$CaCu$_2$O$_8$ can only be understood by accounting for the tails of the Cu Wannier functions, which include significant weight on apical O sites in neighboring unit cells. This calculation thus puts earlier crude "filter" theories on a microscopic foundation and solves a long standing puzzle. We then study quasiparticle interference phenomena induced by out-of-plane weak potential scatterers, and show how patterns long observed in cuprates can be understood in terms of the interference of Wannier functions above the surface. Our results show excellent agreement with experiment and enable a better understanding of novel phenomena in the cuprates via STM imaging.Comment: 5 pages, 5 figures, published version (Supplemental Material: 5 pages, 11 figures) for associated video file, see http://itp.uni-frankfurt.de/~kreisel/QPI_BSCCO_BdG_p_W.mp

Knight Shift and Leading Superconducting Instability From Spin Fluctuations in Sr2RuO4

Recent nuclear magnetic resonance studies [A. Pustogow {\it et al.}, arXiv:1904.00047] have challenged the prevalent chiral triplet pairing scenario proposed for Sr$_2$RuO$_4$. To provide guidance from microscopic theory as to which other pair states might be compatible with the new data, we perform a detailed theoretical study of spin-fluctuation mediated pairing for this compound. We map out the phase diagram as a function of spin-orbit coupling, interaction parameters, and band-structure properties over physically reasonable ranges, comparing when possible with photoemission and inelastic neutron scattering data information. We find that even-parity pseudospin singlet solutions dominate large regions of the phase diagram, but in certain regimes spin-orbit coupling favors a near-nodal odd-parity triplet superconducting state, which is either helical or chiral depending on the proximity of the $\gamma$ band to the van Hove points. A surprising near-degeneracy of the nodal $s^\prime$- and $d_{x^2-y^2}$-wave solutions leads to the possibility of a near-nodal time-reversal symmetry broken $s^\prime+id_{x^2-y^2}$ pair state. Predictions for the temperature dependence of the Knight shift for fields in and out of plane are presented for all states.Comment: 5 pages (3 figures) + supplementary informatio

Pairing symmetry of the one-band Hubbard model in the paramagnetic weak-coupling limit: a numerical RPA study

We study the spin-fluctuation-mediated superconducting pairing gap in a weak-coupling approach to the Hubbard model for a two dimensional square lattice in the paramagnetic state. Performing a comprehensive theoretical study of the phase diagram as a function of filling, we find that the superconducting gap exhibits transitions from p-wave at very low electron fillings to d_{x^2-y^2}-wave symmetry close to half filling in agreement with previous reports. At intermediate filling levels, different gap symmetries appear as a consequence of the changes in the Fermi surface topology and the associated structure of the spin susceptibility. In particular, the vicinity of a van Hove singularity in the electronic structure close to the Fermi level has important consequences for the gap structure in favoring the otherwise sub-dominant triplet solution over the singlet d-wave solution. By solving the full gap equation, we find that the energetically favorable triplet solutions are chiral and break time reversal symmetry. Finally, we also calculate the detailed angular gap structure of the quasi-particle spectrum, and show how spin-fluctuation-mediated pairing leads to significant deviations from the first harmonics both in the singlet d_{x^2-y^2} gap as well as the chiral triplet gap solution.Comment: 11 pages 11 figure

Role of the impurity-potential range in disordered d-wave superconductors

We analyze how the range of disorder affects the localization properties of quasiparticles in a two-dimensional d-wave superconductor within the standard non-linear sigma-model approach to disordered systems. We show that for purely long-range disorder, which only induces intra-node scattering processes, the approach is free from the ambiguities which often beset the disordered Dirac-fermion theories, and gives rise to a Wess-Zumino-Novikov-Witten action leading to vanishing density of states and finite conductivities. We also study the crossover induced by internode scattering due to a short range component of the disorder, thus providing a coherent non-linear sigma-model description in agreement with all the various findings of different approaches.Comment: 38 pages, 1 figur

Infrared conductivity of a d_{x^2-y^2}-wave superconductor with impurity and spin-fluctuation scattering

Calculations are presented of the in-plane far-infrared conductivity of a d_{x^2-y^2}-wave superconductor, incorporating elastic scattering due to impurities and inelastic scattering due to spin fluctuations. The impurity scattering is modeled by short-range potential scattering with arbitrary phase shift, while scattering due to spin fluctuations is calculated within a weak-coupling Hubbard model picture. The conductivity is characterized by a low-temperature residual Drude feature whose height and weight are controlled by impurity scattering, as well as a broad peak centered at 4 Delta_0 arising from clean-limit inelastic processes. Results are in qualitative agreement with experiment despite missing spectral weight at high energies.Comment: 29 pages (11 tar-compressed-uuencoded Postscript figures), REVTeX 3.0 with epsf macro

Gap Renormalization in Dirty Anisotropic Superconductors: Implications for the Order Parameter of the Cuprates

We contrast the effects of non-magnetic impurities on the properties of superconductors having a \dw\ order parameter, and a highly anisotropic s-wave (ASW) gap with the same nodal structure. The non-vanishing, impurity induced, off-diagonal self-energy in the ASW state is shown to gap out the low energy excitations present in the clean system, leading to a qualitatively different impurity response of the single particle density of states compared to the \dw\ state. We discuss how this behaviour can be employed to distinguish one state from the other by an analysis of high-resolution angle-resolved photoemission spectra.Comment: 12 pages, uuencoded Postscrip