Impurity scattering and localization in dd-wave superconductors

Strong evidence is presented for the localization of low energy quasiparticle states in disordered $d$-wave superconductors. Within the framework of the Bogoliubov-de Gennes (BdG) theory applied to the extended Hubbard model with a finite concentration of non-magnetic impurities, we carry out a fully self-consistent numerical diagonalization of the BdG equations on finite clusters containing up to $50\times 50$ sites. Localized states are identified by probing their sensitivity to the boundary conditions and by analyzing the finite size dependence of inverse participation ratios.Comment: 4 pages REVTeX with 2 embedded .ps figures; submitted to PRB as Rapid Communicatio

Polar Kerr Effect as Probe for Time-Reversal Symmetry Breaking in Unconventional Superconductors

The search for broken time reversal symmetry (TRSB) in unconventional superconductors intensified in the past year as more systems have been predicted to possess such a state. Following our pioneering study of TRSB states in Sr$_2$RuO$_4$ using magneto-optic probes, we embarked on a systematic study of several other of these candidate systems. The primary instrument for our studies is the Sagnac magneto-optic interferometer, which we recently developed. This instrument can measure magneto-optic Faraday or Kerr effects with an unprecedented sensitivity of 10 nanoradians at temperatures as low as 100 mK. In this paper we review our recent studies of TRSB in several systems, emphasizing the study of the pseudogap state of high temperature superconductors and the inverse proximity effect in superconductor/ferromagnet proximity structures.Comment: A review pape

Proximity Effect and Josephson Coupling in the SO(5) Theory of High-Tc Superconductivity

We consider proximity effect coupling in Superconducting/Antiferromagnetic/Superconducting (S-A-S) sandwiches using the recently developed SO(5) effective theory of high temperature superconductivity. We find that, for narrow junctions, the A region acts like a strong superconductor, and that there is a critical junction thickness which depends on the effective SO(5) coupling constants and on the phase difference across the junction, at which the A region undergoes a Freedericksz-like transition to a state which is intermediate between superconductor and antiferromagnet. For thick junctions, the current-phase relation is sinusoidal, as in standard S-N-S and S-I-S junctions, but for thin junctions it shows a sharp break in slope at the Freedericksz point.Comment: 4 pages, LATEX, 5 eps fig

Is Sr2RuO4 a Chiral P-Wave Superconductor?

Much excitement surrounds the possibility that strontium ruthenate exhibits chiral p-wave superconducting order. Such order would be a solid state analogue of the A phase of He-3, with the potential for exotic physics relevant to quantum computing. We take a critical look at the evidence for such time-reversal symmetry breaking order. The possible superconducting order parameter symmetries and the evidence for and against chiral p-wave order are reviewed, with an emphasis on the most recent theoretical predictions and experimental observations. In particular, attempts to reconcile experimental observations and theoretical predictions for the spontaneous supercurrents expected at sample edges and domain walls of a chiral p-wave superconductor and for the polar Kerr effect, a key signature of broken time-reversal symmetry, are discussed.Comment: To appear in the proceedings of LT25 (Amsterdam, August 2008

Microwave Conductivity due to Impurity Scattering in a d-wave Superconductor

The self-consistent t-matrix approximation for impurity scattering in unconventional superconductors is used to interpret recent measurements of the temperature and frequency dependence of the microwave conductivity of YBCO crystals below 20K. In this theory, the conductivity is expressed in terms of a fequency dependent single particle self-energy, determined by the impurity scattering phase shift which is small for weak (Born) scattering and approaches $\pi / 2$ for unitary scattering. Inverting this process, microwave conductivity data are used to extract an effective single-particle self-energy and obtain insight into the nature of the operative scattering processes. It is found that the effective self-energy is well approximated by a constant plus a linear term in frequency with a small positive slope for thermal quasiparticle energies below 20K. Possible physical origins of this form of self-energy are discussed.Comment: 5 pages, 4 figure

GINZBURG-LANDAU THEORY OF VORTICES IN dd-WAVE SUPERCONDUCTORS

Ginzburg-Landau theory is used to study the properties of single vortices and of the Abrikosov vortex lattice in a $d_{x^2-y^2}$ superconductor. For a single vortex, the $s$-wave order parameter has the expected four-lobe structure in a ring around the core and falls off like $1/r^2$ at large distances. The topological structure of the $s$-wave order parameter consists of one counter-rotating unit vortex, centered at the core, surrounded by four symmetrically placed positive unit vortices. The Abrikosov lattice is shown to have a triangular structure close to $T_c$ and an oblique structure at lower temperatures. Comparison is made to recent neutron scattering data.Comment: 4 pages, REVTeX, 3 figures available upon reques