Broken Time Reversal Symmetry and Superconducting States in the Cuprates

Recently, Kaminski et al. have reported that time reversal symmetry is broken in the pseudogap phase in the high temperature superconducting material Bi_2Sr_2CaCu_2O_{2+\delta} (Bi-2212). Here we examine the role of translationally invariant broken time reversal states on d_{x^2-y^2} superconductors. In particular, we determine the change in the superconducting order parameter structure. We find that the broken time reversal pseudogap state that is consistent with the experiment of Kaminski et al., gives rise to a novel mixed singlet-triplet pairing d+ip phase. This d+ip state is shown to give rise to a helical superconducting phase. Consequences of this d+ip state on Josephson experiments are discussed.Comment: 5 pages, 1 figur

Mixtures of multiplicative cascade models in geochemistry

International audienceMultifractal modeling of geochemical map data can help to explain the nature of frequency distributions of element concentration values for small rock samples and their spatial covariance structure. Useful frequency distribution models are the lognormal and Pareto distributions which plot as straight lines on logarithmic probability and log-log paper, respectively. The model of de Wijs is a simple multiplicative cascade resulting in discrete logbinomial distribution that closely approximates the lognormal. In this model, smaller blocks resulting from dividing larger blocks into parts have concentration values with constant ratios that are scale-independent. The approach can be modified by adopting random variables for these ratios. Other modifications include a single cascade model with ratio parameters that depend on magnitude of concentration value. The Turcotte model, which is another variant of the model of de Wijs, results in a Pareto distribution. Often a single straight line on logarithmic probability or log-log paper does not provide a good fit to observed data and two or more distributions should be fitted. For example, geochemical background and anomalies (extremely high values) have separate frequency distributions for concentration values and for local singularity coefficients. Mixtures of distributions can be simulated by adding the results of separate cascade models. Regardless of properties of background, an unbiased estimate can be obtained of the parameter of the Pareto distribution characterizing anomalies in the upper tail of the element concentration frequency distribution or lower tail of the local singularity distribution. Computer simulation experiments and practical examples are used to illustrate the approach

Quasi-classical determination of the in-plane magnetic field phase diagram of superconducting Sr_2RuO_4

We have carried out a determination of the magnetic-field-temperature (H-T) phase diagram for realistic models of the high field superconducting state of tetragonal Sr_2RuO_4 with fields oriented in the basal plane. This is done by a variational solution of the Eilenberger equations.This has been carried for spin-triplet gap functions with a {\bf d}-vector along the c-axis (the chiral p-wave state) and with a {\bf d}-vector that can rotate easily in the basal plane. We find that, using gap functions that arise from a combination of nearest and next nearest neighbor interactions, the upper critical field can be approximately isotropic as the field is rotated in the basal plane. For the chiral {\bf d}-vector, we find that this theory generically predicts an additional phase transition in the vortex state. For a narrow range of parameters, the chiral {\bf d}-vector gives rise to a tetracritical point in the H-T phase diagram. When this tetracritical point exists, the resulting phase diagram closely resembles the experimentally measured phase diagram for which two transitions are only observed in the high field regime. For the freely rotating in-plane {\bf d}-vector, we also find that additional phase transition exists in the vortex phase. However, this phase transition disappears as the in-plane {\bf d}-vector becomes weakly pinned along certain directions in the basal plane.Comment: 12 pages, 8 figure

Exotic ground states and impurities in multiband superconductors

We consider the effect of isotropic impurity scattering on the exotic superconducting states that arise from the usual BCS mechanism in substances of cubic and hexagonal symmetry where the Fermi surface contains inequivalent but degenerate pockets (e.g. around several points of high symmetry). As examples we look at CeCo$_2$, CeRu$_2$, and LaB$_6$; all of which have such Fermi surface topologies and the former exhibits unconventional superconducting behavior. We find that while these non s-wave states are suppressed by non-magnetic impurities, the suppression is much weaker than would be expected for unconventional superconductors with isotropic non-magnetic impurity scattering.Comment: 4 pages, no figure