Singular current response from isolated impurities in d-wave superconductors

The current response of a d-wave superconductor containing a single impurity is calculated and shown to be singular in the low-temperature limit, leading in the case of strong scattering to a 1/T term in the penetration depth $\lambda(T)$ similar to that induced by Andreev surface bound states. For a small number of such impurities, we argue this low-$T$ upturn could be observable in cuprate superconductors.Comment: 4 pages, 2 .eps figures. Minor changes to match the published versio

Cubic Curves, Finite Geometry and Cryptography

Some geometry on non-singular cubic curves, mainly over finite fields, is surveyed. Such a curve has 9,3,1 or 0 points of inflexion, and cubic curves are classified accordingly. The group structure and the possible numbers of rational points are also surveyed. A possible strengthening of the security of elliptic curve cryptography is proposed using a `shared secret' related to the group law. Cubic curves are also used in a new way to construct sets of points having various combinatorial and geometric properties that are of particular interest in finite Desarguesian planes.Comment: This is a version of our article to appear in Acta Applicandae Mathematicae. In this version, we have corrected a sentence in the third paragraph. The final publication is available at springerlink.com at http://www.springerlink.com/content/xh85647871215644

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

Residual absorption at zero temperature in d-wave superconductors

In a d-wave superconductor with elastic impurity scattering, not all the available optical spectral weight goes into the condensate at zero temperature, and this leads to residual absorption. We find that for a range of impurity parameters in the intermediate coupling regime between Born (weak) and unitary (strong) limit, significant oscillator strength remains which exhibits a cusp like behavior of the real part of the optical conductivity with upward curvature as a function of frequency, as well as a quasilinear temperature dependence of the superfluid density. The calculations offer an explanation of recent data on ortho-II YBa$_2$Cu$_3$O$_{6.5}$ which has been considered anomalous.Comment: Accepted for publication by Phys. Rev. B 7 Pages and 4 Figure

Optical conductivity in non-equilibrium d-wave superconductors

We consider the optical conductivity of a d-wave BCS superconductor in the presence of a non-equilibrium distribution of excess quasiparticles. Two different simplified models used in the past for the s-wave case are considered and results compared. In the $T^\ast$-model of Parker the excess quasiparticles are assumed to be in a thermal distribution at some temperature $T^\ast$ larger than the equilibrium sample temperature. In the $\mu^\ast$- model of Owen and Scalapino a chemical potential is introduced to accommodate the excess quasiparticles. Some of the results obtained are specific to the model, most are qualitatively similar in both.Comment: 11 pages, 6 figures this manuscript has been accepted for publication in abbreviated form by Physical Review

Spin fluctuations and superconductivity in a 3D tight-binding model for BaFe2As2

Despite the wealth of experimental data on the Fe-pnictide compounds of the KFe2As2-type, K = Ba, Ca, or Sr, the main theoretical work based on multiorbital tight-binding models has been restricted so far to the study of the related 1111 compounds. This can be ascribed to the more three dimensional electronic structure found by ab initio calculations for the 122 materials, making this system less amenable to model development. In addition, the more complicated Brillouin zone (BZ) of the body-centered tetragonal symmetry does not allow a straightforward unfolding of the electronic band structure into an effective 1Fe/unit cell BZ. Here we present an effective 5-orbital tight-binding fit of the full DFT band structure for BaFeAs including the kz dispersions. We compare the 5-orbital spin fluctuation model to one previously studied for LaOFeAs and calculate the RPA enhanced susceptibility. Using the fluctuation exchange approximation to determine the leading pairing instability, we then examine the differences between a strictly two dimensional model calculation over a single kz cut of the BZ and a completely three dimensional approach. We find pairing states quite similar to the 1111 materials, with generic quasi-isotropic pairing on the hole sheets and nodal states on the electron sheets at kz = 0 which however are gapped as the system is hole doped. On the other hand, a substantial kz dependence of the order parameter remains, with most of the pairing strength deriving from processes near kz = pi. These states exhibit a tendency for an enhanced anisotropy on the hole sheets and a reduced anisotropy on the electron sheets near the top of the BZ.Comment: 12 pages, 15 figure

Surface effects in multiband superconductors. Application to MgB2_2

Metals with many bands at the Fermi level can have different band dependent gaps in the superconducting state. The absence of translational symmetry at an interface can induce interband scattering and modify the superconducting properties. We dicuss the relevance of these effects to recent experiments in MgB$_2$

Impurity-Induced Quasiparticle Transport and Universal Limit Wiedemann-Franz Violation in d-Wave Superconductors

Due to the node structure of the gap in a d-wave superconductor, the presence of impurities generates a finite density of quasiparticle excitations at zero temperature. Since these impurity-induced quasiparticles are both generated and scattered by impurities, prior calculations indicate a universal limit (\Omega -> 0, T -> 0) where the transport coefficients obtain scattering-independent values, depending only on the velocity anisotropy v_f/v_2. We improve upon prior results, including the contributions of vertex corrections and Fermi liquid corrections in our calculations of universal limit electrical, thermal, and spin conductivity. We find that while vertex corrections modify electrical conductivity and Fermi liquid corrections renormalize both electrical and spin conductivity, only thermal conductivity maintains its universal value, independent of impurity scattering or Fermi liquid interactions. Hence, low temperature thermal conductivity measurements provide the most direct means of obtaining the velocity anisotropy for high T_c cuprate superconductors.Comment: 22 pages, 6 figures; revised version to be published in Phys Rev