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

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

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

Theory of Thermal Conductivity in YBa_2Cu_3O_{7-\delta}

We calculate the electronic thermal conductivity in a d-wave superconductor, including both the effect of impurity scattering and inelastic scattering by antiferromagnetic spin fluctuations. We analyze existing experiments, particularly with regard to the question of the relative importance of electronic and phononic contributions to the heat current, and to the influence of disorder on low-temperature properties. We find that phonons dominate heat transport near T_c, but that electrons are responsible for most of the peak observed in clean samples, in agreement with a recent analysis of Krishana et al. In agreement with recent data on YBa_2(Cu_1-xZn_x)_3O_7-\delta the peak position is found to vary nonmonotonically with disorder.Comment: 4 pages, 4 figures, to be published in Phys. Rev. Let

Effect of electron irradiation on superconductivity in single crystals of Ba(Fe1−x_{1-x}Rux_{x})2_2As2_2 (x=x=0.24)

A single crystal of isovalently substituted Ba(Fe$_{1-x}$Ru$_{x}$)$_2$As$_2$ ($x=0.24$) was sequentially irradiated with 2.5 MeV electrons up to a maximum dose of $2.1 \times 10^{19}$ electrons/cm^2. The electrical resistivity was measured \textit{in - situ} at $T=$22 K during the irradiation and \textit{ex - situ} as a function of temperature between subsequent irradiation runs. Upon irradiation, the superconducting transition temperature, $T_c$, decreases and the residual resistivity, $\rho_0$, increases. We find that electron irradiation leads to the fastest suppression of $T_c$ compared to other types of artificially introduced disorder, probably due to the strong short-range potential of the point-like irradiation defects. A more detailed analysis within a multiband scenario with variable scattering potential strength shows that the observed $T_c$ vs. $\rho_0$ is fully compatible with $s_\pm$ pairing, in contrast to earlier claims that this model leads to a too rapid a suppression of $T_c$ with scattering

Anisotropic Optical Conductivity of Nd2-xCexCuO4 Thin Films

Opticcal conductivity spectra $\sigma_1(\omega)$ of Nd2-xCexCuO4 thin films, measured by the reflectance-transmittance method (R-T method) which has been proposed to investigate far-infrared spectroscopy, are investigated based on the anisotropic pairing model. Precise measurements of the frequency-dependent conductivity enable us to examine quantitatively the nature of the superconducting gap through infrared properties in the electron-doped high-Tc superconductors. We show that the behavior of optical conductivity $\sigma_1$ is consistent with the anisotropic superconducting gap and is well explained by the formula for d-wave pairing in the low-energy regime of the far-infrared region. Our results suggest that the electron-doped cuprate superconductors Nd2-xCexCuO4 have nodes in the superconducting gap.Comment: 4 pages, 3 figure

Finite Density of States in a Mixed State of d_x^2-y^2+id_xy Superconductor

We have calculated the density of states of quasiparticles in a d_x^2-y^2+id_xy superconductor, and show that in the mixed state the quasiparticle spectrum remains gapless because of the Doppler shift by superflow. It was found that if the d_{xy} order gap $\Delta_1\propto \sqrt{H}$ as suggested by experiments, then thermal conductivity $\kappa \propto \sqrt{H}$ in accord with experimental data at lowest temperatures. This is an appended version of the paper published in Phys. Rev. {\bf B 59}, 6024, (1999). We now also discuss the disorder effects and analyze the H log H crossover at small fields. We argue that H log H regime is present and disorder effect is dominant as the field-induced seconary gap is small at small fields.Comment: This is an appended version of the paper published in Phys. Rev. {\bf B 59}, 6024, (1999). We now also discuss the disorder effects and analyze the H log H crossover at small fields. 3 pages, Latex file with 2 eps figure file

d-Wave Model for Microwave Response of High-Tc Superconductors

We develop a simple theory of the electromagnetic response of a d- wave superconductor in the presence of potential scatterers of arbitrary s-wave scattering strength and inelastic scattering by antiferromagnetic spin fluctuations. In the clean London limit, the conductivity of such a system may be expressed in "Drude" form, in terms of a frequency-averaged relaxation time. We compare predictions of the theory with recent data on YBCO and BSSCO crystals and on YBCO films. While fits to penetration depth measurements are promising, the low temperature behavior of the measured microwave conductivity appears to be in disagreement with our results. We discuss implications for d-wave pairing scenarios in the cuprate superconductors.Comment: 33 pages, plain TeX including all macros. 16 uuencoded, compressed postscript figures are appended at the en

On Invariant Notions of Segre Varieties in Binary Projective Spaces

Invariant notions of a class of Segre varieties \Segrem(2) of PG(2^m - 1, 2) that are direct products of $m$ copies of PG(1, 2), $m$ being any positive integer, are established and studied. We first demonstrate that there exists a hyperbolic quadric that contains \Segrem(2) and is invariant under its projective stabiliser group \Stab{m}{2}. By embedding PG(2^m - 1, 2) into \PG(2^m - 1, 4), a basis of the latter space is constructed that is invariant under \Stab{m}{2} as well. Such a basis can be split into two subsets whose spans are either real or complex-conjugate subspaces according as $m$ is even or odd. In the latter case, these spans can, in addition, be viewed as indicator sets of a \Stab{m}{2}-invariant geometric spread of lines of PG(2^m - 1, 2). This spread is also related with a \Stab{m}{2}-invariant non-singular Hermitian variety. The case $m=3$ is examined in detail to illustrate the theory. Here, the lines of the invariant spread are found to fall into four distinct orbits under \Stab{3}{2}, while the points of PG(7, 2) form five orbits.Comment: 18 pages, 1 figure; v2 - version accepted in Designs, Codes and Cryptograph

Extinction of impurity resonances in large-gap regions of inhomogeneous d-wave superconductors

Impurity resonances observed by scanning tunneling spectroscopy in the superconducting state have been used to deduce properties of the underlying pure state. Here we study a longstanding puzzle associated with these measurements, the apparent extinction of these resonances for Ni and Zn impurities in large-gap regions of the inhomogeneous BSCCO superconductor. We calculate the effect of order parameter and hopping suppression near the impurity site, and find that these two effects are sufficient to explain the missing resonances in the case of Ni. There are several possible scenarios for the extinction of the Zn resonances, which we discuss in turn; in addition, we propose measurements which could distinguish among them.Comment: 10 pages, 8 figure