Can Impurity Effects Help to Identify the Symmetry of the Order Parameter of the Cuprates?

The effects of non-magnetic impurities on the properties of superconductors with order parameters (OP) of different symmetry are discussed. In particular, we contrast the case of a d_{x^2 - y^2} with various forms of an anisotropic s-wave (ASW) gap. The biggest qualitative difference occurs if the phase of the s-wave OP does not change sign.Comment: 2pages, uuencoded Postscript, to appear in the Proceedings of the M^2-HTSC IV conferenc

Attenuated total reflection enhanced photoejection from cathodes Final report

Optical equations governing interaction between radiation and interface of two media using metallic cathode

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

A Complete Characterization of Irreducible Cyclic Orbit Codes and their Pl\"ucker Embedding

Constant dimension codes are subsets of the finite Grassmann variety. The study of these codes is a central topic in random linear network coding theory. Orbit codes represent a subclass of constant dimension codes. They are defined as orbits of a subgroup of the general linear group on the Grassmannian. This paper gives a complete characterization of orbit codes that are generated by an irreducible cyclic group, i.e. a group having one generator that has no non-trivial invariant subspace. We show how some of the basic properties of these codes, the cardinality and the minimum distance, can be derived using the isomorphism of the vector space and the extension field. Furthermore, we investigate the Pl\"ucker embedding of these codes and show how the orbit structure is preserved in the embedding.Comment: submitted to Designs, Codes and Cryptograph

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

Scattering by impurity-induced order parameter ``holes'' in d-wave superconductors

Nonmagnetic impurities in d-wave superconductors cause strong local suppressions of the order parameter. We investigate the observable effects of the scatterigng off such suppressions in bulk samples by treating the order parameter "hole" as a pointlike off-diagonal scatterer treated within a self-consistent t-matrix approximation. Strong scattering potentials lead to a finite-energy spectral feature in the d-wave "impurity band", the observable effects of which include enhanced low-temperature microwave power absorption and a stronger sensitivity of the London penetration depth to disorder than found previously in simpler ``dirty'' d-wave models.Comment: 5 pp. Revtex including 4 postscript figures, submitted to 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