Nuclear Spin Relaxation Rate of Disordered px+ipyp_x+ip_y-wave Superconductors

Based on an effective Hamiltonian with the binary alloy disorder model defined in the triangular lattice, the impurity scattering effects on the density of states and especially on the spin-lattice relaxation rate $1/T_1$ of $p_x+ip_y$-wave superconductors are studied by solving numerically the Bogoliubov-de Gennes equations. In the clean limit, the coherence peak of $1/T_1$ is observed as expected. More intriguingly, for strong scattering potential, the temperature dependence of $1/T_1$ exhibits the two different power law behaviors near $T_{\text{c}}$ and at low temperatures, respectively, which is in good agreement with the nuclear quadrupolar resonance measurement.Comment: 4 pages, 3 figure

Infrared conductivity of a d_{x^2-y^2}-wave superconductor with impurity and spin-fluctuation scattering

Calculations are presented of the in-plane far-infrared conductivity of a d_{x^2-y^2}-wave superconductor, incorporating elastic scattering due to impurities and inelastic scattering due to spin fluctuations. The impurity scattering is modeled by short-range potential scattering with arbitrary phase shift, while scattering due to spin fluctuations is calculated within a weak-coupling Hubbard model picture. The conductivity is characterized by a low-temperature residual Drude feature whose height and weight are controlled by impurity scattering, as well as a broad peak centered at 4 Delta_0 arising from clean-limit inelastic processes. Results are in qualitative agreement with experiment despite missing spectral weight at high energies.Comment: 29 pages (11 tar-compressed-uuencoded Postscript figures), REVTeX 3.0 with epsf macro

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

Superconductor-Ferromagnet Bi-Layers: a Comparison of s-Wave and d-Wave Order Parameters

We study superconductor-ferromagnet bi-layers, not only for s-wave but also for d-wave superconductors. We observe oscillations of the critical temperature when varying the thickness of the ferromagnetic layer for both s-wave and d-wave superconductors. However, for a rotated d-wave order parameter the critical temperature differs considerably from that for the unrotated case. In addition we calculate the density of states for different thicknesses of the ferromagnetic layer; the results reflect the oscillatory behaviour of the superconducting correlations.Comment: 11 pages, 5 figures, accepted for publication in J. Phys.: Condens. Matte

Gap Renormalization in Dirty Anisotropic Superconductors: Implications for the Order Parameter of the Cuprates

We contrast the effects of non-magnetic impurities on the properties of superconductors having a \dw\ order parameter, and a highly anisotropic s-wave (ASW) gap with the same nodal structure. The non-vanishing, impurity induced, off-diagonal self-energy in the ASW state is shown to gap out the low energy excitations present in the clean system, leading to a qualitatively different impurity response of the single particle density of states compared to the \dw\ state. We discuss how this behaviour can be employed to distinguish one state from the other by an analysis of high-resolution angle-resolved photoemission spectra.Comment: 12 pages, uuencoded Postscrip

Good Random Matrices over Finite Fields

The random matrix uniformly distributed over the set of all m-by-n matrices over a finite field plays an important role in many branches of information theory. In this paper a generalization of this random matrix, called k-good random matrices, is studied. It is shown that a k-good random m-by-n matrix with a distribution of minimum support size is uniformly distributed over a maximum-rank-distance (MRD) code of minimum rank distance min{m,n}-k+1, and vice versa. Further examples of k-good random matrices are derived from homogeneous weights on matrix modules. Several applications of k-good random matrices are given, establishing links with some well-known combinatorial problems. Finally, the related combinatorial concept of a k-dense set of m-by-n matrices is studied, identifying such sets as blocking sets with respect to (m-k)-dimensional flats in a certain m-by-n matrix geometry and determining their minimum size in special cases.Comment: 25 pages, publishe

Ultrasound attenuation in gap-anisotropic systems

Transverse ultrasound attenuation provides a weakly-coupled probe of momentum current correlations in electronic systems. We develop a simple theory for the interpretation of transverse ultrasound attenuation coefficients in systems with nodal gap anisotropy. Applying this theory we show how ultrasound can delineate between extended-s and d-wave scenarios for the cuprate superconductors.Comment: Uuencode file: 4 pages (Revtex), 3 figures. Some references adde

Low Temperature Properties of Anisotropic Superconductors with Kondo Impurities

We present a self-consistent theory of superconductors in the presence of Kondo impurities, using large-$N$ slave-boson methods to treat the impurity dynamics. The technique is tested on the s-wave case and shown to give good results compared to other methods for $T_K > T_c$. We calculate low temperature thermodynamic and transport properties for various superconducting states, including isotropic s-wave and representative anisotropic model states with line and point nodes on the Fermi surface.Comment: 21 pages, RevTeX 3.0, 12 figures available upon request, UF preprin

Hjelmslev Geometry of Mutually Unbiased Bases

The basic combinatorial properties of a complete set of mutually unbiased bases (MUBs) of a q-dimensional Hilbert space H\_q, q = p^r with p being a prime and r a positive integer, are shown to be qualitatively mimicked by the configuration of points lying on a proper conic in a projective Hjelmslev plane defined over a Galois ring of characteristic p^2 and rank r. The q vectors of a basis of H\_q correspond to the q points of a (so-called) neighbour class and the q+1 MUBs answer to the total number of (pairwise disjoint) neighbour classes on the conic.Comment: 4 pages, 1 figure; extended list of references, figure made more illustrative and in colour; v3 - one more figure and section added, paper made easier to follow, references update

Validation of the Chinese version of the "Mood Disorder Questionnaire" for screening bipolar disorder among patients with a current depressive episode

<p>Abstract</p> <p>Background</p> <p>The Mood Disorder Questionnaire (MDQ) is a well-recognized screening tool for bipolar disorder, but its Chinese version needs further validation. This study aims to measure the accuracy of the Chinese version of the MDQ as a screening instrument for bipolar disorder (BPD) in a group of patients with a current major depressive episode.</p> <p>Methods</p> <p>142 consecutive patients with an initial DSM-IV-TR diagnosis of a major depressive episode were screened for BPD using the Chinese translation of the MDQ and followed up for one year. The final diagnosis, determined by a special committee consisting of three trained senior psychiatrists, was used as a 'gold standard' and ROC was plotted to evaluate the performance of the MDQ. The optimal cut-off was chosen by maximizing the Younden's index.</p> <p>Results</p> <p>Of the 142 patients, 122 (85.9%) finished the one year follow-up. On the basis of a semi-structured clinical interview 48.4% (59/122) received a diagnosis of unipolar depression (UPD), 36.9% (45/122) BPDII and 14.8% (18/122) BPDI. At the end of the one year follow-up,9 moved from UPD to BPD, 2 from BPDII to UPD, 1 from BPDII to BPDI, the overall rate of initial misdiagnosis was 16.4%. MDQ showed a good accuracy for BPD: the optimal cut-off was 4, with a sensitivity of 0.72 and a specificity of 0.73. When BPDII and BPDI were calculated independently, the optimal cut-off for BPDII was 4, with a sensitivity of 0.70 and a specificity of 0.73; while the optimal cut-off for BPDI was 5, with a sensitivity of 0.67 and a specificity of 0.86.</p> <p>Conclusions</p> <p>Our results show that the Chinese version of MDQ is a valid tool for screening BPD in a group of patients with current depressive episode on the Chinese mainland.</p