Microwave conductivity of YBa2_2Cu3_3O6.99_{6.99} including inelastic scattering

The fluctuation spectrum responsible for the inelastic scattering in YBa$_2$Cu$_3$O$_{6.99}$ which was recently determined from consideration of the in-plane optical conductivity in the infrared, is used to calculate the temperature dependence of the microwave conductivity at several measured frequencies. Reasonable overall agreement can only be achieved if, in addition, some impurity scattering is included within a model potential intermediate between weak (Born) and strong (unitary) limit.Comment: 15 pages, 5 figures accepted for publication in Phys. Rev.

Fermi-Liquid Interactions in d-Wave Superconductor

This article develops a quantitative quasiparticle model of the low-temperature properties of d-wave superconductors which incorporates both Fermi-liquid effects and band-structure effects. The Fermi-liquid interaction effects are found to be classifiable into strong and negligible renormalizaton effects, for symmetric and antisymmetric combinations of the energies of $k\uparrow$ and $-k\downarrow$ quasiparticles, respectively. A particularly important conclusion is that the leading clean-limit temperature-dependent correction to the superfluid density is not renormalized by Fermi-liquid interactions, but is subject to a Fermi velocity (or mass) renormalization effect. This leads to difficulties in accounting for the penetration depth measurements with physically acceptable parameters, and hence reopens the question of the quantitative validity of the quasiparticle picture.Comment: 4 page

Phase transition from a dx2−y2d_{x^2-y^2} to dx2−y2+dxyd_{x^2-y^2}+d_{xy} superconductor

We study the phase transition from a $d_{x^2-y^2}$ to $d_{x^2-y^2}+d_{xy}$ superconductor using the tight-binding model of two-dimensional cuprates. As the temperature is lowered past the critical temperature $T_c$, first a $d_{x^2-y^2}$ superconducting phase is created. With further reduction of temperature, the $d_{x^2-y^2}+d_{xy}$ phase is created at temperature $T=T_{c1}$. We study the temperature dependencies of the order parameter, specific heat and spin susceptibility in these mixed-angular-momentum states on square lattice and on a lattice with orthorhombic distortion. The above-mentioned phase transitions are identified by two jumps in specific heat at $T_c$ and $T_{c1}$.Comment: Latex file, 5 pages, 6 postscript figures, Accepted in Physical Review

Critical temperature and superfluid density suppression in disordered high-TcT_c cuprate superconductors

We argue that the standard Abrikosov-Gorkov (AG) type theory of $T_c$ in disordered $d$-wave superconductors breaks down in short coherence length high-$T_c$ cuprates. Numerical calculations within the Bogoliubov-de Gennes formalism demonstrate that the correct description of such systems must allow for the spatial variation of the order parameter, which is strongly suppressed in the vicinity of impurities but mostly unaffected elsewhere. Suppression of $T_c$ as measured with respect to the attendant decrease in the superfluid density is found to be significantly weaker than that predicted by the AG theory, in good agreement with experiment.Comment: REVTeX, 4 pages, 3 ps figures included [The version to appear in PRB Sept. 1. Conclusions of the paper unchanged; several changes in text and figures for added clarity, discussion of phase fluctuations added.

Free Energy and Magnetic Penetration Depth of a dd-Wave Superconductor in the Meissner State

We investigate the free energy and the penetration depth of a quasi-two-dimensional d-wave superconductor in the presence of a weak magnetic field by taking account of thermal, nonlocal and nonlinear effects. In an approximation in which the superfluid velocity $v_s$ is assumed to be slowly varying, the free energy is calculated and compared with available results in several limiting cases. It is shown that either nonlocal or nonlinear effects may cut off the linear-$T$ dependence of both the free energy and the penetration depth in all the experimental geometries. At extremely low $T$, the nonlocal effects will also generically modify the linear $H$ dependence of the penetration depth ("nonlinear Meissner effect") in most experimental geometries, but for supercurrents oriented along the nodal directions, the effect may be recovered. We compare our predictions with existing experiments on the cuprate superconductors.Comment: 18 revtex pages with 4 eps figures, final versio

Distinguishing d-wave from highly anisotropic s-wave superconductors

Systematic impurity doping in the Cu-O plane of the hole-doped cuprate superconductors may allow one to decide between unconvention al ("d-wave") and anisotropic conventional ("s-wave") states as possible candidates for the order parameter in these materials. We show that potential scattering of any strength always increases the gap minima of such s-wave states, leading to activated behavior in temperature with characteristic impurity concentration dependence in observable quantities such as the penetration depth. A magnetic component to the scattering may destroy the energy gap and give rise to conventional gapless behavior, or lead to a nonmonotonic dependence of the gap on impurity concentration. We discuss how experiments constrain this analysis.Comment: 5 page

On the low temperature properties and specific anisotropy of pure anisotropically paired superconductors

Dependences of low temperature behavior and anisotropy of various physical quantities for pure unconventional superconductors upon a particular form of momentum direction dependence for the superconducting order parameter (within the framework of the same symmetry type of superconducting pairing) are considered. A special attention is drawn to the possibility of different multiplicities of the nodes of the order parameter under their fixed positions on the Fermi surface, which are governed by symmetry. The problem of an unambiguous identification of a type of superconducting pairing on the basis of corresponding experimental results is discussed. Quasiparticle density of states at low energy for both homogeneous and mixed states, the low temperature dependences of the specific heat, penetration depth and thermal conductivity, the I-V curves of SS and NS tunnel junctions at low voltages are examined. A specific anisotropy of the boundary conditions for unconventional superconducting order parameter near $T_c$ for the case of specular reflection from the boundary is also investigated.Comment: 20 page

Upper critical field pecularities of superconducting YNi2B2C and LuNi2B2C

We present new upper critical field Hc2(T) data in a broad temperature region from 0.3K to Tc for LuNi2B2C and YNi2B2C single crystals with well characterized low impurity scattering rates. The absolute values for all T, in particular Hc2(0), and the sizeable positive curvature (PC) of Hc2(T) at high and intermediate T are explained quantitatively within an effective two-band model. The failure of the isotropic single band approach is discussed in detail. Supported by de Haas van Alphen data, the superconductivity reveals direct insight into details of the electronic structure. The observed maximal PC near Tc gives strong evidence for clean limit type II superconductors.Comment: 4 pages, 2 figures, Phys. Rev. Lett. accepte

Effect of Proximity Coupling of Chains and Planes on the Penetration Depth Anisotropy in Y_1Ba_2Cu_3O_7

We calculate the penetration depth $\lambda$ in the $a$, $b$ and $c$ directions for a simple model of YBa$_2$Cu$_3$O$_7$. In this model there are two layers---representing a CuO$_2$ plane and a CuO chain---per unit cell. There is a BCS--like pairing (both $s$ wave and $d$ wave are considered) interaction localised in the CuO$_2$ planes. The CuO chains become superconducting at temperatures lower than $T_c$ because of their proximity to the planes, and there is an induced gap in the chains. Since the temperature dependence of the penetration depth in the $b$ direction (along the chains) is sensitive to the size of the induced gap, the difference between the shapes of the penetration depth curves in the $a$ and $b$ directions reveals a great deal about the nature of the condensate in the chains. We find that in our proximity model there are always regions of the chain Fermi surface on which the induced gap is much smaller than $T_c$, so that the temperature dependence of $\lambda_b$ is always different than that of $\lambda_a$. Experimental observations of the of the $ab$ anisotropy show nearly identical temperature dependences. The main result of our paper, then, is that a simple proximity model in which the pairing interaction is localized to the planes, and the planes are coherently coupled to the chains cannot account for the superfluid on the chains.Comment: 24 Pages, Submitted to Phys. Rev.

Coherent Potential Approximation for `d - wave' Superconductivity in Disordered Systems

A Coherent Potential Approximation is developed for s-wave and d-wave superconductivity in disordered systems. We show that the CPA formalism reproduces the standard pair-breaking formula, the self-consistent Born Approximation and the self-consistent T-matrix approximation in the appropriate limits. We implement the theory and compute T_c for s-wave and d-wave pairing using an attractive nearest neighbor Hubbard model featuring both binary alloy disorder and a uniform distribution of scattering site potentials. We determine the density of states and examine its consequences for low temperature heat capacity. We find that our results are in qualitative agreement with measurements on Zn doped YBCO superconductors.Comment: 35 pages, 23 figures, submitted to Phys Rev.