Effect of magnetic and non-magnetic impurities on highly anisotropic superconductivity

We generalize Abrikosov-Gor'kov solution of the problem of weakly coupled superconductor with impurities on the case of a multiband superconductor with arbitrary interband order parameter anisotropy, including interband sign reversal of the order parameter. The solution is given in terms of the effective (renormalized) coupling matrix and describes not only $T_c$ suppression but also renormalization of the superconducting gap basically at all temperatures. In many limiting cases we find analytical solutions for the critical temperature suppression. We illustrate our results by numerical calculations for two-band model systems.Comment: 18 pages (12pt) RevTeX, 4 postscript figure

On the T-dependence of the magnetic penetration depth in unconventional superconductors at low temperatures: can it be linear?

We present a thermodynamics argument against a strictly linear temperature dependence of the magnetic penetration depth, which applies to superconductors with arbitrary pairing symmetry at low temperatures.Comment: 5 pages, expanded version of cond-mat/971102

Evolution of the pairing pseudogap in the spectral function with interplane anisotropy

We study the pairing pseudogap in the spectral function as a function of interplane coupling. The analytical expressions for the self-energy in the critical regime are obtained for any degree of anisotropy. The frequency dependence of the self-energy is found to be qualitatively different in two and three dimensions, and the crossover from two to three dimensional behavior is discussed. In particular, by considering the anisotropy of the Fermi velocity and gap along the Fermi surface, we can qualitatively explain recent photoemission experiments on high temperature superconductors concerning the temperature dependent Fermi arcs seen in the pseudogap phase.Comment: 20 pages, revtex, 5 encapsulated postscript figures include

Anisotropic impurities in anisotropic superconductors

Physical properties of anisotropic superconductors like the critical temperature and others depend sensitively on the electron mean free path. The sensitivity to impurity scattering and the resulting anomalies are considered a characteristic feature of strongly anisotropic pairing. These anomalies are usually analyzed in terms of s-wave impurity scattering which leads to universal pair breaking effects depending on only two scattering parameters, the mean free path and the impurity cross section. We investigate here corrections coming from anisotropies in the scattering cross section, and find not only quantitative but also qualitative deviations from universal s-wave isotropic pairbreaking. The properties we study are the transition temperature, the density of states, quasiparticle bound states at impurities, and pinning of flux lines by impurities.Comment: 19 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

The London theory of the crossing-vortex lattice in highly anisotropic layered superconductors

A novel description of Josephson vortices (JVs) crossed by the pancake vortices (PVs) is proposed on the basis of the anisotropic London theory. The field distribution of a JV and its energy have been calculated for both dense ($a\lambda_J$) PV lattices with distance $a$ between PVs, and the nonlinear JV core size $\lambda_J$. It is shown that the ``shifted'' PV lattice (PVs displaced mainly along JVs in the crossing vortex lattice structure), formed in high out-of-plane magnetic fields transforms into the PV lattice ``trapped'' by the JV sublattice at a certain field, lower than $\Phi_0/\gamma^2s^2$, where $\Phi_0$ is the flux quantum, $\gamma$ is the anisotropy parameter and $s$ is the distance between CuO$_2$ planes. With further decreasing $B_z$, the free energy of the crossing vortex lattice structure (PV and JV sublattices coexist separately) can exceed the free energy of the tilted lattice (common PV-JV vortex structure) in the case of $\gamma s<\lambda_{ab}$ with the in-plane penetration depth $\lambda_{ab}$ if the low ($B_x<\gamma\Phi_0/\lambda_{ab}^2$) or high ($B_x\gtrsim \Phi_0/\gamma s^2$) in-plane magnetic field is applied. It means that the crossing vortex structure is realized in the intermediate field orientations, while the tilted vortex lattice can exist if the magnetic field is aligned near the $c$-axis and the $ab$-plane as well. In the intermediate in-plane fields $\gamma\Phi_0/\lambda_{ab}^2\lesssim B_x \lesssim \Phi_0/\gamma s^2$, the crossing vortex structure with the ``trapped'' PV sublattice seems to settle in until the lock-in transition occurs since this structure has the lower energy with respect to the tilted vortex structure in the magnetic field ${\vec H}$ oriented near the $ab$-plane.Comment: 15 pages, 6 figures, accepted for publication in PR

Effect of spatial variations of superconducting gap on suppression of the transition temperature by impurities

We calculate correction to the critical temperature of a dirty superconductor, which results from the local variations of the gap function near impurity sites. This correction is of the order of T_c/E_F and becomes important for short-coherence length superconductors. It generally reduces a pair-breaking effect. In s-wave superconductors small amounts of nonmagnetic impurities can increase the transition temperature.Comment: 5 pages, ReVTE

Phase Fluctuations and Single Fermion Spectral Density in 2D Systems with Attraction

The effect of static fluctuations in the phase of the order parameter on the normal and superconducting properties of a 2D system with attractive four-fermion interaction is studied. Analytic expressions for the fermion Green's function, its spectral density, and the density of states are derived in the approximation where the coupling between the spin and charge degrees of freedom is neglected. The resulting single-particle Green's function clearly demonstrates a non-Fermi liquid behavior. The results show that as the temperature increases through the 2D critical temperature, the width of the quasiparticle peaks broadens significantly.Comment: 29 pages, ReVTeX, 12 EPS figures; references added, typos corrected, new comments adde

Vortex Matter Transition in Bi2{}_2Sr2{}_2CaCu2{}_2O8+y{}_{8+y} under Tilted Fields

Vortex phase diagram under tilted fields from the $c$ axis in Bi${}_2$Sr${}_2$CaCu${}_2$O${}_{8+y}$ is studied by local magnetization hysteresis measurements using Hall probes. When the field is applied at large angles from the $c$ axis, an anomaly ($H_p^\ast$) other than the well-known peak effect ($H_p$) are found at fields below $H_p$. The angular dependence of the field $H_p^\ast$ is nonmonotonic and clearly different from that of $H_p$ and depends on the oxygen content of the crystal. The results suggest existence of a vortex matter transition under tilted fields. Possible mechanisms of the transition are discussed.Comment: Revtex, 4 pages, some corrections are adde

Quantum Monte Carlo study of the 3D attractive Hubbard model

We study the three-dimensional (3D) attractive Hubbard model by means of the Determinant Quantum Monte Carlo method. This model is a prototype for the description of the smooth crossover between BCS superconductivity and Bose-Einstein condensation. By detailed finite-size scaling we extract the finite-temperature phase diagram of the model. In particular, we interpret the observed behavior according to a scenario of two fundamental temperature scales; T* associated with Cooper pair formation and Tc with condensation (giving rise to long-range superconducting order). Our results also indicate the presence of a recently conjectured phase transition hidden by the superconducting state. A comparison with the 2D case is briefly discussed, given its relevance for the physics of high-Tc cuprate superconductors.Comment: 4 pages, 4 Postscript figure