Superconductivity

We present a microscopic derivation of the equation of motion for a vortex in a superconductor. A coherent view on vortex dynamics is obtained, in which {\it both} hydrodynamics {\it and} the vortex core contribute to the forces acting on a vortex. The competition between these two provides an interpretation of the observed sign change in the Hall angle in superconductors with mean free path l of the order of the coherence length ξ in terms of broken particle-hole symmetry, which is related to details of the microscopic mechanism of superconductivity.

We present simulations of flux-gradient-driven superconducting vortices interacting with strong columnar pinning defects as an external field H(t) is quasi-statically swept from zero through a matching field B ϕ . We analyze several measurable quantities, including the local flux density B(x,y,H(t)) , magnetization M(H(t)) , critical current J c (B(t)) , and the individual vortex flow paths. We find a significant change in the behavior of these quantities as the local flux density crosses B ϕ , and quantify it for many microscopic pinning parameters. Further, we find that for a given pin density J c (B) can be enhanced by maximizing the distance between the pins for B< B ϕ .

Measurements of the rf penetration depth \lambda(T,H,\theta ) are used to study the superconducting order parameter, vortex dynamics in the mixed state and delineate critical fields in the borocarbide superconductor YNi_2B_2C. The lower critical field has an anomalous T dependence, H_{c1}(T)=1.12[1-(T/T_c)] kOe, which is however consistent with independent superfluid density measurements at microwave frequencies. The vortex response is dominated by viscous flux flow, indicative of extremely weak pinning, and is parametrized by a field scale H_{c2,eff}. The angular dependence of the vortex contribution \lambda(\theta) is in good agreement with the Coffey-Clem model. Structure is seen in the depairing transition in the vicinity of the upper critical field, with the existence of well-defined critical fields H_{c2a}, H_{c2b} and H_{c2c}, with the vortex field scale H_{c2,eff} closest to H_{c2b}. Overall the measurements indicate that YNi_2B_2C has a rich and unusual field dependence of its transport parameters.

The magnetic field distribution, the magnetic flux, and the free energy of an Abrikosov vortex loop near a flat surface of type--II superconductors are calculated in the London approximation. The shape of such a vortex line is a semicircle of arbitrary radius. The interaction of the vortex half--ring and an external homogeneous magnetic field applied along the surface is studied. The magnitude of the energy barrier against the vortex expansion into superconductor is found. The possibilities of formation of an equilibrium vortex line determined by the structure of the applied magnetic field by creating the expanding vortex loops near the surface of type--II superconductor are discussed.

The nature of the resistive transition for a current applied parallel to the magnetic field in high-Tc materials is investigated by numerical simulation on the three dimensional Josephson junction array model. It is shown by using finite size scaling that for samples with disorder the critical temperature Tp for the c axis resistivity corresponds to a percolation phase transition of vortex lines perpendicularly to the applied field. The value of Tp is higher than the critical temperature for j perpendicular to H, but decreases with the thickness of the sample and with anisotropy. We predict that critical behavior around Tp should reflect in experimentally accessible quantities, as the I-V curves.

Vortex structure of pure d x 2 − y 2 -wave superconductors is microscopically analyzed in the framework of the quasi-classical Eilenberger equations. Selfconsistent solution for the d -wave pair potential is obtained for the first time in the case of an isolated vortex. The vortex core structure, i.e., the pair potential, the supercurrent and the magnetic field, is found to be fourfold symmetric even in the case that the mixing of s -wave component is absent. The detailed temperature dependences of these quantities are calculated. The fourfold symmetry becomes clear when temperature is decreased. The local density of states is calculated for the selfconsistently obtained pair potential. From the results, we discuss the flow trajectory of the quasiparticles around a vortex, which is characteristic in the d x 2 − y 2 -wave superconductors. The experimental relevance of our results to high temperature superconductors is also given.

Results of a calculation of the c-axis infrared conductivity sigma_c for a d_{x^2-y^2}-wave superconductor which include both elastic impurity and inelastic spin-fluctuation scattering are presented and compared with the ab-plane conductivity sigma_{ab} in the same model. In this model,the interlayer c-axis coupling is taken to be weak and diffusive. While in clean systems, inelastic scattering leads to a peak at omega = 4*Delta_0 in sigma_{ab} for T < T_c, it has little effect on the corresponding sigma_c, which exhibits structure only at omega = 2*Delta_0 and is directly related to the single-particle density of states N(omega). The c-axis penetration depth lambda_c in the same model is predicted to vary as T^3 at low temperatures in clean samples. We discuss recent optical experiments on the cuprates and compare with these predictions.

Vortex structure of d x 2 − y 2 -wave superconductors is microscopically analyzed in the framework of the quasi-classical Eilenberger equations. If the pairing interaction contains an s -wave ( d xy -wave) component in addition to a d x 2 − y 2 -wave component, the s -wave ( d xy -wave) component of the order parameter is necessarily induced around a vortex in d x 2 − y 2 -wave superconductors. The spatial distribution of the induced s -wave and d xy -wave components is calculated. The s -wave component has opposite winding number around vortex near the d x 2 − y 2 -vortex core and its amplitude has the shape of a four-lobe clover. The amplitude of d xy -component has the shape of an octofoil. These are consistent with results based on the GL theory.

We examine the different possible symmetries of the superconducting gap obtained by solving the Eliashberg equations. We consider an electron-phonon interaction in a strong coupling scenario. The Coulomb pseudopotential plays the crucial role of providing the repulsion needed to favour the d-wave symmetry. But the key parameter that allows very anisotropic solutions even with very strong coupling is the small angular range of the interaction due to predominantly electron-phonon forward scattering that is found in the high-Tc superconductors. We find both s and d-wave solutions whose stability depends mainly on the angular range of the interaction.