Plastic energies in layered superconductors

We estimate the energy cost associated with two pancake vortices colliding in a layered superconductor. It is argued that this energy sets the plastics energy scale and is the analogue of the crossing energy for vortices in the continuum case. The starting point of the calculation is the Lawrence-Doniach version of the Ginzburg-Landau free energy for type-II superconductors. The magnetic fields considered are along the c-direction and assumed to be sufficiently high that the lowest Landau level approximation is valid. For Bi-2212, where it is know that layering is very important, the results are radically different from what would have been obtained using a three-dimensional anisotropic continuum model. We then use the plastic energy for Bi-2212 to successfully explain recent results from Hellerqvist {\em et al.}\ on its longitudinal resistance.Comment: 5 Pages Revtex, 4 uuencoded postscript figure

Energy cost associated with vortex crossing in superconductors

Starting from the Ginzburg-Landau free energy of a type II superconductor in a magnetic field we estimate the energy associated with two vortices crossing. The calculations are performed by assuming that we are in a part of the phase diagram where the lowest Landau level approximation is valid. We consider only two vortices but with two markedly different sets of boundary conditions: on a sphere and on a plane with quasi-periodic boundary conditions. We find that the answers are very similar suggesting that the energy is localised to the crossing point. The crossing energy is found to be field and temperature dependent -- with a value at the experimentally measured melting line of $U_\times \simeq 7.5 k T_m \simeq 1.16/c_L^2$, where $c_L$ is the Lindemann melting criterion parameter. The crossing energy is then used with an extension of the Marchetti, Nelson and Cates hydrodynamic theory to suggest an explanation of the recent transport experiments of Safar {{\em et al.}\ }.Comment: 15 pages, RevTex v3.0, followed by 5 postscript figure

Metals in high magnetic field: a new universality class of Fermi liquids

Parquet equations, describing the competition between superconducting and density-wave instabilities, are solved for a three-dimensional isotropic metal in a high magnetic field when only the lowest Landau level is filled. In the case of a repulsive interaction between electrons, a phase transition to the density-wave state is found at finite temperature. In the opposite case of attractive interaction, no phase transition is found. With decreasing temperature $T$, the effective vertex of interaction between electrons renormalizes toward a one-dimensional limit in a self-similar way with the characteristic length (transverse to the magnetic field) decreasing as $\ln^{-1/6}(\omega_c/T)$ ($\omega_c$ is a cutoff). Correlation functions have new forms, previously unknown for conventional one-dimensional or three-dimensional Fermi-liquids.Comment: 13 pages + 4 figures (included

A Superconducting Instability in the Infinite-U Anderson Lattice in the Presence of Crystal Electric Fields

We report evidence of a superconducting instability (of $T_{1g}$ symmetry) in the infinite-U Anderson lattice in the presence of crystal fields of cubic symmetry. We assume a lattice of $4f$ sites, each with a total angular momentum of $J=5/2$ that is split by crystal fields into a low-lying doublet of $\Gamma_7$ symmetry and an excited quartet of $\Gamma_8$ symmetry. Slave Bosons on the $4f$ sites create and destroy $4f^0$ configurations and Lagrange multipliers at each $4f$ site enforce the occupancy constraint due to the infinite Coulomb repulsion. Quasiparticle interactions are due to exchange of $4f$ density fluctuations, which are represented by fluctuations in the slave Bosons and Lagrange multipliers. We use the so-called analytic tetrahedron method to calculate the dressed (to order 1/N) Boson Green functions. In weak couping, the exchange of the dressed Bosons gives rise to a superconducting instability of $T_{1g}$, $xy(x^2-y^2)$, symmetry. The $A_{1g}$, ``s-wave'', channel has strongly repulsive interactions and hence no pairing instability. The $T_{2g}$ channel exhibits weakly repulsive interactions. Average quasiparticle interactions in the $E_g$, $x^2-y^2$, $3z^2-r^2$, channel fluctuate strongly as a function of the number of tetrahedra used to calculate the Bosonic Green functions,Comment: 66 pages+ 17 postscript figures, LATE