| Magnetic flux lines in high temperature superconductors show an extremely rich phenomenology, due to the anisotropy of these high-Tc materials and to the interplay between the elasticity of flux lines on one hand, and thermal and quenched disorder on the other. This thesis is a contribution to the study of this phenomenology, and consists of four main parts.; In the first part, we use a replica Gaussian variational approach to study positional order of flux lines in a vortex lattice in samples of finite thickness L, and we find that the quasi-long range order found in previous studies is destroyed on asymptotic length scales for the center of mass positions of the flux lines. We then study the pinning of flux lattices in type II superconductors by a system of well separated, identical point pins, and argue that such a distribution of pinning centers can be modeled by a Gaussian random field with a suitably chosen covariance.; The second part of this work is devoted to flux line liquids. In particular, we have constructed, within the framework of classical statistical mechanics, a mean field theory of dilute flux line liquids which goes beyond linear hydrodynamics. Within our approach, we find that interactions between vortices produce a massive term in the Hamiltonian of the internal modes of the flux lines which confines their transverse fluctuations.; In the third part of this thesis, we study the nonequilibrium creep dynamics of a two-dimensional interface driven through a periodic potential, a problem which, in many ways, can be seen as a toy model for the more difficult problem of driven lattices, e.g. vortex lattices, through a periodic potential. Using dynamical renormalization group methods, we find that the nature of transport depends qualitatively on whether the temperature, T, is above or below the equilibrium roughening transition temperature T c. Above Tc, the velocity-force characteristics is Ohmic, with linear mobility exhibiting a jump discontinuity across the transition.; Lastly, in the fourth and final part we study the effect of disorder on the spontaneous vortex (SV) lattice in ferromagnetic superconductors. We study the effects of thermal fluctuations, quenched disorder, and the nonlinear elasticity, all of which are strongly enhanced and lead to a SV solid which is characterized by elastic moduli that are wavevector-dependent out to arbitrary long length scales and exhibits non-Hookean elasticity. At weak external field H these imply a universal scaling of magnetic induction B(H) ∼ B(0) + cH α, with α ≈ 0.72. For weak disorder, we predict the SV solid is a topologically ordered vortex glass that is in the “columnar elastic glass” universality class. (Abstract shortened by UMI.)... |
