The Flux-Line Lattice in Superconductors

Abstract

Magnetic flux can penetrate a type-II superconductor in form of Abrikosov vortices. These tend to arrange in a triangular flux-line lattice (FLL) which is more or less perturbed by material inhomogeneities that pin the flux lines, and in high-$T_c$ supercon- ductors (HTSC's) also by thermal fluctuations. Many properties of the FLL are well described by the phenomenological Ginzburg-Landau theory or by the electromagnetic London theory, which treats the vortex core as a singularity. In Nb alloys and HTSC's the FLL is very soft mainly because of the large magnetic penetration depth: The shear modulus of the FLL is thus small and the tilt modulus is dispersive and becomes very small for short distortion wavelength. This softness of the FLL is enhanced further by the pronounced anisotropy and layered structure of HTSC's, which strongly increases the penetration depth for currents along the c-axis of these uniaxial crystals and may even cause a decoupling of two-dimensional vortex lattices in the Cu-O layers. Thermal fluctuations and softening may melt the FLL and cause thermally activated depinning of the flux lines or of the 2D pancake vortices in the layers. Various phase transitions are predicted for the FLL in layered HTSC's. The linear and nonlinear magnetic response of HTSC's gives rise to interesting effects which strongly depend on the geometry of the experiment.

Review paper for Rep.Prog.Phys., 124 narrow pages. The 30 figures do not exist as postscript files

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• The Structure of the Vortex Liquid at the Surface of a Layered Superconductor
• Massive electrons and unconventional room-temperature superconductivity in superhydrides
• Conventional s-wave superconductivity and hidden peak effect in single crystals of Mo${}_8$Ga${}_{4}1$ superconductor
• The effect of Joule heating on the terahertz radiation in the superconductor media
• Interaction between spin and Abrikosov vortices in doped topological insulators
• Vortex matter and strong pinning in underdoped PrFeAs(O,F) with atomic-sized defects
• Evidence for a square-square vortex lattice transition in a high-$T_{\text{c}}$ cuprate superconductor
• Unconventional superconductivity in the nickel-chalcogenide superconductor, TlNi${}_2$Se${}_2$
• Vortex shear effects in layered superconductors
• Vortex-Line Phase Diagram for Anisotropic Superconductors
• Variational theory of flux-line liquids
• Friction on a Quantized Vortex in a Superfluid
• In situ comparison of the critical current density in $YB{a}_{2}C{u}_3{O}_{7-\delta }$ thin films measured by the screening technique under two criteria
• Vortex Lattice in Bi_{2}Sr_{2}CaCu_{2}O_{8+δ} Well Above the First-Order Phase-Transition Boundary
• Numerical study of vortex system quantum melting
• Magnetic flux trapping in porous superconductors
• Directional driving of vortex lines with oscillating magnetic field
• Fluorine-substitution-dependent phase diagram and superconducting properties of Sm-based oxypnictides synthesized by a high-pressure growth technique
• Object orientation and visualization of physics in two dimensions
• Comparison of the fluctuation influence on the resistive properties of the mixed state of BiSrCaCuO and of thin films of conventional superconductor
• Establishment of global phase coherence in a highly disordered fractal MgO/MgB2 nanocomposite: Roles of interface, morphology and defect
• Vortex Lines Distribution in Inhomogeneous Lattices
• Three-dimensional Ginzburg-Landau simulation of a vortex line displaced by a zigzag of pinning spheres
• Many-body vortex effect on the transverse force acting on a moving vortex
• The influence of the Hall force on the vortex dynamics in type II superconductors
• Use of the Modified Ginzburg-Landau Equations in High Temperature Superconductors
• Theory of the Anderson transition in three-dimensional chiral symmetry classes: Connection to type-II superconductors
• Modified London Equation, Abrikosov-Like Vortices and Knot Solitons in Two-Gap Superconductors
• Nonreciprocal magnon fluxonics upon ferromagnet/superconductor hybrids
• Static and Dynamic irreversible magnetic properties of high temperature superconductors
• Superconducting properties of thin film $\mathrm{N}{\mathrm{b}}_{1-\mathrm{x}}\mathrm{T}{\mathrm{i}}_{\mathrm{x}}\mathrm{N}$ studied via the NMR of implanted ${}^8$Li
• Vortex rivers and multiple voltage transitions in superconducting MgB${}_2$ thin films
• Theory of thermally activated vortex bundles flow over the directional-dependent potential barriers in type-II superocnductors
• Weak point disorder in strongly fluctuating flux-line liquids
• The critical current density in type-II superconducting bulk materials
• Monte Carlo Simulation of the Crossover from Bose Glass to Bragg Glass Phase in Layered BSCCO with Columnar Defects