Magnetic flux can penetrate a type-II superconductor in the form of Abrikosov vortices (also called flux lines, flux tubes, or fluxons) each carrying a quantum of magnetic flux phi 0=h/2e. These tiny vortices of supercurrent tend to arrange themselves in a triangular flux-line lattice (FLL), which is more or less perturbed by material inhomogeneities that pin the flux lines, and in high-Tc superconductors (HTSCs) 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 HTSCs the FLL is very soft mainly because of the large magnetic penetration depth lambda . The shear modulus of the FLL is c66~1/ lambda 2, and the tilt modulus c44(k)~(1+k2 lambda 2)-1 is dispersive and becomes very small for short distortion wavelengths 2 pi /k<< lambda . This softness is enhanced further by the pronounced anisotropy and layered structure of HTSCs, which strongly increases the penetration depth for currents along the c axis of these (nearly 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 ofthe two-dimensional `pancake vortices` in the layers. Various phase transitions are predicted for the FLL in layered HTSCs. Although large pinning forces and high critical currents have been achieved, the small depinning energy so far prevents the application of HTSCs as conductors at high temperatures except in cases when the applied current and the surrounding magnetic field are small.

https://iopscience.iop.org/article/10.1088/0034-4885/58/11/003/pdf

The flux-line lattice in superconductors

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.

The Flux-Line Lattice in Superconductors

Size dependence of nanostructures: Impact of bond order deficiency

The interacting disordered electron problem is reviewed with emphasis on the quantum phase transitions that occur in a model system and on the field-theoretic methods used to describe them. An elementary discussion of conservation laws and diffusive dynamics is followed by a detailed derivation of the extended nonlinear sigma model, which serves as an effective field theory for the problem. A general scaling theory of metal-insulator and related transitions is developed, and explicit renormalization-group calculations for the various universality classes are reviewed and compared with experimental results. A discussion of pertinent physical ideas and phenomenological approaches to the metal-insulator transition not contained in the sigma-model approach is given, and phase-transition aspects of related problems, like disordered superconductors and the quantum Hall effect, are discussed. The review concludes with a list of open problems.

The Anderson-Mott transition

We review experimental studies of the time decay of the nonequilibrium magnetization in high-temperature superconductors, a phenomenon known as magnetic relaxation. This effect has its origin in motion of flux lines out of their pinning sites due to thermal activation or quantum tunneling. The combination of relatively weak flux pinning and high temperatures leads to rich properties that are unconventional in the context of low temperature superconductivity and that have been the subject to intense studies. The results are assessed from a purely experimental perspective and discussed in the context of present phenomenological theories. [S0034-6861(96)00403-5]

Magnetic relaxation in high-temperature superconductors

Severe decreases are observed in the superconducting transition temperatures of metallic films as they are made thinner and more disordered. Explanations for these decreases in the transition temperature are discussed. These include changes in the phonon spectrum, the effect of the metal-insulator boundary, size quantization in small particles, the effect of an activated conduction mechanism in the normal state, and, finally, the effect of order-parameter fluctuations.

Destruction of Superconductivity in Disordered Near-Monolayer Films

The leading correction to the normal-state conductivity due to superconducting fluctuations is calculated as a function of temperature, externally applied magnetic field, and internal pair breaking for anisotropic high-${T}_{c}$ superconductors.

Fluctuation conductivity of high- T c superconductors

17-β-Estradiol (E2) is a steroid hormone involved in numerous brain functions. E2 regulates synaptic plasticity in part by enhancing NMDA receptor function and spine density in the hippocampus, resulting in increased long-term potentiation and facilitation of learning and memory. As the calcium-dependent neutral protease, calpain, is also involved in these processes, we tested whether E2 could activate calpain and examined the functional consequences of E2-mediated calpain activation in hippocampus. Calpain activity was analyzed by a fluorescence resonance energy transfer (FRET)-based assay that allows both quantitative determination and spatial resolution. E2 rapidly activated calpain in cultured cortical and hippocampal neurons, prominently in dendrites and dendritic spines. E2-induced calpain activation was mediated through mitogen-activated protein kinase (MAPK), as it was completely blocked by MEK inhibitors. It was also calcium-independent, as it was still evident in presence of the calcium chelator, BAPTA-AM. Activation of ERα and ERβ receptors by specific agonists stimulated calpain activity. Finally, the rapid E2-mediated increase in excitability in acute hippocampal slices was prevented by a membrane-permeable calpain inhibitor. Furthermore, E2 treatment of acute hippocampal slices resulted in increased actin polymerization and membrane levels of GluR1 but not GluR2/3 subunits of AMPA receptors; both effects were also blocked by a calpain inhibitor. Our results indicate that E2 rapidly stimulates calpain activity through MAP kinase-mediated phosphorylation, resulting in increased membrane levels of AMPA receptors. These effects could be responsible for E2-mediated increase in neuronal excitability and facilitation of cognitive processes.

https://www.pnas.org/content/pnas/106/51/21936.full.pdf

17-β-Estradiol increases neuronal excitability through MAP kinase-induced calpain activation

Template‐based Synthesis and Magnetic Properties of Cobalt Nanotube Arrays

We have reexamined the recent theories by Caroli and Maki of the dynamic response of dirty superconductors and find them inconsistent and incomplete. Additional contributions, which were not included by them, are calculated, and new expressions are presented for the microwave and flux-flow resistance. In particular, we find that the use of the time-dependent Ginzburg-Landau equation for the order parameter, coupled with the static Ginzburg-Landau equation for the current, is not generally adequate to calculate the leading superconducting contributions to the resistance. These results imply that the theory of Aslamazov and Larkin for the extra conductivity due to fluctuations above the transition temperature is also incomplete and that, in general, additional contributions of the type suggested by Maki must be included.

Richard S. Thompson

Papers

Destruction of Superconductivity in Disordered Near-Monolayer Films

Fluctuation conductivity of high- T c superconductors

17-β-Estradiol increases neuronal excitability through MAP kinase-induced calpain activation

Template‐based Synthesis and Magnetic Properties of Cobalt Nanotube Arrays

Microwave, Flux Flow, and Fluctuation Resistance of Dirty Type-II Superconductors