Magnetic flux line structures and phase transitions in unconventional and conventional superconductors

When a magnetic field is applied to any superconductor, its initial response is to exclude the field: this leads to the phenomenon of levitation of magnets by superconductors. However, many superconductors allow larger magnetic fields to penetrate, which they do as individual lines of magnetic flux. One of the practically important aspects of these flux lines is that currents passed through the superconductor may force them to move. If this occurs, energy will be dissipated, and the superconductor will become resistive. However, if the flux lines are pinned to impurities in the material, the superconductor may carry large currents without dissipation. Some of our research is directed towards understanding pinning, by measuring how the flux lines interact with the pinning centres and with each other. Another important aim is to use the observation of flux lines to tell us more about the superconductors themselves. A well-established example of this is the amount of magnetic flux in each line, which is given by the ratio of Planck's constant (which relates the wavelength of quantum particles to their momentum) to twice the electronic charge (which demonstrates that in superconductors, the electrons are coupled together in pairs). Electrons pair up in all known superconductors, but the type of pairing can be greatly different in different materials. For instance, in high-temperature superconductors, the electrons in each pair are circulating around each other. This should cause the cores of the flux lines to have a four-leaved clover-like structure, arising from the standing electron waves making up the pairs. When the flux lines are squeezed by increasing the magnetic field, the interaction between these odd-shaped cores becomes important. We are using neutron diffraction to observe these flux lines; if on a rainy night, you view the light from a sodium street lamp through the material of an umbrella, it is found to be surrounded by a pattern of diffraction spots,. These arise from the interference of light waves passing through the regularly-spaced fibres in the umbrella material. In a similar way, if one views a source of slow neutrons, such as a research reactor, through a superconductor containing flux lines, the main neutron beam is found to be surrounded by diffracted neutrons. The neutron diffraction pattern tells us about the arrangement of flux lines in the material. In the simplest case, this would be a hexagonal packing, like that adopted by a handful of pencils. In practice, we are finding many other arrangements, which change with the density of flux lines and tell us about their interactions with each other and with the underlying crystal structure of the superconductor. Our measurements rely on two properties of neutrons: firstly, that they have quantum-wave-like properties, and secondly, that they behave like microscopic magnets, so that they are diffracted by something as apparently insubstantial as a magnetic field. In this research, we are applying these methods to a wide variety of superconductors, and extending them to new extremes of high magnetic field at ultra-low temperatures. Here we have indications of a new kind of flux line, with a magnetic core like the lead in a pencil. We are also interested in the role of increasing temperature, which will tend to make the flux lines move from their equilibrium positions, and possibly get into an arrangement like cooked spaghetti, which is certainly associated with the appearance of electrical resistance. This phenomenon has been clearly observed at elevated temperatures in High-Tc materials, but so far it has evaded clear demonstration in conventional superconductors, which suggests that our understanding is imperfect. In summary, we are pushing forward an interlocking programme, which will increase our understanding of the many ways in which the fascinating and useful phenomenon of superconductivity can occur.