Basic Properties of Superconductors

Superconductors were first discovered in 1911 by the scientist Heike Kamerlingh Onnes, when he observed that at the temperature 4.2 K the resistivity of mercury dropped to zero.  All superconductors exhibit certain basic properties, the most famous of which is the existence of a "critical temperature."  Above the critical temperature, a superconductor behaves like a normal material, often with a relatively high resistivity.  Below the critical temperature, however, the resistivity of the material not only becomes very small, but actually drops to zero.  Scientists have shown that a current trapped in a loop of superconducting material can continue to flow for a long period of time without significant decay, as opposed to a normal conductor, in which a current dissipates quickly.  Besides working only under its critical temperature, the superconductor also only exhibits superconductive properties under its critical magnetic field and critical current density. The discovery in the 1980's of High Temperature Superconductors (HTSCs) such as YBCO (yttrium-barium-copper oxide, with a critical temperature of 90 K) has made the study of superconductors and their practical applications more widely achievable.

Why a Superconductor Works: BCS Theory

In 1957, John Bardeen, Leon Cooper, and Robert Schrieffer developed a theory explaining the unique properties of superconductors: BCS theory.  The central supposition of BCS theory is the idea that electrons in the atomic lattice of a material couple together to form groupings known as "Cooper pairs."  When the temperature of a material is near absolute zero, negligible movement occurs among the material's ions.  The material's atomic lattice warps slightly when an electron passes through, due to the force of attraction between the electron and the lattice's positive ions.  This region of the crystal consequentially has a high net positive charge relative to the surrounding material, and this net charge attracts another electron into the region -- the second member of the Cooper pair.  When they come together, these pairs possess a lower net energy than two normal electrons in a conductive material.  The pair's binding energy results in a gap at E_f (the Fermi energy or a solid's highest occupied energy level).  In a space occupied by one Cooper pair, many other pairs also exist.  Below the critical temperature, the lattice cannot provide enough thermal energy to scatter the pairs, as would happen in an ordinary conductor.  Altering  one electron's direction of motion requires not only breaking the connection of that Cooper pair, but that of many other pairs due to nature of the multiple-electron BCS wavefunction.  Therefore, instead of individual electrons scattering (as they do in a normal metal), the electron pair travels forward unimpeded and zero resistivity is observed.

Why Levitation Occurs, Part A: the Meissner Effect

The zero resistivity of a superconductor means that it can act as a perfect diamagnet.  Because the material can produce arbitrarily large currents, when the superconductor is exposed to a changing magnetic flux it is capable of producing a current on its surface that will completely counteract the change in flux.  In the case of type I superconductors (these usually consist of pure metals, like mercury), the superconductor completely expels the flux lines from itself.  The exterior magnetic field produced by these induced currents, in turn, resembles that of another magnetic dipole, resulting in a repulsive force between the magnet and the superconductor.  This repulsive force causes the relatively stable levitation of the magnet.  However, the magnet must have horizontal supports, or the superconductor must be bowl-shaped to prevent the magnet from sliding off the surface.

Why Levitation Occurs, Part B: Flux Pinning in Type II Superconductors

Unlike type I materials, type II superconductors are manufactured to contain mpurities that prevent the Meissner effect from occurring in all parts of the superconductor.  Instead, when a type II superconductor is exposed to a magnetic field with a magnitude somewhere between its first and second critical magnetic field value, the impurities permit a small amount of magnetic flux to pass through "filaments" in the superconductor.  The flux lines then become "pinned" in place.  Any attempt to move the superconductor and change the position of the flux lines will result in a restoring force, either repulsing the magnet away from or attracting the magnet toward the superconductor.  A combination of the repulsive force of the Meissner effect and the restoring force of the flux trapping results in a much more stable  form of levitation than that which occurs in type I superconductors -- the position of the magnet is fixed, and no external support or unusally shaped superconductor  is required to keep the magnet stationary.  Type II superconductors, such as YBCO, also typically have higher critical temperatures than type I materials, making them better candidates for research and practical applications.

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