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  • Condensed Matter Theory


    Superconductivity is a fascinating phenomenon, which exhibits the effects of quantum mechanics on a macroscopic scale. In particular, the electrons move coherently in a single quantum state. In conventional superconductors, this coherence has come about because of an effective attraction between electrons due to the lattice vibrations (phonons) and sees the electrons paired together (as Cooper pairs). Cooper pairs have integer spin, so have the properties of bosons, and indeed, superconductivity can be considered as the Bose-Einstein condensation of Cooper pairs.

    Superconductors are named as such, because of their ability to conduct electricity with zero energy loss, or zero resistance (up to a critical current density). This is principally because the current carrying state is also a quantum ground state of the superconductor, and there is a finite energy gap (Delta) to any excited state. This means that individual electrons are scattered by impurities or thermal vibrations, which are the normal causes of resistance. At temperatures high enough such that the thermal energy (kT) is of the order of the gap (Delta) the superconducting properties disappear. Hence superconductors only work below a critical temperature, Tc, which ranges from 0-23 degrees Kelvin for conventional superconductors, but has reached over 130K for high-temperature superconductors. Note that high-temperature in this field is still at colder than -140 degrees Celsius or -220 degrees Fahrenheit!

    The more fundamental signature of a superconductor, though, is its ability to expel a magnetic field from within its interior, so long as the field is below a critical value (Hc). The expulsion of magnetic field is called the Meissner Effect, and results in a repulsive force between a superconductor and any magnet placed near it. Many demonstrations of superconductors show the Meissner Effect as a small magnet levitating above the superconductor. The effect has a large scale technological application in Japan, where it is used to levitate high speed trains.

    Fundamental Quantum Theory

    The EPR paradox appears to show that certain "common sense" questions about an electron (or other "quantum" particle) have no meaning until an observation is made. Such a positivist interpretation is unsatisfactory, but generally ignored. The Dirac equation, which is the fundamental description of electron, as it is relativistic and produces the spin properties of electrons, contains an infinity of solutions which are of negative energy, and assumed to be occupied by an infinite number (or "Dirac sea") of electrons, which do not interact, but whose absence is observed as a "hole" or positron. This state of affairs may be considered unsatisfactory by Occham's rasor, if a simpler solution is at hand. Both problems may be resolved if a more time-symmetric theory is established, and boundary conditions in time are considered in an equivalent manner to boundary conditions in space, as Einstein's special relativity might suggest. See John Gribbin's interesting discussions.

    Last modified December 29, 1997

    Paul Miller, pmiller@brandeis.edu

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