fenomenološka teorija supravodljivosti - Odjel za fiziku - Sveučilište ...

5. ABSTRACT :
In this work, we study the remarkabel phenomenon of superconductivity. These theories
were suprisingly accurate and profoundly influenced the present many-body theory of
superconductors. The later ( BSC ) theory represents one of the most successful applications of
many-body techniques; in addition to its new predictions, it also justifies the earlier descriptions
and allows an evaluation of the phenomenological constants.
Basic experimental facts:
Infinite conductivity: When any one of a large class of metallic elements or compounds
is cooled to within a few degrees of absolute zero, it abruptly losses all trace of electrical
resistivity at a definite critical temperature T c. As a first approximation, we assume the
usual constitutive equation ( Ohm'¨s law )
r r
j = σE
A combination with Maxwell's equation
∂B
r
= − curlE
∂t
Meissner effect: When the sample is cooled and become superconducting, experiments
first first performed by Meissner and Ochsenfeld demonstrate that all magnetic flux is
expelled from the interior. Note that this results does not contradict the previous
conclusion of constant B in the superconducting state; rather it indicates that the constant
value must always be taken as zero.
Critical field: For simplicity, we consider a long cylinder of pure superconductor in a
parallel appplied field H, where there are no demagnetizing effects. If the semple is
superconducting at temperature T in zero field, there is a unique critical field H c ( T )
above which the sample become normal.
H
c
( T ) = H ( 0)
c
⎡ ⎛
⎢1
−
⎜
⎢⎣
⎝
Persistent currents and flux quantization: as a different example of magnetic behavior,
consider a normal metallic ring place din a magnetic field perpendicular to its plane.
When the temperature is lowered, the metal becomes superconducting and expels the
flux. Suppose the external field is then removed; no flux can pass through the
T
T
c
2
⎞ ⎤
⎟ ⎥
⎠ ⎥⎦
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