bei48482_FM

The Solid State 383

at the critical temperature Tc, the energy gap disappears, there are no more Cooper

pairs, and the material is no longer superconducting.

The electrons in a Cooper pair have opposite spins, so the pair has a total spin of

zero. As a result, the electron pairs in a superconductor are bosons (unlike individual

electrons, which have spins of^12 and are fermions), and any number of them can exist

in the same quantum state at the same time. When there is no current in the super-

conductor, the linear momenta of the electrons in a Cooper pair are equal and opposite

for a total of zero. All the pairs are then in the same ground state and make up a giant

system the size of the superconductor. A single wave function represents this system,

whose total energy is less than that of a system of the same number of electrons with

a Fermi energy distribution.

A current in a superconductor involves the entire system of electron pairs acting as

a unit. Every pair now has a non-zero momentum. To alter such a current means that

the correlated states of motion of allthe electron pairs, not just the states of motion of

some individual electrons as in an ordinary conductor, must be changed. Because such

a change requires a relatively large amount of energy, the current persists indefinitely

F

igure 10.54 shows a superconducting ring of area Athat carries a current. The amount of

magnetic flux BApasses through the ring as a result. According to Faraday’s law of

electromagnetic induction, any change in the flux will change the current in the ring so as to

oppose the change in flux. Because the ring has no resistance, the change in flux will be per-

fectly canceled out. The flux therefore is permanently trapped.

Because the phase of the wave function of the Cooper pairs in the ring must be continuous

around the ring, it turns out that is quantized. The only values that can have are

Flux quantization n n 0 n1, 2, 3,... (10.26)

The quantum of magnetic flux is

Flux quantum  0 2.068 10 ^15 Tm^2

h

2 e

h

2 e

Flux Quantization

Area = A

B

Figure 10.54The magnetic flux BAthat passes through a superconducting ring can only have

the values n 0 where  0 is the flux quantum and n1, 2, 3,...

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