bei48482_FM

382 Chapter Ten

a Cooper pair, called the energy gapEg, is of the order of 10^3 eV, which is why

superconductivity is a low-temperature phenomenon. The energy gap can be measured

by directing microwave radiation of frequency at a superconductor. When h Eg,

strong absorption occurs as the Cooper pairs break apart.

The BCS theory relates the energy gap of a superconductor at 0 K to its critical

temperature Tcby the formula

Energy gap at 0 K Eg(0)3.53kTc (10.25)

Equation (10.25) agrees fairly well with the observed values of Egand Tc. At temper-

atures above 0 K, some Cooper pairs break up. The resulting individual electrons in-

teract with the remaining Cooper pairs and reduce the energy gap (Fig. 10.53). Finally,

0 0.2 0.4 0.6 0.8 1.0

0.2

0.4

0.6

0.8

1.0

Relative temperature T/Tc

Relative energy gap

Eg

(T

)/

Eg

(0)

Figure 10.53Variation of the superconducting energy gap with temperature. Here Eg(T) is the energy

gap at the temperature Tand Eg(0) is the gap at T0; Tcis the critical temperature of the material.

John Bardeen(1908–1991) was

born in Madison, Wisconsin, and

studied electrical engineering at

the University of Wisconsin and

solid-state physics at Princeton

University. After working at several

universities and, during World

War II, at the Naval Ordnance Lab-

oratory, he went to Bell Telephone

Laboratories in 1945 where he

joined a semiconductor research

group led by William Shockley. In

1948 the group produced the first

transistor, for which Shockley, Bardeen, and their collaborator

Walter Brattain received a Nobel Prize in 1956. Bardeen later

said, “I knew the transistor was important, but I never foresaw

the revolution in electronics it would bring.”

In 1951 Bardeen left Bell Labs for the University of Illinois

where, together with Leon Cooper and J. Robert Schrieffer, he

developed the theory of superconductivity. Compared with his

earlier work on the transistor, “Superconductivity was more dif-

ficult to solve, and it required some radically new concepts.”

According to the theory, the motions of two electrons can be-

come correlated through their interactions with a crystal lattice,

which enables the pair to move with complete freedom through

the crystal. Bardeen received his second Nobel Prize in 1972

for this theory along with Cooper and Schrieffer; he was the

first person to receive two such prizes in the same field.

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