Superconductors

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  • Topic: Superconductivity, Magnetic field, BCS theory
  • Pages : 11 (3606 words )
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  • Published : April 20, 2013
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TERM PAPER ON SUPERCONDUCTIVITY BY: VISHAL K YADAV (B.TECH 1ST yr) Superconductivity

"The discovery of superconductors"

The phenomenon of superconductivity, in which the electrical resistance of certain materials completely vanishes at low temperatures, is one of the most interesting and sophisticated in condensed matter physics. It was first discovered by the Dutch physicist Heike Kamerlingh Onnes, who was the first to liquefy helium (which boils at 4.2 Kelvin at standard pressure). In 1911 Kamerlingh Onnes and one of his assistants discovered the phenomenon of superconductivity while studying the resistance of metals at low temperatures. They studied mercury because very pure samples could easily be prepared by distillation. The historic measurement of superconductivity in mercury is shown in Figure 1. As in many other metals, the electrical resistance of mercury decreased steadily upon cooling, but dropped suddenly at 4.2 K, and became undetectably small. Soon after this discovery, many other elemental metals were found to exhibit zero resistance when their temperatures were lowered below a certain characteristic temperature of the material, called the critical temperature, Tc, some of which are given in Figure 2.

Figure 1. The resistance of mercury measured by Onnes.

Figure 2. The critical temperatures of some superconductors.

In 1933, Walter Meissner and Robert Ochsenfeld discovered a magnetic phenomenon that showed that superconductors are not just perfect conductors. Figure 3 illustrates a thought experiment that highlights this difference. Imagine that both the ideal conductor and superconductor are above their critical temperature, Tc. That is, they both are in a normal conducting state and have electrical resistance. A magnetic field, Ba, is then applied. This results in the field penetrating both materials. Both samples are then cooled so that the ideal conductor now has zero resistance. It is found that the superconductor expels the magnetic field from inside it, while the ideal conductor maintains its interior field. Note that energy is needed by the superconductor to expel the magnetic field. This energy comes from the exothermic superconducting transition. Switching off the field induces currents in the ideal conductor that prevent

The Meissner effect

changes in the magnetic field inside it – by Lenz’s law. However, the superconductor returns to its initial state, i.e. no magnetic field inside or outside it.

Figure 3. The Meissner effect.

High magnetic fields destroy superconductivity and restore the normal conducting state. Depending on the character of this transition, we may distinguish between type I and II superconductors. The graph shown in Figure 4 illustrates the internal magnetic field strength, Bi, with increasing applied magnetic field. It is found that the internal field is zero (as expected from the Meissner effect) until a critical magnetic field, Bc, is reached where a sudden transition to the normal state occurs. This results in the penetration of the applied field into the interior. Superconductors that undergo this abrupt transition to the normal state above a critical magnetic field are known as type I superconductors. Most of the pure elements in Figure 2 tend to be type I superconductors. Type II superconductors, on the other hand, respond differently to an applied magnetic field, as shown in Figure 5. An increasing field from zero results in two critical fields, Bc1 and Bc2. At Bc1 the applied field begins to partially penetrate the interior of the superconductor. However, the superconductivity is maintained at this point. The superconductivity vanishes above the second, much higher, critical field, Bc2. For applied fields between Bc1 and Bc2, the applied field is able to partially penetrate the superconductor, so the Meissner effect is incomplete, allowing the superconductor to tolerate very high magnetic fields.

Type I and II superconductors...
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