# Superconductivity

Superconductivity is one of most exciting phenomena in Physics, both because of the vary nature of the phenomenon and also of its prospective applications of immense potential. It was the Dutch physicist Heike Kamerlingh Onnes, who discovered phenomenon of superconductivity. He was a professor of physics at Leiden in Western Netherlands. He made cryogenic laboratory of the Leiden University to become the cold research centre of the world of his time. His interest was in liquefying gases, the attempt which he succeeded in 1908. As an extension of his low temperature work, while studying the temperature dependence of resistance of metals, he made starting discovery that, the electrical resistance in certain metals such as lead and mercury is completely wiped out without any trace at low temperatures, very near to absolute zero in 1911. In 1913, he received the Noble prize for his work.,

Further work on the nature of superconductivity by W. Hans Meissner and Robert Ochsenfeld in 1933, revealed that, when a superconductor enters into superconducting phase, the magnetic flux lines are expelled from its interior. On the other hand, a sufficiently strong field brings the superconducting material to the normal phase and then flux lines can freely pass through the body.

A reasonable successful theory for explaining the phenomenon was provided by John Bardeen, Leon N. Copper and Robert Schrieffer in 1957, and the trio was awarded the Nobel prize in 1972 (John Bardean picked the Noble prize for the second time in Physics-first time with Brattain and Shockley in 1956 for inventing transistor).

11.9.1 The temperature Dependence of Resistance of a Superconductor

The dependence of resistance of a superconductor on temperature is shown in Figure 11.29. The resistance of a superconductor in the non-superconducting state decreases with decrease in temperature as in the case of normal metal, and at a particular temperature Tc, the resistance abruptly drops to zero. Tc is called the critical temperature and signifies the transition from normal state to the superconducting state of the material under study. The critical temperature is different for different superconductors. Mercury (Hg) loses its resistance completely and turns into a superconductor at 4.2 K.

DEFINITION OF SUPERCONDUCTIVITY AND CRITICAL TEMPERATURE

The resistance offered by certain metals, alloys, and chemical compounds to the flow of electric current abruptly drops to zero below a threshold temperature. The phenomenon is called superconductivity and threshold temperature is called critical temperature.

11.9.2 Critical Magnetic Field: (Effect of Magnetic Field)

The existence of superconducting state of a metal in a magnetic field depends on the strength of the field in which it is placed and also on temperature. The condition for superconducting state to exist in metal is that some combination of temperature and field strength should be less than a critical value. Superconductivity is destroyed and normal conductivity is restored if the temperature of the specimen is raised above the critical value Tc or if a magnetic field greater than a critical value Hc is applied to the specimen. The minimum value of applied magnetic field when the material loses its superconductivity is called critical field. The variation of critical magnetic field with temperature can be represented by

11.9.4 Persistent Current

If an electric current is set up in a perfect superconductor, it can persist for a very long time without any applied e.m.f. A current can be induced in ring of superconducting material by cooling it in magnetic field below a transition temperature and then switching OFF the field. When the field is switched OFF, the magnetic field outside the ring disappears but the flux inside the entire ring is trapped. The collapse of the magnetic field outside the ring induces a large persistent current inside the ring itself and maintains the trapped flux. Once the current large persistent current inside the ring itself and maintains the trapped flux. Once the current starts even when the field is switched OFF, it persists for an indefinite period (Figure 11.31).

Once the current is set up, it persists for more than 105 years. Persistent current is one of most important properties of a superconductor.

11.9.5 Isotope Effect

It has been observed that the critical temperature (Te) of superconductors varies with the ionic or isotropic mass. The relation valid for some simple metals is given by

11.9.7 Meissner’s Effect

The second hallmark of superconductors, other than its zero resistance, was perfect diamagnetism, which was discovered by Meissner and Ochsenfeld in 1933. They found the magnetic field is pushed out of the superconducting material no matter how this field is created by an external magnet or by passing a current through the material itself. This means that the magnetic induction B inside the superconductor is always zero as long as it is in the superconducting state i.e.,

where B is the magnetic induction inside the material at time t. For a superconductor is using equation (3) in equation (4) gives B as constant. However, the Meissner effect shows the other way. Thus the conditions defining the superconducting state are

E = 0 from the absence of resistivity

and B = 0 from Meissner effect                                                  … (5)

The Meissner effect can be understood using Figures 11.32(a) and 11.32 (b). When a material is kept in magnetic field at T>Tc, it is magnetized [Fig 11.32 (a)]. However, when, the temperature of the material is reduced suddenly to T <Tc, the flux is pushed out from the material [Figure 11.32 (b)].

Experimental Verification of Meissner’s Effect. Cosider a superconducting material above its critical temperature. A primary coil and secondary coil, are wound on the material (Figure 11.33). The primary coil is connected to a battery and a key K. The secondary coil is connected to a ballistic galvanometer (B.G.). When the key K is pressed, the primary circuit is closed and a current flows through the primary coil which sets up a magnetic field in secondary coil, and hence a momentary current is driven through the B.G., which shows the magnetic flux will also become steady, and the flux linkage with the secondary become uncharging. When there is no further change in flux linkage in the secondary coil, the current will no more be driven in the secondary circuit.

Now the temperature of the superconductor is decreased gradually. As soon as the temperature crosses below the critical temperature, the B.G. suddenly shows deflection, is attributed to the expulsion of the magnetic flux from the body of the superconducting material as shown in Figure 11.32 (b).

11.9.8 Type I and Type II Superconductors

Superconducting materials are classified as either soft (Type I) or hard (Type II).

Type I Superconductor. A superconductor, which exhibits complete Meissner’s effect is called Type I superconductor. Type I materials are often pure metals and have low values of critical material is perfectly diamagnetic. Figure 11.34 shows the graph of Type I superconductor. If the magnetic field produced exceeds Hc, the material becomes normal and current cannot be sustained by itself. This was noted by Silsbee and is known as Silsbee effect.

Type II Superconductors. Type II superconductors are generally alloys or compounds, such as high temperature superconducting oxides like YBCO or BSSCO, which are able to carry very high current density in high transverse magnetic field without becoming normal. At low magnetic fields, Type II materials too will exhibit perfect diamagnetism. Figure 11.35 shows the graph for Type II superconductors.

However, another state exists in which flux penetrates the materials in clusters of flux lines. In this case, screening currents circulate around each flux bundle like small vortices. The centre of each vortex is normal, whereas the region of zero to low magnetic field is superconducting. Type II superconductors are a new kind of magnetic phase ; they are characterized by a lower critical field Hc1 at which the magnetic flux begins to enter ; and an upper critical field Hc2 at which superconductivity disappears. High temperature ceramic superconductor such as YBCO are examples of Type II superconductors.

FIGURE 11.35 Type II Superconductors

11.9.9 The difference between Type I and Type II superconductors

 Type I Superconductor Type II Superconductor Has only one critical field Hc.Named as soft superconductors.Below Hc the material exhibits complte Meissner effect. Has two critical fields Hc1 and Hc2.Named as hard superconductors.In the vertex region Hc1 and Hc2 Meissner effect is incomplete.

11.9.10 Explanation of Superconductivity (BCS Theory)

In 1957, Bardee, Copper and Scrieffer gave a theory to explain the phenomenon of superconductivity, which is knows as BCS theory.

The BCS theory is based upon the formation of Copper pairs, which is purely a quantum mechanical concept. During the flow of current in a superconductor, when an electron comes near a positive ion core of the lattice, it experiences an attractive force, because of the opposite charge polarity between electron and the ion core. The ion core will be displaced from position due to this interaction, which is called lattice distortion. Now, an electron which comes near that place will also interact with the distorted lattice, which tends to reduce the energy of the electron. This process is looked upon as equivalent to interaction between the two electrons via the lattice.

The lattice vibrations are quantized in terms of what are called phonons. Thus the process is called “electron-lattice electron interaction via the phonon field”. Because of the reduction of energy during the interaction, it is treated as equivalent to establish an attractive force between the two electrons, which is shown by Cooper to become maximum if the two electrons have equal and opposite spins and opposite momentum. The attractive force thus established may exceed the Coulomb repulsive force between the two electrons at temperatures below the critical temperature, leading to the formation of Cooper pairs.

Cooper pairs is a bound pair of electrons formed by the interaction between the electrons with opposite spin or momentum in a phonon field.

As per quantum mechanical rules, a wave function could be associated with a Cooper pair by treating it as a single entity. Such a wave function has a property that it extends over a fairly large volume with finite value for its amplitude all over the region. As a result, the wave functions associated with similar Cooper pairs start overlapping. Typically for a given Cooper pair, such an overlapping may extend over 106 other pairs. Thus it extends virtually over the entire volume of the superconductor. This leads to a union of vast number of Cooper pairs in which motion of all such pairs are under strong correlation – one aiding the motion of the other. It results in an effect equivalent to the entire union moving as a single unit. The resistance encountered by any single Cooper pair is simply overcome by the cooperative action of other pairs in the union. Thus we can define superconductivity as follows:

When the electron flow in the form of Cooper pairs in materials, they do not encounter any scattering and the resistance factor vanishes or in other words, conductivity becomes infinity, which named as superconductivity.

In addition to the isotope effect, the idea that the electron-lattice interaction plays a crucial role in superconductivity is supported by the fact that, the best of the conductors such as gold, silver and copper do not exhibit superconductivity. The reason attributed is that the electrons in those metals, move so freely in the lattice that, the electron-lattice interactions is virtually absent. This rules out the possibility of formation of Cooper pairs and also that of occurrences of superconductivity in the material.

11.9.11 Applications of Superconductivity

The capability of retaining superconductivity at high fields, high current densities make superconductors useful in a variety of applications in electric power engineering, transportation, medical diagnostics and microelectrics.

Some futuristic applications of superconductors include transmission lines that carry power without resistance medical diagnostic equipment that eliminate the need for surgery, levitating trains and so on.

Some of the current uses of superconductors and some that hold the most promise for near future are:

Magnet resonance imaging (MRI) machines enhance medical diagnostics by imaging internal organs often eliminating the need for invasive surgeries. MRIs which are currently made from low temperature superconductors, will be smaller and less expensive when made with HTS.

Maglev trains that seem to float on air because of superconducting magnets. These trains have been under development in Japan for two decade, the nearest prototype may exceed 547 km/h.

Energy storage in flywheel systems will ensure the quality and reliability of power transmitted to utility customers. In addition, energy storage provides utilities with cost saving by allowing them to store energy when the demand for the electricity is low and generating power is cheap. This energy is then dispended when demand is high and power production is more expensive.

Power transmission cables that carry current without energy losses, will increase the capacity of the transmission system saving money, space and energy.

Current controllers help utilities deliver reliable power to their customers. HTS fault current limiters detect abnormally high current in utility grid. Then they reduce the fault current so that the system equipment can handle it.

Generators with superconducting wire in place of iron magnets will be smaller and lighter. New generators may also generate more power from less fuel.

Motors made with superconducting wire will be smaller and more efficient.

These are only a few of many possible uses of superconductors, research and development of HTS may still yield many more uses for materials that can carry electricity without resistances.