Zero Resistance

How can occur zero resistance and what is the reason of these phenomena?
Superconductivity was not sufficiently explained until 1957 when John Bardeen and his graduate assistants Leon Cooper and John Schrieffer proposed a microscopic explanation that would later be their namesake: the BCS Theory. This theoretical explanation later earned them the Nobel prize.

The BCS Theory is, in its simplest form, actually contradictory to our crude macroscopic view expressed earlier. As discussed earlier, superconductivity arises because electrons do not interact destructively with atoms in the crystal lattice of the material. The BCS Theory says that electrons do actually interact with the atoms, but constructively.

Cooper realized that atomic lattice vibrations were directly responsible for unifying the entire current. They forced the electrons to pair up into teams that could pass all of the obstacles which caused resistance in the conductor. These teams of electrons are known as Cooper pairs. Cooper and his colleagues knew that electrons which normally repel one another must feel an overwhelming attraction in superconductors. The answer to this problem was found to be in phonons, packets of sound waves present in the lattice as it vibrates. Although this lattice vibration cannot be heard, its role as a moderator is indispensable.

According to the theory, as one negatively charged electron passes by positively charged ions in the lattice of the superconductor, the lattice distorts. This in turn causes phonons to be emitted which form a trough of positive charges around the electron.

Before the electron passes by and before the lattice springs back to its normal position, a second electron is drawn into the trough. It is through this process that two electrons, which should repel one another, link up. The forces exerted by the phonons overcome the electrons' natural repulsion. The electron pairs are coherent with one another as they pass through the conductor in unison. The electrons are screened by the phonons and are separated by some distance. When one of the electrons that make up a Cooper pair and passes close to an ion in the crystal lattice, the attraction between the negative electron and the positive ion cause a vibration to pass from ion to ion until the other electron of the pair absorbs the vibration. The net effect is that the electron has emitted a phonon and the other electron has absorbed the phonon. It is this exchange that keeps the Cooper pairs together. It is important to understand, however, that the pairs are constantly breaking and reforming. Because electrons are indistinguishable particles, it is easier to think of them as permanently paired. Figure illustrates how two electrons, called Cooper pairs, become locked together.

By pairing off two by two the electrons pass through the superconductor more smoothly. The electron may be thought of as a car racing down a highway. As it speeds along, the car cleaves the air in front of it. Trailing behind the car is a vacuum, a vacancy in the atmosphere quickly filled by inrushing air. A tailgating car would be drawn along with the returning air into this vacuum. The rear car is, effectively, attracted to the one in front. As the negatively charged electrons pass through the crystal lattice of a material they draw the surrounding positive ion cores toward them. As the distorted lattice returns to its normal state another electron passing nearby will be attracted to the positive lattice in much the same way that a tailgater is drawn forward by the leading car.

The BCS theory successfully shows that electrons can be attracted to one another through interactions with the crystalline lattice. This occurs despite the fact that electrons have the same charge. When the atoms of the lattice oscillate as positive and negative regions, the electron pair is alternatively pulled together and pushed apart without a collision. The electron pairing is favorable because it has the effect of putting the material into a lower energy state. When electrons are linked together in pairs, they move through the superconductor in an orderly fashion.

As long as the superconductor is cooled to very low temperatures, the Cooper pairs stay intact, due to the reduced molecular motion. As the superconductor gains heat energy the vibrations in the lattice become more violent and break the pairs. As they break, superconductivity diminishes. This explains (roughly) why superconductivity requires low temperatures- the thermal vibration


a) Electrons carrying an electrical current through a metal wire typically encounter resistance, which is caused by collisions and scattering as the particles move through the vibrating lattice of metal atoms and electrical resistance occurs.

b) As the metal is cooled to low temperatures, the lattice vibration slows. A moving electron attracts nearby metal atoms, which create a positively charged wake behind the electron. This wake can attract another nearby electron

c) The two electrons form weak bond, called a Cooper pair, which encounters less resistance than two electrons moving separately. When more Cooper pairs form, they behave in the same way.

d) If a pair is scattered by an impurity, it will quickly get back in step with other pairs. This allows the electrons to flow un disturb through the lattice of metal atoms. With no resistance, the current may persist for years.

of the lattice must be small enough to allow the forming of Cooper pairs. In a superconductor, the current is made up of these Cooper pairs, rather than individual electrons

This BCS theory prediction of Cooper pair interaction with the crystal lattice has been verified experimentally by the isotope effect. That is, the critical temperature of a material depends on the mass of the nucleus of the atoms. If an isotope is used (neutrons are added to make it more massive), the critical temperature decreases. This effect is most evident in Type-I, and appears only weakly in Type-II.

This superconductivity of Cooper pairs is somewhat related to Bose-Einstein Condensation. The Cooper pairs act somewhat like bosons, which condense into their lowest energy level below the critical temperature, and lose electrical resistance.


The BCS Theory did exactly what a physical theory should do: it explained properties already witnessed in experiment, and it predicted experimentally verifiable phenomena. Though its specific quantitative elements were quite limited in their application (it only explained Type-I s-wave superconductivity), its essence was quite broad and has been modified applied to various other superconductors, such as Type-II perovskites.
Here the transition temperature Tc varies as where M is the mass of an isotope of a particular element. This pointed to the importance of lattice vibrations (whose frequency would be proportional to ) in mediating superconductivity.


In fact in the superconducting state the resistance falls to very small value, not zero. The resistance of any specimen may always be just less than the sensitivity of our apparatus allows us to detect. A more sensitive test, however, is to start a curret flowing round a closed superconducting ring and then see whether there is any decay in the current after a long period of time. Suppose the self inductance of the ring is L; then if at time t=0 we start a current i(0) flowing round the ring, at later time t the current will have decayed to

i(t) =i(0) e^–(R/L) t (2.2)


where R is the resistance of the ring. We can not measure the current into the circuit but can measure the magnetic field that the circulating current produces and see if the decays with time. The measurement of the magnetic field does not draw energy from the circuit, and we should be able to observe whether the current circulates indefinitely (Equation 2.2).


As can bee seen from equation for the smaller the inductance L of the circuit the more rapid the decay of current for a given value of resistance R and the more sensitive experiment

Superconductivity

Superconductivity




If mercury is cooled below 4.1 K, it loses all electric resistance. This discovery of superconductivity by H. Kammerlingh Onnes in 1911 was followed by the observation of other metals which exhibit zero resistivity below a certain critical temperature. The fact that the resistance is zero has been demonstrated by sustaining currents in superconducting lead rings for many years with no measurable reduction. An induced current in an ordinary metal ring would decay rapidly from the dissipation of ordinary resistance, but superconducting rings had exhibited a decay constant of over a billion years!

One of the properties of a superconductor is that it will exclude magnetic fields, a phenomenon called the Meissner effect.

The disappearance of electrical resistivity was modeled in terms of electron pairing in the crystal lattice by John Bardeen, Leon Cooper, and Robert Schrieffer in what is commonly called the BCS theory.

A new era in the study of superconductivity began in 1986 with the discovery of high critical temperature superconductors.


Critical Temperature for Superconductors

The critical temperature for superconductors is the temperature at which the electrical resistivity of a metal drops to zero. The transition is so sudden and complete that it appears to be a transition to a different phase of matter; this superconducting phase is described by the BCS theory. Several materials exhibit superconducting phase transitions at low temperatures. The highest critical temperature was about 23 K until the discovery in 1986 of some high temperature superconductors.


Materials with critical temperatures in the range 120 K have received a great deal of attention because they can be maintained in the superconducting state with liquid nitrogen (77 K).
The temperature at which electrical resistance is zero is called the critical temperature (Tc) and this temperature is a characteristic of the material as it is shown in the following table:




The cooling of the materials is achieved using liquid nitrogen or liquid helium for even lower temperatures.There is already in this small table a clear separation between the low and high temperature superconductors. While superconductivity at low temperature is well understood, there is no clear explanation as yet of this phenomena at "high temperatures".