A WRITEUP ON SUPERCONDUCTIVITY

Superconductivity is a phenomenon occurring in certain materials at very low temperatures, characterized by exactly zero electrical resistance and the exclusion of the interior magnetic field (this is known as Meissner effect).
The electrical resistivity of a metallic conductor decreases gradually as the temperature is lowered. However, in ordinary conductors such as copper and silver, impurities and other defects impose a lower limit. Even near absolute zero a real sample of copper shows a non-zero resistance. The resistance of a superconductor, on the other hand, drops abruptly to zero when the material is cooled below its "critical temperature". An electric current flowing in a loop of superconducting wire can persist indefinitely with no power source. Like ferromagnetism and atomic spectral lines, superconductivity is a quantum mechanical phenomenon. It cannot be understood simply as the idealization of "perfect conductivity" in classical physics.
Superconductivity occurs in a wide variety of materials, including simple elements like tin and aluminium, various metallic alloys and some heavily-doped semiconductors. Superconductivity does not occur in noble metals like gold and silver, nor in most ferromagnetic metals.
In 1986 the discovery of a family of cuprate-perovskite ceramic materials known as high-temperature superconductors, with critical temperatures in excess of 90 Kelvin, spurred renewed interest and research in superconductivity for several reasons. As a topic of pure research, these materials represented a new phenomenon not explained by the current theory. And, because the superconducting state persists up to more manageable temperatures, past the economically-important boiling point of liquid nitrogen (77 Kelvin), more commercial applications are feasible, especially if materials with even higher critical temperatures could be discovered.
Elementary properties of superconductors
Most of the physical properties of superconductors vary from material to material, such as the heat capacity and the critical temperature, critical field, and critical current density at which superconductivity is destroyed.
On the other hand, there is a class of properties that are independent of the underlying material. For instance, all superconductors have exactly zero resistivity to low applied currents when there is no magnetic field present. The existence of these "universal" properties implies that superconductivity is a thermodynamic phase, and thus possess certain distinguishing properties which are largely independent of microscopic details.
Theories of superconductivity
Since the discovery of superconductivity, great efforts have been devoted to finding out how and why it works. During the 1950s, theoretical condensed matter physicists arrived at a solid understanding of "conventional" superconductivity, through a pair of remarkable and important theories: the phenomenological Ginzburg-Landau theory (1950) and the microscopic BCS theory (1957). Generalizations of these theories form the basis for understanding the closely related phenomenon of superfluidity, because they fall into the Lambda transition universality class, but the extent to which similar generalizations can be applied to unconventional superconductors as well is still controversial. The four-dimensional extension of the Ginzburg-Landau theory, the Coleman-Weinberg model, is important in quantum field theory and cosmology.

Classification
There is not just one criterion to classify superconductors. The most common are:
By their physical properties: they can be Type I (if their phase transition is of first order) or Type II (if their phase transition is of second order).
By the theory to explain them: they can be conventional (if they are explained by the BCS theory or its derivates) or unconventional (if not).
By their critical temperature: they can be high temperature (generally considered if they reach the superconducting state just cooling them with liquid nitrogen, that is, if Tc > 77K), or low temperature (generally if they need other techniques to be cooled under their critical temperature).
By material: they can be chemical elements (as mercury or lead), alloys (as niobium-titanium or germanium-niobium), ceramics (as YBCO or the magnesium diboride), or organic superconductors (as fullerens or carbon nanotubes, which technically might be included between the chemical elements as they are made of carbon).

Applications
[1] Superconducting magnets are some of the most powerful electromagnets known. They are used in maglev trains, MRI and NMR machines and the beam-steering magnets used in particle accelerators.
[2] They can also be used for magnetic separation, where weakly magnetic particles are extracted from a background of less or non-magnetic particles, as in the pigment industries.
[3]Superconductors have also been used to make digital circuits (e.g. based on the Rapid Single Flux Quantum technology) and RF and microwave filters for mobile phone base stations.
[4] Superconductors are used to build Josephson junctions which are the building blocks of SQUIDs (superconducting quantum interference devices), the most sensitive magnetometers known. Series of Josephson devices are used to define the SI volt. Depending on the particular mode of operation, a Josephson junction can be used as photon detector or as mixer. The large resistance change at the transition from the normal- to the superconducting state is used to build thermometers in cryogenic micro-calorimeter photon detectors.
[5] Other early markets are arising where the relative efficiency, size and weight advantages of devices based on HTS outweigh the additional costs involved.
[6] Promising future applications include high-performance transformers, power storage devices, electric power transmission, electric motors (e.g. for vehicle propulsion, as in vactrains or maglev trains), magnetic levitation devices, and Fault Current Limiters.
However superconductivity is sensitive to moving magnetic fields so applications that use alternating current (e.g. transformers) will be more difficult to develop than those that rely upon direct current.