Superconductivity is a property exhibited by some materials at very low temperatures. It was discovered by Kamerlingh Onnes in 1911. Superconductivity is characterized by two phenomena. First, the disappearance of all electrical resistance below a certain temperature (known as the critical temperature). Second, the exclusion of any magnetic fields from the bulk of the material below the same temperature. This second property is known as the "Meissner Effect".
There are two types of superconductors. Type I superconductors are usually pure metals or alloys. They are characterized by having a single critical magnetic field, above which the superconductivity is destroyed. Lead (critical temperature Tc 7.2K) and aluminium (critical temperature 1.2K) are both type I superconductors. A microscopic theory explaining the behaviour of type I superconductors was developed by Bardeen, Cooper and Schrieffer.
A type II superconductor has both an upper (Hc2) and lower (Hc1) critical magnetic field. When the applied field (H) is less than Hc1, the field is excluded, as with a type I superconductor. When H>Hc2, superconductivity is destroyed. Between these limits, the field penetrates the bulk of the superconductor along thin lines of "normal" (non-superconducting) regions. Type II superconductors can operate under significantly higher magnetic fields; they are used commercially to make strong magnets. Examples of type II superconductors include Nb3Sn (Tc=18K) and the high-temperature copper-oxide materials such as YBa2Cu3O7 (Tc=90K).
The oxide superconductors represent a new class of materials, with critical temperatures as high as 138K. As yet these is no widely accepted theory to describe the microscopic behaviour of these superconductors.