If the voltage is zero, then the resistance is zero, which means that the electric current is flowing freely through the sample and the sample is in its superconducting state.

      Superconductors are also able to maintain a current with no applied voltage whatsoever, a property exploited in superconducting electromagnets such as those found in MRI machines. Experiments have demonstrated that currents in superconducting coils can persist for years without any measurable degradation. Experimental evidence points to a current lifetime of at least 100,000 years, and theoretical estimates for the lifetime of persistent current exceed the lifetime of the universe.

      In a normal conductor, an electrical current may be visualized as a fluid of electrons moving across a heavy lattice (the conducting material), consisting of atoms that are electrically neutral. The electrons are constantly colliding with the ions (electrically neutral atoms) in the lattice, and during each collision some of the energy carried by the current is absorbed by the lattice and converted into (which is essentially the vibrational , energy due to motion of the lattice ions). As a result, the energy carried by the current is constantly dissipated. This is the phenomenon of electrical resistance.

      In superconductors, on the other hand, the electronic fluid is not made up of individual electrons, but rather pairs of electrons called Cooper pairs, held together by an attractive force arising from the microscopic vibrations in the lattice. According to quantum mechanics, this Cooper pair fluid requires a minimum amount of energy, ∆E, for it to conduct an electrical current. Specifically, the energy supplied to the fluid needs to be greater than the thermal energy (temperature) of the lattice in order for superconductivity to appear. This is why superconductivity is achieved at extremely low temperatures.

      Superconducting phase transition

      In superconducting materials, the characteristics of superconductivity appear when the temperature T is lowered below a critical temperature T_c. The value of this critical temperature varies from material to material. Conventional superconductors usually have critical temperatures ranging from less than 1 K to around 20 K. Solid , for example, has a critical temperature of 4.2 K. As of 2001, the highest critical temperature found for a conventional superconductor is 39 K for magnesium diboride (MgB₂), although this material displays rather exotic properties that there is doubt about classifying it as a "conventional" superconductor. Cuprate superconductors can have much higher critical temperatures: YBCO (YBa₂Cu₃O₇), one of the first cuprate (copper based) superconductors to be discovered, has a critical temperature of 92 K, and mercury-based cuprates have been found with critical temperatures in excess of 130 K. The explanation for these high critical temperatures remains unknown.

      The onset of superconductivity is accompanied by abrupt changes in various physical properties, which is the hallmark of a phase transition (when a material changes state, such as from solid to liquid). One such change, as seen above with the Cooper pairing, is that the electronic fluid in a normal conductor becomes a Cooper pair fluid in the superconducting state and this fluid also becomes a superfluid.

      Meissner effect

      When a superconductor is placed in a weak external , the field penetrates the superconductor for only a short distance, called the penetration depth, after which it decays rapidly to zero. This is called the Meissner effect, and is a defining characteristic of superconductivity. For most superconductors, the penetration depth is on the order of 100 nanometers.

      The Meissner effect states that a superconductor expels all magnetic fields. Suppose we have a material in its normal state, containing a constant internal magnetic field. When the material is cooled below the critical temperature, we would observe the abrupt expulsion of the internal magnetic field. An equation (known as the London equation) predicts that the magnetic field in a superconductor decays exponentially from whatever value it possesses at the surface.

      The Meissner effect breaks down when the applied magnetic field is too large. Superconductors can be divided into two classes according to how this breakdown occurs.

      In Type I superconductors, superconductivity is abruptly lost when the strength of the applied field rises above a critical value. Depending on the geometry of the sample, one may obtain an intermediate state consisting of regions of normal material carrying a magnetic field mixed with regions of superconducting material containing no field.

      In Type II superconductors, raising the applied field past a critical value leads to a mixed state in which an increasing amount of magnetic flux (an amount of something that flows through a unit area in a unit time) penetrates the material, but there remains no resistance to the flow of electrical current as long as the current is not too large.

      At a second critical field strength, superconductivity is destroyed. Most pure superconductors (except , , and ) are Type I, while almost all impure and compound superconductors are Type II.

      Applications

      Superconductors are used to make some of the most powerful electromagnets known to man, including those used in MRI machines and the beam-steering magnets used in . They can also be used for magnetic separation, where weak magnetic particles are extracted from a background of less or non-magnetic particles, as in the industries.

      Superconductors have also been used to make digital circuits and filters for mobile phone base stations.

      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 a 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 photon detectors.

      Other early markets are arising where the relative efficiency, size, and weight advantages