Superconductors can be classified in accordance with several criteria that depend on our interest in their physical properties, on the understanding we have about them, on how expensive is cooling them or on the material they are made of.

By their physical properties

• Type I superconductor
  Type I superconductor
  Superconductors cannot be penetrated by magnetic flux lines . This Meissner state breaks down when the applied magnetic field is too large. Superconductors can be divided into two classes according to how this breakdown occurs...
  
  s: those having just one critical field, H_c, and changing abruptly from one state to the other when it is reached.
• Type II superconductors: having two critical fields, H_c1 and H_c2, being a perfect superconductor under the lower critical field (H_c1) and leaving completely the superconducting state above the upper critical field
  Upper critical field
  -Upper critical field:The upper critical field is the magnetic field which completely suppresses superconductivity in a Type II superconductor at 0K ....
  
   (H_c2), being in a mixed state when between the critical fields.

By the understanding we have about them

• Conventional superconductor
  Conventional superconductor
  Conventional superconductors are materials that display superconductivity as described by BCS theory or its extensions.Critical temperatures of some simple metals:ElementTc Al1.20Hg4.15Mo0.92Nb9.26Pb7.19...
  
  s: those that can be fully explained with the BCS theory
  BCS theory
  BCS theory — proposed by Bardeen, Cooper, and Schrieffer in 1957 — is the first microscopic theory of superconductivity since its discovery in 1911. The theory describes superconductivity as a microscopic effect caused by a "condensation" of pairs of electrons into a boson-like state...
  
   or related theories.
• Unconventional superconductor
  Unconventional superconductor
  Unconventional superconductors are materials that display superconductivity which does not conform to either the conventional BCS theory or the Nikolay Bogolyubov's theory or its extensions....
  
  s: those that failed to be explained using such theories.

This criterion is important, as the BCS theory is explaining the properties of conventional superconductors since 1957, but on the other hand there have been no satisfactory theory to explain fully unconventional superconductors. In most of cases type I superconductors are conventional, but there are several exceptions as niobium

Niobium

Niobium or columbium , is a chemical element with the symbol Nb and atomic number 41. It's a soft, grey, ductile transition metal, which is often found in the pyrochlore mineral, the main commercial source for niobium, and columbite...

, which is both conventional and type II.

By their critical temperature

• Low-temperature superconductors, or LTS: those whose critical temperature is below 77K.
• High-temperature superconductors, or HTS: those whose critical temperature is above 77K.

This criterion is used when we want to emphasize whether or not we can cool the sample with liquid nitrogen

Liquid nitrogen

Liquid nitrogen is nitrogen in a liquid state at a very low temperature. It is produced industrially by fractional distillation of liquid air. Liquid nitrogen is a colourless clear liquid with density of 0.807 g/mL at its boiling point and a dielectric constant of 1.4...

 (whose boiling point

Boiling point

The boiling point of an element or a substance is the temperature at which the vapor pressure of the liquid equals the environmental pressure surrounding the liquid....

 is 77K), which is much more feasible than liquid helium

Liquid helium

Helium exists in liquid form only at extremely low temperatures. The boiling point and critical point depend on the isotope of the helium; see the table below for values. The density of liquid helium-4 at its boiling point and 1 atmosphere is approximately 0.125 g/mL Helium-4 was first liquefied...

 (the alternative to achieve the temperatures needed to get low-temperature superconductors).

By material

• Some Pure element
  Chemical element
  A chemical element is a pure chemical substance consisting of one type of atom distinguished by its atomic number, which is the number of protons in its nucleus. Familiar examples of elements include carbon, oxygen, aluminum, iron, copper, gold, mercury, and lead.As of November 2011, 118 elements...
  
  s, such as lead
  Lead
  Lead is a main-group element in the carbon group with the symbol Pb and atomic number 82. Lead is a soft, malleable poor metal. It is also counted as one of the heavy metals. Metallic lead has a bluish-white color after being freshly cut, but it soon tarnishes to a dull grayish color when exposed...
  
   or mercury
  Mercury (element)
  Mercury is a chemical element with the symbol Hg and atomic number 80. It is also known as quicksilver or hydrargyrum...
  
   (but not all pure elements, as some never reach the superconducting phase).
  • Some allotropes of carbon
    Allotropes of carbon
    This is a list of the allotropes of carbon.-Diamond:Diamond is one of the most well known allotropes of carbon. The hardness and high dispersion of light of diamond make it useful for both industrial applications and jewellery. Diamond is the hardest known natural mineral. This makes it an...
    
    , such as fullerene
    Fullerene
    A fullerene is any molecule composed entirely of carbon, in the form of a hollow sphere, ellipsoid, or tube. Spherical fullerenes are also called buckyballs, and they resemble the balls used in association football. Cylindrical ones are called carbon nanotubes or buckytubes...
    
    s, nanotubes, or diamond
    Covalent superconductors
    Covalent semiconductors are such solids as diamond, silicon, germanium, silicon carbide and silicon-germanium where atoms are linked by covalent bonds. Most of those materials, at least in their bulk form, are well studied and rarely hit the front pages of the top scientific journals in the last...
    
    .

Most superconductors made of pure elements are type I (except niobium, technetium

Technetium

Technetium is the chemical element with atomic number 43 and symbol Tc. It is the lowest atomic number element without any stable isotopes; every form of it is radioactive. Nearly all technetium is produced synthetically and only minute amounts are found in nature...

, vanadium

Vanadium

Vanadium is a chemical element with the symbol V and atomic number 23. It is a hard, silvery gray, ductile and malleable transition metal. The formation of an oxide layer stabilizes the metal against oxidation. The element is found only in chemically combined form in nature...

, silicon and the abovementioned carbons).

• Alloy
  Alloy
  An alloy is a mixture or metallic solid solution composed of two or more elements. Complete solid solution alloys give single solid phase microstructure, while partial solutions give two or more phases that may or may not be homogeneous in distribution, depending on thermal history...
  
  s, such as
  • Niobium-titanium
    Niobium-titanium
    Niobium-titanium is an alloy of niobium and titanium, used industrially as a type II superconductor wire for superconducting magnets...
    
    (NbTi), whose superconducting properties were discovered in 1962.

• Ceramic
  Ceramic
  A ceramic is an inorganic, nonmetallic solid prepared by the action of heat and subsequent cooling. Ceramic materials may have a crystalline or partly crystalline structure, or may be amorphous...
  
  s, which include
  • The YBCO family, which are several yttrium
    Yttrium
    Yttrium is a chemical element with symbol Y and atomic number 39. It is a silvery-metallic transition metal chemically similar to the lanthanides and it has often been classified as a "rare earth element". Yttrium is almost always found combined with the lanthanides in rare earth minerals and is...
    
    -barium
    Barium
    Barium is a chemical element with the symbol Ba and atomic number 56. It is the fifth element in Group 2, a soft silvery metallic alkaline earth metal. Barium is never found in nature in its pure form due to its reactivity with air. Its oxide is historically known as baryta but it reacts with...
    
    -copper
    Copper
    Copper is a chemical element with the symbol Cu and atomic number 29. It is a ductile metal with very high thermal and electrical conductivity. Pure copper is soft and malleable; an exposed surface has a reddish-orange tarnish...
    
     oxides, especially YBa₂Cu₃O₇. They are the most famous high-temperature superconductors.
  • Magnesium diboride
    Magnesium diboride
    Magnesium diboride is a simple ionic binary compound that has proven to be an inexpensive and useful superconducting material.Its superconductivity was announced in the journal Nature in March 2001. Its critical temperature of is the highest amongst conventional superconductors...
    
    (MgB₂), whose critical temperature is 39K, being the conventional superconductor with the highest known temperature.

See also

• Conventional superconductor
  Conventional superconductor
  Conventional superconductors are materials that display superconductivity as described by BCS theory or its extensions.Critical temperatures of some simple metals:ElementTc Al1.20Hg4.15Mo0.92Nb9.26Pb7.19...
  
  
• covalent superconductors
  Covalent superconductors
  Covalent semiconductors are such solids as diamond, silicon, germanium, silicon carbide and silicon-germanium where atoms are linked by covalent bonds. Most of those materials, at least in their bulk form, are well studied and rarely hit the front pages of the top scientific journals in the last...
  
  
• List of superconductors
• High-temperature superconductivity
  High-temperature superconductivity
  High-temperature superconductors are materials that have a superconducting transition temperature above . From 1960 to 1980, 30 K was thought to be the highest theoretically possible Tc...
  
  
• Room temperature superconductor
  Room temperature superconductor
  A room-temperature superconductor is a material yet to be discovered which would be capable of exhibiting superconducting properties at operating temperatures above 0° C . This is not strictly speaking "room temperature" A room-temperature superconductor is a material yet to be discovered...
  
  
• Superconductivity
  Superconductivity
  Superconductivity is a phenomenon of exactly zero electrical resistance occurring in certain materials below a characteristic temperature. It was discovered by Heike Kamerlingh Onnes on April 8, 1911 in Leiden. Like ferromagnetism and atomic spectral lines, superconductivity is a quantum...
  
  
• Technological applications of superconductivity
  Technological applications of superconductivity
  Some of the technological applications of superconductivity include:* the production of sensitive magnetometers based on SQUIDs* fast digital circuits ,...
  
  
• Timeline of low-temperature technology
  Timeline of low-temperature technology
  The following is a timeline of low-temperature technology and cryogenic technology .-16th century BCE – 17th century CE :...
  
  
• Type-I superconductor
• Type-II superconductor
  Type-II superconductor
  A Type-II superconductor is a superconductor characterized by the formation of vortex lattices in magnetic field. It has a continuous second order phase transition from the superconducting to the normal state within an increasing magnetic field....
  
  
• Unconventional superconductor
  Unconventional superconductor
  Unconventional superconductors are materials that display superconductivity which does not conform to either the conventional BCS theory or the Nikolay Bogolyubov's theory or its extensions....