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Superconductivity

58 sources, listed at the end · last revised 7 October 2026

Superconductivity is a state of matter in which a material carries a steady electric current with no resistance and expels weak magnetic fields from its interior. It appears abruptly when the material is cooled below a critical temperature, written T_c, and it is destroyed if the temperature, the magnetic field or the current density (the current per unit of cross-section) exceeds a limit that depends on the material. The effect was discovered in 1911 in mercury cooled with liquid helium to about 4.2 kelvin (K), which is −269 °C.^[1]

Below T_c the electrons that carry current bind into pairs, and all the pairs move together as one quantum state. Breaking a pair costs a minimum energy, and a pair cannot be scattered without being broken, so the small scattering events that cause resistance in an ordinary metal do not degrade the current. In elements, alloys and hydrogen-rich compounds the pairing is caused by vibrations of the crystal lattice, as described by the theory of Bardeen, Cooper and Schrieffer (BCS theory) published in 1957.^[2][6] In the copper oxides, which hold the record T_c of 133 to 138 K at ambient pressure, and in several other families of materials, the pairing has another origin and there is no agreed theory of it.^[3][4][6]

No material is known to superconduct at room temperature and ambient pressure (see Room-temperature superconductor). The highest reproduced T_c is about 250 K, in a hydrogen-rich compound at about 170 gigapascals (GPa), about 1.7 million atmospheres.^[5] Superconductors in use are typically cooled with liquid helium at 4.2 K or, in the case of the copper oxides, with liquid nitrogen at 77 K.^[7] Those used in high-field magnets are of type II: they admit a strong field in thin tubes of flux and stay superconducting, in some materials beyond 100 tesla (T).^[8][7]

Zero electrical resistance

In an ordinary metal the moving electrons collide with the vibrating atoms of the crystal and with impurities, and the collisions turn electrical energy into heat.^[9][10] Cooling lowers the resistivity, which levels off at a residual value set by the impurities.^[1] A superconductor follows the same curve down to T_c, where its resistance drops to zero.

On 8 April 1911 the laboratory of Heike Kamerlingh Onnes in Leiden recorded the resistance of mercury in a helium bath as "practically zero". A measurement that October placed the drop at 4.20 K (see History of superconductivity).^[1]

An experiment can only set an upper bound on a resistance, and the tightest bounds come from persistent currents. A current is started in a closed superconducting loop, the power supply is removed, and the magnetic field of the loop is watched for the decline that any resistance would cause. In 1963 File and Mills measured the field of a current circulating in a superconducting solenoid by nuclear magnetic resonance and set a lower bound of 100,000 years on its decay time.^[11][12][13] The resistivity of a superconductor is below 10⁻²⁵ ohm meter (Ω m), or 10⁻²³ ohm centimeter, more than 10¹⁷ times lower than the resistivity of copper at room temperature (1.68 × 10⁻⁸ Ω m).^[13][10]

The bounds apply to steady currents. In an alternating field a superconductor has some resistance at any temperature above absolute zero, because the changing field acts on electrons that are not bound in pairs.^[14] In the vortex state described below, a steady current can also decay slowly as flux lines move, a process called creep.^[15] The usual test on a new material is a four-probe resistance measurement, whose pitfalls are described in Verifying a superconductor.

The Meissner effect

In 1933 Walther Meissner and Robert Ochsenfeld found that a superconductor also expels magnetic field from its interior.^[16][17] When a sample in a weak magnetic field is cooled through T_c, currents begin to flow in a thin layer at its surface, and the field they produce cancels the applied field inside.^[17] A material with zero field inside is called a perfect diamagnet.^[18] The thickness of the surface layer, the penetration depth, is 16 to 39 nanometers (nm) in aluminum, tin, lead and niobium and about 140 nm in the copper oxide YBa₂Cu₃O₇ (yttrium barium copper oxide).^[19][20]

Field expulsion does not follow from zero resistance. A material that only conducted perfectly would oppose any change in the field inside it: it would keep out a field applied after cooling, but a field already present during cooling would stay in place. A superconductor ends up free of field in both cases.^[18][21] Its state is therefore fixed by the present temperature and field, whatever the order in which they were applied. BCS theory describes the change at T_c as a phase transition.^[2]

In real type II materials (described below), the field expelled on cooling can be a small fraction of the field applied (about 1% or less in one study of iron-based crystals), in part because defects hold flux in place, while a field applied after cooling is still kept out.^[22] Zero resistance and the diamagnetism of the Meissner effect are the electrical and magnetic signatures looked for in a new superconductor (see Verifying a superconductor).^[23]

Critical temperature, field and current

Superconductivity exists only within three limits.^[7]

• The critical temperature T_c is 1.2 K in aluminum, 7.2 K in lead and 133 to 138 K in the mercury-based copper oxides that hold the ambient-pressure record.^[18][3][4]
• The critical field H_c is the magnetic field that destroys the superconducting state. Kamerlingh Onnes found in 1914 that lead at 4.25 K became resistive in a field of 0.06 tesla (T).^[1]
• The critical current density J_c is the largest current per unit of cross-section that the material carries without resistance. In niobium-titanium it is about 4 × 10⁵ amperes per square centimeter (A/cm²) at 4.2 K in a field of 5 T.^[7]

The limits depend on each other: the critical field is largest at absolute zero and falls to zero at T_c, approximately as H_c(T) = H_c(0)[1 − (T/T_c)²], and the critical current density falls as either the temperature or the field rises.^[18][24][25] Niobium-titanium magnets reach up to 9 T at 4.2 K and 11 T at 1.8 K.^[7] The niobium-titanium dipole magnets that bend the beams of the Large Hadron Collider (LHC) at CERN are designed for 8.3 T and run at 1.9 K, far below the alloy's zero-field T_c of 9.5 K.^{[7][26][27][28]}

Type I and type II superconductors

A type I superconductor expels the field completely up to H_c and then becomes normal throughout. Most superconducting elements are of this type.^[18] Depending on the shape of the sample, normal regions can appear below H_c (the intermediate state): in a sphere, from two thirds of H_c.^[29][30]

A type II superconductor has two critical fields. Below the lower one, H_c1, it expels the field completely. Between H_c1 and the upper critical field H_c2 it is in the mixed state, also called the vortex state: the field passes through the material in thin tubes called vortices or flux lines while the material between them stays superconducting. Above H_c2 it is normal.^[18][15] In work published in 1957, Alexei Abrikosov derived the mixed state from the Ginzburg-Landau theory, which describes the superconducting state mathematically without starting from individual electrons.^[8][13] Type II materials are generally alloys and compounds.^[18]

Type I entries are H_c at absolute zero; type II entries are H_c2 at 4.2 K. Fields are given in tesla, as μ₀H.^[18][7][31]

Vortices and flux pinning

Each vortex has a core where superconductivity is suppressed, about two coherence lengths across, surrounded by a current that circulates out to the penetration depth.^[15] The coherence length is the shortest distance over which the superconducting state can change.^[19] A vortex carries one quantum of magnetic flux, h/2e ≈ 2.07 × 10⁻¹⁵ weber (Wb; 1 Wb is a field of 1 T over 1 square meter), where h is Planck's constant and 2e is the charge of an electron pair.^[15][32][13] A field of 1 T therefore corresponds to about 480 vortices per square micrometer. A material is type II when the ratio of its penetration depth to its coherence length is greater than 1/√2, about 0.71: in YBa₂Cu₃O₇ the two are about 140 nm and 1.6 nm.^[33][20][15]

A current exerts a sideways force on the vortices, and a moving vortex dissipates energy, so a type II material whose vortices move freely has resistance although it is still superconducting.^[15] In real materials the vortices are held by crystal defects such as dislocations and precipitates. This is flux pinning, and the critical current density of a type II material is the current density at which the force on the vortices exceeds the pinning. J_c therefore depends on how a wire is processed as well as on its composition.^[15][7] Above the irreversibility field, which lies below H_c2, pinning fails and J_c is zero.^[24][7]

The superconductors used in high-field magnets are type II.^[8] The critical field of lead, 0.080 T, is about one hundredth of the 8.3 T design field of an LHC dipole, whereas niobium-titanium, niobium-tin and the copper oxides stay superconducting in the mixed state at 10 T and above.^[18][7][27]

Cooper pairs and BCS theory

Pairing and the energy gap

A microscopic explanation, BCS theory, came in 1957, 46 years after the discovery, from John Bardeen, Leon Cooper and J. Robert Schrieffer, who received the 1972 Nobel Prize in Physics for it.^[2][18]

Electrons repel each other, but inside a metal they can also attract each other indirectly. An electron passing through the crystal pulls the positively charged ions slightly toward its path. The ions are heavy and slow, so the region stays positively charged for a short time after the electron has gone, and a second electron is drawn to it. The attraction is carried by vibrations of the lattice, whose quanta are called phonons, and in a superconductor it outweighs the repulsion.^[2][18] It binds electrons of opposite spin (an electron's intrinsic angular momentum) into Cooper pairs, named after Cooper's 1956 paper on bound electron pairs.^[34][18]

The pairs are large, of the order of the coherence length across (38 nm in niobium, 83 nm in lead, 1,600 nm in aluminum), so each one overlaps many others, and all of them move together as one quantum state that extends through the sample.^[13][19][18] Pairs can also tunnel through a thin insulating barrier between two superconductors, as Brian Josephson predicted in 1962; such Josephson junctions are the basis of the superconducting quantum interference device (SQUID), a magnetometer with a threshold of about 10⁻¹⁴ T.^[35][36]

Breaking a pair takes a minimum energy, the energy gap. BCS theory gives it as about 3.5 k_BT_c at absolute zero, where k_B is Boltzmann's constant, falling to zero at T_c.^[2] In the elemental superconductors it is about 1 millielectronvolt (meV), the scale of thermal energy at about 12 K.^[18][37] Resistance in a normal metal comes from collisions that change the energy of single electrons by small amounts. No such small change is available to a paired electron: the lattice can scatter a pair only by breaking it, which would disturb the motion of all the pairs together.^[18] Heat breaks some pairs at any temperature above absolute zero, but the pairs that remain carry a steady current without loss.^[14] The theory also accounts for the Meissner effect and for the measured penetration depth and specific heat, the heat needed to warm the material.^[2]

Lattice vibrations and the isotope effect

The evidence that the lattice is involved predates the theory: in 1950 two groups measured mercury samples of different isotopic mass and found that T_c changes with the mass of the atoms.^[38][39][13] Isotopes of an element have the same chemistry and differ only in nuclear mass, which changes how fast the lattice vibrates. In many superconductors T_c is proportional to M^−α, where M is the isotopic mass and α is 0.45 to 0.5, with exceptions such as ruthenium and molybdenum; simple BCS theory gives 0.5.^[13][40] The isotope effect is still used as a test of the mechanism: in the sulfur hydride H₃S under pressure, replacing hydrogen with deuterium lowers T_c, with α about 0.3.^[40]

In the theory T_c rises with the frequency of the vibrations and with the strength of their coupling to the electrons, the electron-phonon coupling.^[41] Light atoms vibrate fast, which is why hydrogen-rich compounds were sought as superconductors (see High-pressure hydrides and, for calculations of T_c, Predicting superconductors).

Conventional and unconventional superconductors

A conventional superconductor is one whose pairs are bound by phonons, as BCS theory and its extensions describe. In an unconventional superconductor the pairs are bound by something else.^[42][6]

The conventional classes include the superconducting elements, the niobium alloys and compounds used in magnets, magnesium diboride (39 K) and the hydrides that superconduct under pressure, such as H₃S at 203 K and 155 GPa (about 1.5 million atmospheres) and lanthanum hydride (LaH₁₀) at about 250 K and about 170 GPa.^{[6][43][40][5]}

Unconventional superconductivity was first seen in 1979 in CeCu₂Si₂, at about 0.5 K.^[44][42] It is a heavy-fermion compound, a metal whose electrons behave as if about 200 times heavier than free electrons.^[45] The cuprates, which are layered copper oxides, followed in 1986 at about 35 K and reached 93 K in 1987 and 133 K in 1993.^[46][31][3] The iron-based superconductors reached 55 to 56 K in 2008.^[47][48]

In the cuprates the pairs have d-wave symmetry, meaning that the pair state changes sign with direction in the crystal, as experiments that detect the sign change have shown.^[49] Fluctuations in the alignment of the electron spins are a candidate for the pairing interaction, but there is no consensus on which mechanisms operate in the unconventional classes.^[42][6][50] The nickelates, nickel oxides with crystal structures related to those of the cuprates, are a newer family: 9 to 15 K in thin films in 2019, and signs of superconductivity near 80 K under pressure in 2023.^[51][52]

The T_c of a conventional superconductor can be calculated from its crystal structure; for the superconducting elements the calculated values usually fall within about 20% of the measured ones.^[53][54] The heavy-fermion, cuprate and iron-based superconductors were each found by experiment, unanticipated by theory.^[55]

Operating temperatures and coolants

At atmospheric pressure helium boils at about 4.2 K (−269 °C) and nitrogen at 77.3 K (−196 °C).^[26][56] Until 1986 the highest known T_c was about 23 K, so superconductors were cooled with liquid helium.^[57] YBa₂Cu₃O₇, reported in 1987 with a T_c of 93 K, was the first superconductor that liquid nitrogen could cool.^[31]

Nitrogen is more abundant than helium, and cooling with it costs much less.^[18][7] An ideal refrigerator rejecting heat at 300 K needs about 70 watts (W) of input power for each watt of heat removed at 4.2 K, and about 2.9 W at 77 K.^[58]

Because the critical current and the irreversibility field shrink as the temperature approaches T_c, cuprate conductors run at 65 to 77 K in fields below about 1 T, as in power cables, and are cooled below 50 K for fields above 1 T.^[7][25] The same margin would apply at room temperature: one review estimates that a superconductor for use near 300 K would need a T_c of 375 to 400 K.^[41]

See also

• Room-temperature superconductor
• Superconducting materials
• History of superconductivity
• Applications of superconductors
• Verifying a superconductor
• Glossary

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