High-temperature superconductivity

Selected list of superconductors

Superconductors Cooling agents

Properties

The "high-temperature" superconductor class has had many definitions.

The label high-T_c should be reserved for materials with critical temperatures greater than the boiling point of liquid nitrogen. However, a number of materials – including the original discovery and recently discovered pnictide superconductors – have critical temperatures below 77 K (−196.2 °C) but nonetheless are commonly referred to in publications as high-T_c class.

A substance with a critical temperature above the boiling point of liquid nitrogen, together with a high critical magnetic field and critical current density (above which superconductivity is destroyed), would greatly benefit technological applications. In magnet applications, the high critical magnetic field may prove more valuable than the high T_c itself. Some cuprates have an upper critical field of about 100 tesla. However, cuprate materials are brittle ceramics that are expensive to manufacture and not easily turned into wires or other useful shapes. Furthermore, high-temperature superconductors do not form large, continuous superconducting domains, rather clusters of microdomains within which superconductivity occurs. They are therefore unsuitable for applications requiring actual superconductive currents, such as magnets for magnetic resonance spectrometers. For a solution to this (powders), see HTS wire.

There has been considerable debate regarding high-temperature superconductivity coexisting with magnetic ordering in YBCO, iron-based superconductors, several ruthenocuprates and other exotic superconductors, and the search continues for other families of materials. HTS are Type-II superconductors, which allow magnetic fields to penetrate their interior in quantized units of flux, meaning that much higher magnetic fields are required to suppress superconductivity. The layered structure also gives a directional dependence to the magnetic field response.

All known high-T_c superconductors are Type-II superconductors. In contrast to Type-I superconductors, which expel all magnetic fields due to the Meissner effect, Type-II superconductors allow magnetic fields to penetrate their interior in quantized units of flux, creating "holes" or "tubes" of normal metallic regions in the superconducting bulk called vortices. Consequently, high-T_c superconductors can sustain much higher magnetic fields.

Cuprates

Cuprate superconductors are a family of high-temperature superconducting materials made of layers of copper oxides (CuO
₂) alternating with layers of other metal oxides, which act as charge reservoirs. At ambient pressure, cuprate superconductors are the highest temperature superconductors known.

Cuprates have a structure close to that of a two-dimensional material. Their superconducting properties are determined by electrons moving within weakly coupled copper-oxide (CuO
₂) layers. Neighbouring layers contain ions such as lanthanum, barium, strontium, or other atoms that act to stabilize the structures and dope electrons or holes onto the copper-oxide layers. The undoped "parent" or "mother" compounds are Mott insulators with long-range antiferromagnetic order at sufficiently low temperatures. Single band models are generally considered to be enough to describe the electronic properties.

The cuprate superconductors adopt a perovskite structure. The copper-oxide planes are checkerboard lattices with squares of O²⁻ ions with a Cu²⁺ ion at the centre of each square. The unit cell is rotated by 45° from these squares. Chemical formulae of superconducting materials contain fractional numbers to describe the doping required for superconductivity.

Several families of cuprate superconductors have been identified. They can be categorized by their elements and the number of adjacent copper-oxide layers in each superconducting block. For example, YBCO and BSCCO can be referred to as Y123 and Bi2201/Bi2212/Bi2223 depending on the number of layers in each superconducting block (n). The superconducting transition temperature peaks at an optimal doping value (p=0.16) and an optimal number of layers in each block, typically three.

Possible mechanisms for cuprate superconductivity remain the subject of considerable debate and research. Similarities between the low-temperature state of undoped materials and the superconducting state that emerges upon doping, primarily the d_x²−y² orbital state of the Cu²⁺ ions, suggest that electron–electron interactions are more significant than electron–phonon interactions in cuprates – making the superconductivity unconventional. Recent work on the Fermi surface has shown that nesting occurs at four points in the antiferromagnetic Brillouin zone where spin waves exist and that the superconducting energy gap is larger at these points. The weak isotope effects observed for most cuprates contrast with conventional superconductors that are well described by BCS theory.

Iron-based

Iron-based superconductors contain layers of iron and a pnictogen – such as arsenic or phosphorus – , a chalcogen, or a crystallogen. This is currently the family with the second highest critical temperature, behind the cuprates. Interest in their superconducting properties began in 2006 with the discovery of superconductivity in LaFePO at 4 K (−269.15 °C) and gained much greater attention in 2008 after the analogous material LaFeAs(O,F) was found to superconduct at up to 43 K (−230.2 °C) under pressure. The highest critical temperatures in the iron-based superconductor family exist in thin films of FeSe, where a critical temperature in excess of 100 K (−173 °C) was reported in 2014.

Since the original discoveries several families of iron-based superconductors have emerged:

• LnFeAs(O,F) or LnFeAsO_1−x (Ln=lanthanide) with T_c up to 56 K (−217.2 °C), referred to as 1111 materials. A fluoride variant of these materials was subsequently found with similar T_c values.
• (Ba,K)Fe₂As₂ and related materials with pairs of iron-arsenide layers, referred to as 122 compounds. T_c values range up to 38 K (−235.2 °C). These materials also superconduct when iron is replaced with cobalt.
• LiFeAs and NaFeAs with T_c up to around 20 K (−253.2 °C). These materials superconduct close to stoichiometric composition and are referred to as 111 compounds.
• FeSe with small off-stoichiometry or tellurium doping.
• LaFeSiH with T_c around 11 K (−262.1 °C) in its stoichiometric composition. This superconducting crystallogenide has oxide and fluoride variants LaFeSiO_x and LaFeSiF_x.

Most undoped iron-based superconductors show a tetragonal-orthorhombic structural phase transition followed at lower temperature by magnetic ordering, similar to the cuprate superconductors. However, they are poor metals rather than Mott insulators and have five bands at the Fermi surface rather than one. The phase diagram emerging as the iron-arsenide layers are doped is remarkably similar, with the superconducting phase close to or overlapping the magnetic phase. Strong evidence that the T_c value varies with the As–Fe–As bond angles has already emerged and shows that the optimal T_c value is obtained with undistorted FeAs₄ tetrahedra. The symmetry of the pairing wavefunction is still widely debated, but an extended s-wave scenario is currently favoured.

Magnesium diboride

Magnesium diboride is occasionally referred to as a high-temperature superconductor because its T_c value of 39 K (−234.2 °C) is above that historically expected for BCS superconductors. However, it is more generally regarded as the highest T_c conventional superconductor, the increased T_c resulting from two separate bands being present at the Fermi level.

Carbon-based

In 1991 Hebard et al. discovered Fulleride superconductors, where alkali-metal atoms are intercalated into C₆₀ molecules.

In 2008 Ganin et al. demonstrated superconductivity at temperatures of up to 38 K (−235.2 °C) for Cs₃C₆₀.

P-doped Graphane was proposed in 2010 to be capable of sustaining high-temperature superconductivity.

On 31 December 2023 "Global Room-Temperature Superconductivity in Graphite" was published in the journal Advanced Quantum Technologies, claiming to demonstrate superconductivity at room temperature and ambient pressure in highly oriented pyrolytic graphite with dense arrays of nearly parallel line defects.

Nickelates

In 1999, Anisimov et al. conjectured superconductivity in nickelates, proposing nickel oxides as direct analogs to the cuprate superconductors. Superconductivity in an infinite-layer nickelate, Nd_0.8Sr_0.2NiO₂, was reported at the end of 2019 with a superconducting transition temperature between 9 and 15 K (−264.15 and −258.15 °C). This superconducting phase is observed in oxygen-reduced thin films created by the pulsed laser deposition of Nd_0.8Sr_0.2NiO₃ onto SrTiO₃ substrates that is then reduced to Nd_0.8Sr_0.2NiO₂ via annealing the thin films at 533–553 K (260–280 °C) in the presence of CaH₂. The superconducting phase is only observed in the oxygen reduced film and is not seen in oxygen reduced bulk material of the same stoichiometry, suggesting that the strain induced by the oxygen reduction of the Nd_0.8Sr_0.2NiO₂ thin film changes the phase space to allow for superconductivity. Of important is further to extract access hydrogen from the reduction with CaH₂, otherwise topotactic hydrogen may prevent superconductivity.

Production

Liquid nitrogen can be produced relatively cheaply, even on-site. The higher temperatures additionally help to avoid some of the problems that arise at liquid helium temperatures, such as the formation of plugs of frozen air that can block cryogenic lines and cause unanticipated and potentially hazardous pressure buildup.

Ongoing research

The question of how superconductivity arises in high-temperature superconductors is one of the major unsolved problems of theoretical condensed matter physics. The mechanism that causes the electrons in these crystals to form pairs is not known. Despite intensive research and many promising leads, an explanation has so far eluded scientists. One reason for this is that the materials in question are generally very complex, multi-layered crystals (for example, BSCCO), making theoretical modelling difficult.

Improving the quality and variety of samples also gives rise to considerable research, both with the aim of improved characterisation of the physical properties of existing compounds, and synthesizing new materials, often with the hope of increasing T_c. Technological research focuses on making HTS materials in sufficient quantities to make their use economically viable as well as in optimizing their properties in relation to applications.

In March 2026, University of Houston researchers reported a superconducting material exhibiting a critical temperature of approximately 151 K at ambient pressure. This new record without sustained high-pressure conditions was achieved using a "pressure quenching" technique. This exceeded the previous ambient-pressure record of 133 K.

Theoretical models

Multiple hypotheses attempt to account for HTS.

Resonating valence bond theory

Spin fluctuation hypothesis proposed that electron pairing in high-temperature superconductors is mediated by short-range spin waves known as paramagnons.

Gubser, Hartnoll, Herzog, and Horowitz proposed holographic superconductivity, which uses holographic duality or AdS/CFT correspondence theory as a possible explanation of high-temperature superconductivity in certain materials.

Weak coupling theory suggests superconductivity emerges from antiferromagnetic spin fluctuations in a doped system. It predicts that the pairing wave function of cuprate HTS should have a d_x²-y² symmetry. Thus, determining whether the pairing wave function has d-wave symmetry is essential to test the spin fluctuation mechanism. That is, if the HTS order parameter (a pairing wave function as in Ginzburg–Landau theory) does not have d-wave symmetry, then a pairing mechanism related to spin fluctuations can be ruled out. (Similar arguments can be made for iron-based superconductors but the different material properties allow a different pairing symmetry.)

Interlayer coupling theory proposes that a layered structure consisting of BCS-type (s-wave symmetry) superconductors can explain superconductivity by itself. By introducing an additional tunnelling interaction between layers, this model explained the anisotropic symmetry of the order parameter as well as the emergence of HTS.

In order to resolve this question, experiments such as photoemission spectroscopy, NMR, specific heat measurements, were conducted. The results remain ambiguous, with some reports supporting d symmetry, with others supporting s symmetry.

Such explanations assume that superconductive properties can be treated by mean-field theory. It also does not consider that in addition to the superconductive gap, the pseudogap must be explained. The cuprate layers are insulating, and the superconductors are doped with interlayer impurities to make them metallic.

The transition temperature can be maximized by varying the dopant concentration. The simplest example is La₂CuO₄, which consists of alternating CuO₂ and LaO layers that are insulating when pure. When 8% of the La is replaced by Sr, the latter acts as a dopant, contributing holes to the CuO₂ layers, and making the sample metallic. The Sr impurities also act as electronic bridges, enabling interlayer coupling. Proceeding from this picture, some theories argue that the pairing interaction is with phonons, as in conventional superconductors with Cooper pairs. While the undoped materials are antiferromagnetic, even a few percent of impurity dopants introduce a smaller pseudogap in the CuO₂ planes that is also caused by phonons. The gap decreases with increasing charge carriers, and as it nears the superconductive gap, the latter reaches its maximum. The transition temperature is then argued to be due to the percolating behaviour of the carriers, which follow zig-zag percolative paths, largely in metallic domains in the CuO₂ planes, until blocked by charge density wave domain walls, where they use dopant bridges to cross over to a metallic domain of an adjacent CuO₂ plane. The transition temperature maxima are reached when the host lattice has weak bond-bending forces, which produce strong electron–phonon interactions at the interlayer dopants.

D symmetry in YBCO

An experiment based on flux quantization of a three-grain ring of YBa₂Cu₃O₇ (YBCO) was proposed to test the symmetry of the order parameter in the HTS. The symmetry of the order parameter could best be probed at the junction interface as the Cooper pairs tunnel across a Josephson junction or weak link. It was expected that a half-integer flux, that is, a spontaneous magnetization could only occur for a junction of d symmetry superconductors. But, even if the junction experiment is the strongest method to determine the symmetry of the HTS order parameter, the results have been ambiguous. John R. Kirtley and C. C. Tsuei thought that the ambiguous results came from the defects inside the HTS, leading them to an experiment where both clean limit (no defects) and dirty limit (maximal defects) were considered simultaneously. Spontaneous magnetization was clearly observed in YBCO, which supported the d symmetry of the order parameter in YBCO. But, since YBCO is orthorhombic, it might inherently have an admixture of s symmetry. By tuning their technique, they found an admixture of s symmetry in YBCO within about 3%. Also, they found a pure d_x²−y² order parameter symmetry in tetragonal Tl₂Ba₂CuO₆.

Spin-fluctuation mechanism

The lack of exact theoretical computations on such strongly interacting electron systems has complicated attempts to validate spin-fluctuation. However, most theoretical calculations, including phenomenological and diagrammatic approaches, converge on magnetic fluctuations as the pairing mechanism.

Qualitative explanation

In a superconductor, the flow of electrons cannot be resolved into individual electrons, but instead consists of pairs of bound electrons, called Cooper pairs. In conventional superconductors, these pairs are formed when an electron moving through the material distorts the surrounding crystal lattice, which attracts another electron and forms a bound pair. This is sometimes called the "water bed" effect. Each Cooper pair requires a certain minimum energy to be displaced, and if the thermal fluctuations in the crystal lattice are smaller than this energy the pair can flow without dissipating energy. Electron flow without resistance is superconductivity.

In a high-T_c superconductor, the mechanism is extremely similar to a conventional superconductor, except that phonons play virtually no role, replaced by spin-density waves. Just as all known conventional superconductors are strong phonon systems, all known high-T_c superconductors are strong spin-density wave systems, within close vicinity of a magnetic transition to, for example, an antiferromagnet. When an electron moves in a high-T_c superconductor, its spin creates a spin-density wave around it. This spin-density wave in turn causes a nearby electron to fall into the spin depression created by the first electron (water-bed). When the system temperature is lowered, more spin density waves and Cooper pairs are created, eventually leading to superconductivity. High-T_c systems are magnetic systems due to the Coulomb interaction, creating a strong Coulomb repulsion between electrons. This repulsion prevents pairing of the Cooper pairs on the same lattice site. Instead, pairing occurs at near-neighbor lattice sites. This is the so-called d-wave pairing, where the pairing state has a node (zero) at the origin.

Examples

Examples of high-T_c cuprate superconductors include YBCO and BSCCO, which are the most known materials that achieve superconductivity above the boiling point of liquid nitrogen.