High-temperature superconductivity
Encyclopedia
High-temperature superconductors (abbreviated high-Tc or HTS) are materials that have a superconducting
transition temperature (Tc) above 30 kelvin (-243.2 °C). From 1960 to 1980, 30 K was thought to be the highest theoretically
possible Tc. The first high-Tc superconductor was discovered in 1986 by IBM researchers Karl Müller
and Johannes Bednorz
, for which they were awarded the Nobel Prize in Physics
in 1987.
Until Fe-based
superconductors were discovered in 2008, the term high-temperature superconductor was used interchangeably with cuprate
superconductor for compounds such as bismuth strontium calcium copper oxide (BSCCO) and yttrium barium copper oxide (YBCO).
"High-temperature" has two common definitions in the context of superconductivity:
The label high-Tc may be reserved by some authors for those with critical temperature greater than the boiling point of liquid nitrogen
(77 K or −196 °C
). However, a number of materials - including the original discovery and recently discovered pnictide superconductors - had critical temperatures below 77K but are commonly referred to in publication as being in the high-Tc class.
Technological applications benefit from both the higher critical temperature being above the boiling point of liquid nitrogen and also the higher critical magnetic field (and critical current density) at which superconductivity is destroyed. In magnet applications the high critical magnetic field may be more valuable than the high Tc itself. Some cuprates have an upper critical field around 100 teslas. However, cuprate materials are brittle ceramics which are expensive to manufacture and not easily turned into wires or other useful shapes.
Two decades of intense experimental and theoretical research, with over 100,000 published papers on the subject, have discovered many common features in the properties of high-temperature superconductors, but , there is no widely accepted theory to explain their properties. Cuprate superconductors (and other unconventional superconductor
s) differ in many important ways from conventional superconductor
s, such as elemental mercury or lead, which are adequately explained by the BCS theory. There also has been much debate as to high-temperature superconductivity coexisting with magnetic ordering
in YBCO, iron-based superconductor
s, several ruthenocuprates and other exotic superconductors, and the search continues for other families of materials. HTS are Type-II superconductor
s, which allow magnetic field
s 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.
, the highest-temperature superconductor (at ambient pressure) is mercury barium calcium copper oxide (HgBa2Ca2Cu3Ox), at 135 K and is held by a cuprate-perovskite material, which possibly reaches 164 K under high pressure.
After more than twenty years of intensive research the origin of high-temperature superconductivity is still not clear, but it seems that instead of electron-phonon attraction mechanisms, as in conventional superconductivity, one is dealing with genuine electronic mechanisms (e.g. by antiferromagnetic correlations), and instead of s-wave pairing, d-waves are substantial.
One goal of all this research is room-temperature superconductivity. However following numerous announcements of room-temperature superconductivity that were discredited on examination, most condensed matter physicists
now treat with extreme skepticism any claims of this nature.
-Barium
-Copper
-Oxide
), which is famous as the first material to achieve superconductivity above the boiling point of liquid nitrogen.
superconductors are generally considered to be quasi-two-dimensional materials with their superconducting properties determined by electrons moving within weakly coupled copper-oxide (CuO2) layers. Neighbouring layers containing ions such as lanthanum
, barium
, strontium
, or other atoms act to stabilize the structure and dope electrons or holes onto the copper-oxide layers. The undoped 'parent' or 'mother' compounds are Mott insulator
s with long-range antiferromagnetic order at low enough temperature. Single band
models are generally considered to be sufficient to describe the electronic properties.
The cuprate superconductors adopt a perovskite structure. The copper-oxide planes are checkerboard
lattice
s 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 generally contain fractional numbers to describe the doping required for superconductivity. There are several families of cuprate superconductors and they can be categorized by the elements they contain and the number of adjacent copper-oxide layers in each superconducting block. For example, YBCO and BSCCO can alternatively be referred to as Y123 and Bi2201/Bi2212/Bi2223 depending on the number of layers in each superconducting block (n). The superconducting transition temperature has been found to peak at an optimal doping value (p =0.16) and an optimal number of layers in each superconducting block, typically n = 3.
Possible mechanisms for superconductivity in the cuprates are still the subject of considerable debate and further research. Certain aspects common to all materials have been identified. Similarities between the antiferromagnetic low-temperature state of the undoped materials and the superconducting state that emerges upon doping, primarily the dx2-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.
Similarities and differences in the properties of hole-doped and electron doped cuprates:
and a pnictogen—such as arsenic
or phosphorus
—or a chalcogen
. 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 and gained much greater attention in 2008 after the analogous material LaFeAs(O,F) was found to superconduct at up to 43 K under pressure.
Since the original discoveries several families of iron-based superconductors have emerged:
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 band
s 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 Tc value varies with the As-Fe-As bond angles has already emerged and shows that the optimal Tc 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.
is occasionally referred to as a high-temperature superconductor because its Tc value of 39 K is above that historically expected for BCS
superconductors. However, it is more generally regarded as the highest Tc conventional superconductor, the increased Tc resulting from two separate bands being present at the Fermi energy
.
Fulleride superconductors where alkali-metal atoms are intercalated into C60 molecules show superconductivity at temperatures of up to 38 K for Cs3C60.
Some organic superconductors and heavy fermion
compounds are considered to be high-temperature superconductors because of their high Tc values relative to their Fermi energy, despite the Tc values being lower than for many conventional superconductors. This description may relate better to common aspects of the superconducting mechanism than the superconducting properties.
Theoretical work by Neil Ashcroft predicted that solid metallic hydrogen
at extremely high pressure should become superconducting at approximately room-temperature because of its extremely high speed of sound
and expected strong coupling
between the conduction electrons and the lattice vibrations. This prediction is yet to be experimentally verified.
All known high-Tc 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. Consequently, high-Tc superconductors can sustain much higher magnetic fields.
. 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 Tc. Technological research focuses on making HTS materials in sufficient quantities to make their use economically viable and optimizing their properties in relation to applications
.
A cable containing Gadolinium
has been demonstrated to carry 2800 A at 76 K. The cable has an outside diameter of 7.5mm and a bend radius of 12.5 cm.
, NMR
, specific heat measurements, etc. But, unfortunately, the results were ambiguous, some reports supported the d symmetry for the HTS whereas others supported the s symmetry. This muddy situation possibly originated from the indirect nature of the experimental evidence, as well as experimental issues such as sample quality, impurity scattering, twinning, etc.
There was a clever experimental design to overcome the muddy situation. 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. J. R. Kirtley and C. C. Tsuei thought that the ambiguous results came from the defects inside the HTS, so that they designed an experiment where both clean limit (no defects) and dirty limit (maximal defects) were considered simultaneously. In the experiment, the 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. So, by tuning their technique further, they found that there was an admixture of s symmetry in YBCO within about 3%. Also, they found that there was a pure dx2-y2 order parameter symmetry in the tetragonal Tl2Ba2CuO6.
In a normal conductor, a hole is created whenever an electron is moved. This causes a resistivity because charge neutrality must be conserved and as electrons move under an electric field, they drag holes behind them through defects and thermal oscillations in the system. In contrast, in a superconductor, one gets an unlimited supply of electrons without creating holes behind. This is through the creation of so-called Cooper pairs in a superconductor. Cooper pairs are pairs of electrons. In a normal conductor, creation of an electron leads to creation of a hole, which conserves the number of particles. But in a superconductor, it's possible to create a Cooper pair without creating holes and therefore not to conserve the number of particles, hence leading to the unlimited supply of electrons.
In a conventional superconductor, Cooper pairs are created as follows. When an electron moves through the system, it creates a depression in the atomic lattice through lattice vibrations known as phonons. If the depression of the lattice is strong enough, another electron can fall into the depression created by the first electron—the so-called water-bed effect—and a Cooper pair is formed. When this effect becomes strong enough, Cooper pairs win over the creation of holes behind the electrons, and the normal conductor turns into a superconductor through an unlimited supply of electrons by the creation of Cooper pairs.
In a high-Tc superconductor, the mechanism is extremely similar to a conventional superconductor. Except, in this case, phonons virtually play no role and their role is replaced by spin-density waves. As all conventional superconductors are strong phonon systems, all high-Tc 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-Tc 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 effect again). Hence, again, a Cooper pair is formed. Eventually, when the system temperature is lowered, more spin density waves and Cooper pairs are created and superconductivity begins when an unlimited supply of Cooper pairs, denoted as a phase transition, happens. Note that in high-Tc systems, as these systems are magnetic systems due to the Coulomb interaction, there is a strong Coulomb repulsion between electrons. This Coulomb repulsion prevents pairing of the Cooper pairs on the same lattice site. The pairing of the electrons occur at near-neighbor lattice sites as a result. This is the so-called d-wave pairing, where the pairing state has a node (zero) at the origin.
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...
transition temperature (Tc) above 30 kelvin (-243.2 °C). From 1960 to 1980, 30 K was thought to be the highest theoretically
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...
possible Tc. The first high-Tc superconductor was discovered in 1986 by IBM researchers Karl Müller
Karl Alexander Müller
Karl Alexander Müller is a Swiss physicist and Nobel laureate. He received the Nobel Prize in Physics in 1987 with Johannes Georg Bednorz for their work in superconductivity in ceramic materials.-Biography:...
and Johannes Bednorz
Johannes Georg Bednorz
Johannes Georg Bednorz is a physicist at the IBM Zürich Research Laboratory. He is best known for his role in the discovery of high-temperature superconductivity, for which he shared the 1987 Nobel Prize in Physics.-Life and work:...
, for which they were awarded the Nobel Prize in Physics
Nobel Prize in Physics
The Nobel Prize in Physics is awarded once a year by the Royal Swedish Academy of Sciences. It is one of the five Nobel Prizes established by the will of Alfred Nobel in 1895 and awarded since 1901; the others are the Nobel Prize in Chemistry, Nobel Prize in Literature, Nobel Peace Prize, and...
in 1987.
Until Fe-based
Iron-based superconductor
Iron-based superconductors are chemical compounds with superconducting properties. In 2008, led by recently discovered iron pnictide compounds , they were in the first stages of experimentation and implementation...
superconductors were discovered in 2008, the term high-temperature superconductor was used interchangeably with cuprate
Cuprate
Cuprates are chemical compounds containing copper anion. Cuprates have been known for centuries and are widely used in inorganic and organic chemistry...
superconductor for compounds such as bismuth strontium calcium copper oxide (BSCCO) and yttrium barium copper oxide (YBCO).
"High-temperature" has two common definitions in the context of superconductivity:
- Above the temperature of 30 K that had historically been taken as the upper limit allowed by BCS theoryBCS theoryBCS 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...
. This is also above the 1973 record of 23 K that had lasted until copper-oxide materials were discovered in 1986. - Having a transition temperature that is a larger fraction of the Fermi temperatureFermi levelThe Fermi level is a hypothetical level of potential energy for an electron inside a crystalline solid. Occupying such a level would give an electron a potential energy \epsilon equal to its chemical potential \mu as they both appear in the Fermi-Dirac distribution function,which...
than for conventional superconductors such as elemental mercuryMercury (element)Mercury is a chemical element with the symbol Hg and atomic number 80. It is also known as quicksilver or hydrargyrum...
or lead. This definition encompasses a wider variety of unconventional superconductorUnconventional superconductorUnconventional 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 and is used in the context of theoretical models.
The label high-Tc may be reserved by some authors for those with critical temperature greater than the boiling point of 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...
(77 K or −196 °C
Celsius
Celsius is a scale and unit of measurement for temperature. It is named after the Swedish astronomer Anders Celsius , who developed a similar temperature scale two years before his death...
). However, a number of materials - including the original discovery and recently discovered pnictide superconductors - had critical temperatures below 77K but are commonly referred to in publication as being in the high-Tc class.
Technological applications benefit from both the higher critical temperature being above the boiling point of liquid nitrogen and also the higher critical magnetic field (and critical current density) at which superconductivity is destroyed. In magnet applications the high critical magnetic field may be more valuable than the high Tc itself. Some cuprates have an upper critical field around 100 teslas. However, cuprate materials are brittle ceramics which are expensive to manufacture and not easily turned into wires or other useful shapes.
Two decades of intense experimental and theoretical research, with over 100,000 published papers on the subject, have discovered many common features in the properties of high-temperature superconductors, but , there is no widely accepted theory to explain their properties. Cuprate superconductors (and other 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) differ in many important ways from 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, such as elemental mercury or lead, which are adequately explained by the BCS theory. There also has been much debate as to high-temperature superconductivity coexisting with magnetic ordering
Magnetism
Magnetism is a property of materials that respond at an atomic or subatomic level to an applied magnetic field. Ferromagnetism is the strongest and most familiar type of magnetism. It is responsible for the behavior of permanent magnets, which produce their own persistent magnetic fields, as well...
in YBCO, iron-based superconductor
Iron-based superconductor
Iron-based superconductors are chemical compounds with superconducting properties. In 2008, led by recently discovered iron pnictide compounds , they were in the first stages of experimentation and implementation...
s, several ruthenocuprates and other exotic superconductors, and the search continues for other families of materials. HTS are 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....
s, which allow magnetic field
Magnetic field
A magnetic field is a mathematical description of the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude ; as such it is a vector field.Technically, a magnetic field is a pseudo vector;...
s to penetrate their interior in quantized
Quantum
In physics, a quantum is the minimum amount of any physical entity involved in an interaction. Behind this, one finds the fundamental notion that a physical property may be "quantized," referred to as "the hypothesis of quantization". This means that the magnitude can take on only certain discrete...
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.
History and progress
- April 1911 - Kamerlingh Onnes discovers superconductivity.
- April 1986 - The term high-temperature superconductor was first used to designate the new family of cuprate-perovskitePerovskiteA perovskite structure is any material with the same type of crystal structure as calcium titanium oxide , known as the perovskite structure, or XIIA2+VIB4+X2−3 with the oxygen in the face centers. Perovskites take their name from this compound, which was first discovered in the Ural mountains of...
ceramicCeramicA 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...
materials discovered by Johannes Georg Bednorz and Karl Alexander Müller, for which they won the Nobel Prize in Physics the following year. Their discovery of the first high-temperature superconductor, LaLanthanumLanthanum is a chemical element with the symbol La and atomic number 57.Lanthanum is a silvery white metallic element that belongs to group 3 of the periodic table and is the first element of the lanthanide series. It is found in some rare-earth minerals, usually in combination with cerium and...
BaBariumBarium 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...
CuOCopper(II) oxideCopper oxide or cupric oxide is the higher oxide of copper. As a mineral, it is known as tenorite.-Chemistry:It is a black solid with an ionic structure which melts above 1200 °C with some loss of oxygen...
, with a transition temperature of 30 K, generated great excitement.
- LSCO (La2-xSrxCuO4) discovered the same year.
- January 1987 - YBCO was discovered to have a Tc of 90 K.
- 1988 - BSCCO discovered with Tc up to 108 K, and TBCCO (T=thallium) discovered to have Tc of 127 K.
, the highest-temperature superconductor (at ambient pressure) is mercury barium calcium copper oxide (HgBa2Ca2Cu3Ox), at 135 K and is held by a cuprate-perovskite material, which possibly reaches 164 K under high pressure.
- Recently, iron-based superconductors with critical temperatures as high as 56 K have been discovered. These are often also referred to as high-temperature superconductors.
After more than twenty years of intensive research the origin of high-temperature superconductivity is still not clear, but it seems that instead of electron-phonon attraction mechanisms, as in conventional superconductivity, one is dealing with genuine electronic mechanisms (e.g. by antiferromagnetic correlations), and instead of s-wave pairing, d-waves are substantial.
One goal of all this research is room-temperature superconductivity. However following numerous announcements of room-temperature superconductivity that were discredited on examination, most condensed matter physicists
Condensed matter physics
Condensed matter physics deals with the physical properties of condensed phases of matter. These properties appear when a number of atoms at the supramolecular and macromolecular scale interact strongly and adhere to each other or are otherwise highly concentrated in a system. The most familiar...
now treat with extreme skepticism any claims of this nature.
Examples
Examples of high-Tc cuprate superconductors include La1.85Ba0.15CuO4, and YBCO (YttriumYttrium
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...
-Oxide
Oxygen
Oxygen is the element with atomic number 8 and represented by the symbol O. Its name derives from the Greek roots ὀξύς and -γενής , because at the time of naming, it was mistakenly thought that all acids required oxygen in their composition...
), which is famous as the first material to achieve superconductivity above the boiling point of liquid nitrogen.
| Transition temperature (in kelvin) |
Material | Class |
|---|---|---|
| 133 | HgBa2Ca2Cu3Ox | Copper-oxide superconductors |
| 110 | Bi2Sr2Ca2Cu3O10(BSCCO) | |
| 90 | YBa2Cu3O7 (YBCO) | |
| 77 | Boiling point of 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... |
|
| 55 | SmFeAs(O,F) | Iron-based superconductors |
| 41 | CeFeAs(O,F) | |
| 26 | LaFeAs(O,F) | |
| 20 | Boiling point of liquid hydrogen Liquid hydrogen Liquid hydrogen is the liquid state of the element hydrogen. Hydrogen is found naturally in the molecular H2 form.To exist as a liquid, H2 must be pressurized above and cooled below hydrogen's Critical point. However, for hydrogen to be in a full liquid state without boiling off, it needs to be... |
|
| 18 | Nb3Sn Niobium-tin Niobium-tin or triniobium-tin is a metallic chemical compound of niobium and tin , used industrially as a type II superconductor. This intermetallic compoundis a A15 phases superconductor... |
Metallic low-temperature superconductors |
| 10 | NbTi Niobium-titanium Niobium-titanium is an alloy of niobium and titanium, used industrially as a type II superconductor wire for superconducting magnets... |
|
| 9.2 | Nb 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... |
|
| 4.2 | Boiling point of 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... |
|
| 4.2 | Hg (mercury Mercury (element) Mercury is a chemical element with the symbol Hg and atomic number 80. It is also known as quicksilver or hydrargyrum... ) |
Metallic low-temperature superconductors |
Cuprates
CuprateCuprate
Cuprates are chemical compounds containing copper anion. Cuprates have been known for centuries and are widely used in inorganic and organic chemistry...
superconductors are generally considered to be quasi-two-dimensional materials with their superconducting properties determined by electrons moving within weakly coupled copper-oxide (CuO2) layers. Neighbouring layers containing ions such as lanthanum
Lanthanum
Lanthanum is a chemical element with the symbol La and atomic number 57.Lanthanum is a silvery white metallic element that belongs to group 3 of the periodic table and is the first element of the lanthanide series. It is found in some rare-earth minerals, usually in combination with cerium and...
, 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...
, strontium
Strontium
Strontium is a chemical element with the symbol Sr and the atomic number 38. An alkaline earth metal, strontium is a soft silver-white or yellowish metallic element that is highly reactive chemically. The metal turns yellow when exposed to air. It occurs naturally in the minerals celestine and...
, or other atoms act to stabilize the structure and dope electrons or holes onto the copper-oxide layers. The undoped 'parent' or 'mother' compounds are Mott insulator
Mott insulator
Mott insulators are a class of materials that should conduct electricity under conventional band theories, but are insulators when measured...
s with long-range antiferromagnetic order at low enough temperature. Single band
Electronic band structure
In solid-state physics, the electronic band structure of a solid describes those ranges of energy an electron is "forbidden" or "allowed" to have. Band structure derives from the diffraction of the quantum mechanical electron waves in a periodic crystal lattice with a specific crystal system and...
models are generally considered to be sufficient to describe the electronic properties.
The cuprate superconductors adopt a perovskite structure. The copper-oxide planes are checkerboard
Checkerboard
A checkerboard or chequerboard is a board of chequered pattern on which English draughts is played. It is an 8×8 board and the 64 squares are of alternating dark and light color, often red and black....
lattice
Crystal structure
In mineralogy and crystallography, crystal structure is a unique arrangement of atoms or molecules in a crystalline liquid or solid. A crystal structure is composed of a pattern, a set of atoms arranged in a particular way, and a lattice exhibiting long-range order and symmetry...
s 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 generally contain fractional numbers to describe the doping required for superconductivity. There are several families of cuprate superconductors and they can be categorized by the elements they contain and the number of adjacent copper-oxide layers in each superconducting block. For example, YBCO and BSCCO can alternatively be referred to as Y123 and Bi2201/Bi2212/Bi2223 depending on the number of layers in each superconducting block (n). The superconducting transition temperature has been found to peak at an optimal doping value (p =0.16) and an optimal number of layers in each superconducting block, typically n = 3.
Brillouin zone
In mathematics and solid state physics, the first Brillouin zone is a uniquely defined primitive cell in reciprocal space. The boundaries of this cell are given by planes related to points on the reciprocal lattice. It is found by the same method as for the Wigner–Seitz cell in the Bravais lattice...
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.
Similarities and differences in the properties of hole-doped and electron doped cuprates:
- Presence of a pseudogap phase up to at least optimal doping.
- Different trends in the Uemura plot relating transition temperature to the superfluid density. The inverse square of the London penetration depthLondon penetration depthIn superconductors, the London penetration depth characterizes the distance to which a magnetic field penetrates into a superconductor and becomes equal to 1/e times that of the magnetic field at the surface of the superconductor...
appears to be proportional to the critical temperature for a large number of underdoped cuprate superconductors, but the constant of proportionality is different for hole- and electron-doped cuprates. The linear trend implies that the physics of these materials is strongly two-dimensional. - Universal hourglass-shaped feature in the spin excitations of cuprates measured using inelastic neutron diffraction.
- Nernst effectNernst effectIn physics and chemistry, the Nernst Effect is a thermoelectric phenomenon observed when a sample allowing electrical conduction is subjected to a magnetic field and a temperature gradient normal...
evident in both the superconducting and pseudogap phases.
Iron-based superconductors
Iron-based superconductors contain layers of ironIron
Iron is a chemical element with the symbol Fe and atomic number 26. It is a metal in the first transition series. It is the most common element forming the planet Earth as a whole, forming much of Earth's outer and inner core. It is the fourth most common element in the Earth's crust...
and a pnictogen—such as arsenic
Arsenic
Arsenic is a chemical element with the symbol As, atomic number 33 and relative atomic mass 74.92. Arsenic occurs in many minerals, usually in conjunction with sulfur and metals, and also as a pure elemental crystal. It was first documented by Albertus Magnus in 1250.Arsenic is a metalloid...
or phosphorus
Phosphorus
Phosphorus is the chemical element that has the symbol P and atomic number 15. A multivalent nonmetal of the nitrogen group, phosphorus as a mineral is almost always present in its maximally oxidized state, as inorganic phosphate rocks...
—or a chalcogen
Chalcogen
The chalcogens are the chemical elements in group 16 of the periodic table. This group is also known as the oxygen family...
. 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 and gained much greater attention in 2008 after the analogous material LaFeAs(O,F) was found to superconduct at up to 43 K under pressure.
Since the original discoveries several families of iron-based superconductors have emerged:
- LnFeAs(O,F) or LnFeAsO1-x with Tc up to 56 K, referred to as 1111 materials. A fluorideFluorideFluoride is the anion F−, the reduced form of fluorine when as an ion and when bonded to another element. Both organofluorine compounds and inorganic fluorine containing compounds are called fluorides. Fluoride, like other halides, is a monovalent ion . Its compounds often have properties that are...
variant of these materials was subsequently found with similar Tc values. - (Ba,K)Fe2As2 and related materials with pairs of iron-arsenide layers, referred to as 122 compounds. Tc values range up to 38 K. These materials also superconduct when iron is replaced with cobaltCobaltCobalt is a chemical element with symbol Co and atomic number 27. It is found naturally only in chemically combined form. The free element, produced by reductive smelting, is a hard, lustrous, silver-gray metal....
- LiFeAs and NaFeAs with Tc up to around 20 K. These materials superconduct close to stoichiometric composition and are referred to as 111 compounds.
- FeSe with small off-stoichiometryStoichiometryStoichiometry is a branch of chemistry that deals with the relative quantities of reactants and products in chemical reactions. In a balanced chemical reaction, the relations among quantities of reactants and products typically form a ratio of whole numbers...
or tellurium doping.
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 band
Electronic band structure
In solid-state physics, the electronic band structure of a solid describes those ranges of energy an electron is "forbidden" or "allowed" to have. Band structure derives from the diffraction of the quantum mechanical electron waves in a periodic crystal lattice with a specific crystal system and...
s at the Fermi surface
Fermi surface
In condensed matter physics, the Fermi surface is an abstract boundary useful for predicting the thermal, electrical, magnetic, and optical properties of metals, semimetals, and doped semiconductors. The shape of the Fermi surface is derived from the periodicity and symmetry of the crystalline...
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 Tc value varies with the As-Fe-As bond angles has already emerged and shows that the optimal Tc 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.
Other materials sometimes referred to as high-temperature superconductors
Magnesium diborideMagnesium 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...
is occasionally referred to as a high-temperature superconductor because its Tc value of 39 K is above that historically expected for BCS
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...
superconductors. However, it is more generally regarded as the highest Tc conventional superconductor, the increased Tc resulting from two separate bands being present at the Fermi energy
Fermi energy
The Fermi energy is a concept in quantum mechanics usually referring to the energy of the highest occupied quantum state in a system of fermions at absolute zero temperature....
.
Fulleride superconductors where alkali-metal atoms are intercalated into C60 molecules show superconductivity at temperatures of up to 38 K for Cs3C60.
Some organic superconductors and heavy fermion
Heavy Fermion
In solid-state physics, heavy fermion materials are a specific type of intermetallic compound, containing elements with 4f or 5f electrons. Electrons, a kind of fermion, found in such materials are sometimes referred to as heavy electrons...
compounds are considered to be high-temperature superconductors because of their high Tc values relative to their Fermi energy, despite the Tc values being lower than for many conventional superconductors. This description may relate better to common aspects of the superconducting mechanism than the superconducting properties.
Theoretical work by Neil Ashcroft predicted that solid metallic hydrogen
Metallic hydrogen
Metallic hydrogen is a state of hydrogen which results when it is sufficiently compressed and undergoes a phase transition; it is an example of degenerate matter. Solid metallic hydrogen is predicted to consist of a crystal lattice of hydrogen nuclei , with a spacing which is significantly smaller...
at extremely high pressure should become superconducting at approximately room-temperature because of its extremely high speed of sound
Speed of sound
The speed of sound is the distance travelled during a unit of time by a sound wave propagating through an elastic medium. In dry air at , the speed of sound is . This is , or about one kilometer in three seconds or approximately one mile in five seconds....
and expected strong coupling
Coupling (physics)
In physics, two systems are coupled if they are interacting with each other. Of special interest is the coupling of two vibratory systems by means of springs or magnetic fields, etc...
between the conduction electrons and the lattice vibrations. This prediction is yet to be experimentally verified.
All known high-Tc superconductors are Type-II superconductors. In contrast to Type-I superconductors, which expel all magnetic fields due to the Meissner effect
Meissner effect
The Meissner effect is the expulsion of a magnetic field from a superconductor during its transition to the superconducting state. The German physicists Walther Meissner and Robert Ochsenfeld discovered the phenomenon in 1933 by measuring the magnetic field distribution outside superconducting tin...
, 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. Consequently, high-Tc superconductors can sustain much higher magnetic fields.
Ongoing research
The question of how superconductivity arises in high-temperature superconductors is one of the major unsolved problems of theoretical condensed matter physicsCondensed matter physics
Condensed matter physics deals with the physical properties of condensed phases of matter. These properties appear when a number of atoms at the supramolecular and macromolecular scale interact strongly and adhere to each other or are otherwise highly concentrated in a system. The most familiar...
. 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 Tc. Technological research focuses on making HTS materials in sufficient quantities to make their use economically viable and optimizing their properties in relation to applications
Technological applications of superconductivity
Some of the technological applications of superconductivity include:* the production of sensitive magnetometers based on SQUIDs* fast digital circuits ,...
.
A cable containing Gadolinium
Gadolinium
Gadolinium is a chemical element with the symbol Gd and atomic number 64. It is a silvery-white, malleable and ductile rare-earth metal. It is found in nature only in combined form. Gadolinium was first detected spectroscopically in 1880 by de Marignac who separated its oxide and is credited with...
has been demonstrated to carry 2800 A at 76 K. The cable has an outside diameter of 7.5mm and a bend radius of 12.5 cm.
Possible mechanism
There have been two representative theories for HTS. Firstly, it has been suggested that the HTS emerges from antiferromagnetic spin fluctuations in a doped system. According to this theory, the pairing wave function of the cuprate HTS should have a dx2-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 (pairing wave function) 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.) Secondly, there was the interlayer coupling model, according to which a layered structure consisting of BCS-type (s-wave symmetry) superconductors can enhance the superconductivity by itself. By introducing an additional tunnelling interaction between each layer, this model successfully explained the anisotropic symmetry of the order parameter as well as the emergence of the HTS. Thus, in order to solve this unsettled problem, there have been numerous experiments such as photoemission spectroscopyPhotoemission spectroscopy
Photoemission spectroscopy , also known as photoelectron spectroscopy, refers to energy measurement of electrons emitted from solids, gases or liquids by the photoelectric effect, in order to determine the binding energies of electrons in a substance...
, NMR
Nuclear magnetic resonance
Nuclear magnetic resonance is a physical phenomenon in which magnetic nuclei in a magnetic field absorb and re-emit electromagnetic radiation...
, specific heat measurements, etc. But, unfortunately, the results were ambiguous, some reports supported the d symmetry for the HTS whereas others supported the s symmetry. This muddy situation possibly originated from the indirect nature of the experimental evidence, as well as experimental issues such as sample quality, impurity scattering, twinning, etc.
Junction experiment supporting the d symmetry
Qualitative explanation of the spin-fluctuation mechanism
While, despite all these years, the mechanism of high-Tc superconductivity is still highly controversial, this being due to mostly the lack of exact theoretical computations on such strongly interacting electron systems, most rigorous theoretical calculations, including phenomenological and diagrammatic approaches, converge on magnetic fluctuations as the pairing mechanism for these systems. The qualitative explanation is as follows. (Note that, in the following argument, one can replace “electron” with “hole” and vice versa depending on the actual material.)In a normal conductor, a hole is created whenever an electron is moved. This causes a resistivity because charge neutrality must be conserved and as electrons move under an electric field, they drag holes behind them through defects and thermal oscillations in the system. In contrast, in a superconductor, one gets an unlimited supply of electrons without creating holes behind. This is through the creation of so-called Cooper pairs in a superconductor. Cooper pairs are pairs of electrons. In a normal conductor, creation of an electron leads to creation of a hole, which conserves the number of particles. But in a superconductor, it's possible to create a Cooper pair without creating holes and therefore not to conserve the number of particles, hence leading to the unlimited supply of electrons.
In a conventional superconductor, Cooper pairs are created as follows. When an electron moves through the system, it creates a depression in the atomic lattice through lattice vibrations known as phonons. If the depression of the lattice is strong enough, another electron can fall into the depression created by the first electron—the so-called water-bed effect—and a Cooper pair is formed. When this effect becomes strong enough, Cooper pairs win over the creation of holes behind the electrons, and the normal conductor turns into a superconductor through an unlimited supply of electrons by the creation of Cooper pairs.
In a high-Tc superconductor, the mechanism is extremely similar to a conventional superconductor. Except, in this case, phonons virtually play no role and their role is replaced by spin-density waves. As all conventional superconductors are strong phonon systems, all high-Tc 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-Tc 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 effect again). Hence, again, a Cooper pair is formed. Eventually, when the system temperature is lowered, more spin density waves and Cooper pairs are created and superconductivity begins when an unlimited supply of Cooper pairs, denoted as a phase transition, happens. Note that in high-Tc systems, as these systems are magnetic systems due to the Coulomb interaction, there is a strong Coulomb repulsion between electrons. This Coulomb repulsion prevents pairing of the Cooper pairs on the same lattice site. The pairing of the electrons occur at near-neighbor lattice sites as a result. This is the so-called d-wave pairing, where the pairing state has a node (zero) at the origin.
See also
- Cooper pairCooper pairIn condensed matter physics, a Cooper pair or BCS pair is two electrons that are bound together at low temperatures in a certain manner first described in 1956 by American physicist Leon Cooper...
- Flux pumpingFlux pumpingFlux pumping is a method for magnetising bulk superconductors to fields in excess of 15 teslas. The method can be applied to any type II superconductor and exploits a fundamental property of superconductors. That is their ability to support and maintain currents on the length scale of the...
- Maxim ChernodubMaxim ChernodubMaxim Nikolaevich Chernodub is a Russian physicist best known for his postulation of the magnetic-field-induced superconductivity of the vacuum.- Beginnings and degrees :...
- PseudogapPseudogapThe term 'pseudogap' was coined by Nevill Mott in 1968 to indicate a minimum in the density of states at the Fermi energy, N, resulting from Coulomb repulsion between electrons in the same atom, a bandgap in a disordered material or a combination of these...
- SQUIDSQUIDA SQUID is a very sensitive magnetometer used to measure extremely weak magnetic fields, based on superconducting loops containing Josephson junctions....
- SuperstripesSuperstripesSuperstripes are metallic heterostructures at the atomic limit where the shape resonance in the energy gap parameters ∆n is the driving mechanism for the amplification of the superconductivity critical temperature...
External links
- High temperature superconductivity research at Cornell University
- Superconductor Science and Technology
- American Superconductor and Consolidaded Edison laying first superconductor grid in New York
- Video of a magnet floating on a HTSC
- High-Temperature Superconductor Technologies
- High-Temperature Superconductivity in Cuprates (2002) Book
- Summary of 3 types of cuprate SC - with structure diagrams
- New LaOFeAs HTS SciAm
- University of Manchester Investigation of High Temperature Superconductivity