Misplaced Pages

#11988

112-436: The major advantage of high-temperature superconductors is that they can be cooled using liquid nitrogen, in contrast to the previously known superconductors that require expensive and hard-to-handle coolants, primarily liquid helium . A second advantage of high- T c materials is they retain their superconductivity in higher magnetic fields than previous materials. This is important when constructing superconducting magnets ,

224-568: A Ball mill . Solution chemistry processes such as coprecipitation , freeze-drying and sol–gel methods are alternative ways for preparing a homogeneous mixture. These powders are calcined in the temperature range from 1,070 to 1,220 K (800 to 950 °C) for several hours. The powders are cooled, reground and calcined again. This process is repeated several times to get homogeneous material. The powders are subsequently compacted to pellets and sintered. The sintering environment such as temperature, annealing time, atmosphere and cooling rate play

336-538: A room-temperature superconductor . By the late 1970s, superconductivity was observed in several metallic compounds (in particular Nb -based, such as NbTi , Nb 3 Sn , and Nb 3 Ge ) at temperatures that were much higher than those for elemental metals and which could even exceed 20 K (−253.2 °C). In 1986, at the IBM research lab near Zürich in Switzerland, Bednorz and Müller were looking for superconductivity in

448-452: A superposition of these elementary vibration modes (cf. Fourier analysis ). While normal modes are wave-like phenomena in classical mechanics, phonons have particle-like properties too, in a way related to the wave–particle duality of quantum mechanics. The equations in this section do not use axioms of quantum mechanics but instead use relations for which there exists a direct correspondence in classical mechanics. For example:

560-420: 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. This ability of the electrons to flow without resistance leads to superconductivity. In a high- T c superconductor, the mechanism is extremely similar to

672-444: A conventional superconductor, except, in this case, phonons virtually play no role and their role is 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

784-713: 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 are layered materials, consisting of superconducting layers of copper oxide , separated by spacer layers. Cuprates generally have

896-796: 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

1008-539: A lattice there could also appear waves that behave like particles. It is customary to deal with waves in Fourier space which uses normal modes of the wavevector as variables instead of coordinates of particles. The number of normal modes is the same as the number of particles. Still, the Fourier space is very useful given the periodicity of the system. A set of N "normal coordinates" Q k may be introduced, defined as

1120-453: A metallic domain of an adjacent CuO 2 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. An experiment based on flux quantization of a three-grain ring of YBa 2 Cu 3 O 7 (YBCO) was proposed to test the symmetry of the order parameter in the HTS. The symmetry of

1232-553: A much higher conductivity parallel to the CuO 2 plane than in the perpendicular direction. Generally, critical temperatures depend on the chemical compositions, cations substitutions and oxygen content. They can be classified as superstripes ; i.e., particular realizations of superlattices at atomic limit made of superconducting atomic layers, wires, dots separated by spacer layers, that gives multiband and multigap superconductivity. An yttrium–barium cuprate, YBa 2 Cu 3 O 7−x (or Y123),

SECTION 10

#1732859281012

1344-453: A natural consequence of the RVB theory. The confirmation of the d -wave nature of the cuprate superconductors was made by a variety of experiments, including the direct observation of the d -wave nodes in the excitation spectrum through angle resolved photoemission spectroscopy (ARPES), the observation of a half-integer flux in tunneling experiments, and indirectly from the temperature dependence of

1456-494: A new class of ceramics : the copper oxides , or cuprates . Bednorz encountered a particular copper oxide whose resistance dropped to zero at a temperature around 35.1 K (−238 °C). Their results were soon confirmed by many groups, notably Paul Chu at the University of Houston and Shoji Tanaka at the University of Tokyo . In 1987, Philip W. Anderson gave the first theoretical description of these materials, based on

1568-432: A primary application of high- T c materials. The majority of high-temperature superconductors are ceramic materials, rather than the previously known metallic materials. Ceramic superconductors are suitable for some practical uses but they still have many manufacturing issues. For example, most ceramics are brittle , which makes the fabrication of wires from them very problematic. However, overcoming these drawbacks

1680-470: A pyramidal arrangement. Cuprate of Tl–Ba–Ca: The first series of the Tl-based superconductor containing one Tl–O layer has the general formula TlBa 2 Ca n −1 Cu n O 2 n +3 , whereas the second series containing two Tl–O layers has a formula of Tl 2 Ba 2 Ca n −1 Cu n O 2 n +4 with n  =1, 2 and 3. In the structure of Tl 2 Ba 2 CuO 6 (Tl-2201), there is one CuO 2 layer with

1792-567: A rigid regular, crystalline (not amorphous ) lattice is composed of N particles. These particles may be atoms or molecules. N is a large number, say of the order of 10 , or on the order of the Avogadro number for a typical sample of a solid. Since the lattice is rigid, the atoms must be exerting forces on one another to keep each atom near its equilibrium position. These forces may be Van der Waals forces , covalent bonds , electrostatic attractions , and others, all of which are ultimately due to

1904-524: A single superconducting phase. For Bi–Sr–Ca–Cu–O, it is relatively simple to prepare the Bi-2212 ( T c  ≈ 85 K) phase, whereas it is very difficult to prepare a single phase of Bi-2223 ( T c  ≈ 110 K). The Bi-2212 phase appears only after few hours of sintering at 1,130–1,140 K (860–870 °C), but the larger fraction of the Bi-2223 phase is formed after a long reaction time of more than

2016-606: 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

2128-430: 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. When the system temperature is lowered, more spin density waves and Cooper pairs are created, eventually leading to superconductivity. Note that in high- T c systems, as these systems are magnetic systems due to

2240-576: 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 which 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

2352-410: A three-dimensional lattice. The wavenumber k is replaced by a three-dimensional wavevector k . Furthermore, each k is now associated with three normal coordinates. The new indices s = 1, 2, 3 label the polarization of the phonons. In the one-dimensional model, the atoms were restricted to moving along the line, so the phonons corresponded to longitudinal waves . In three dimensions, vibration

SECTION 20

#1732859281012

2464-421: A vacuum at temperature above 973 K (700 °C). The preparation of Bi-, Tl- and Hg-based high- T c superconductors is more difficult than the YBCO preparation. Problems in these superconductors arise because of the existence of three or more phases having a similar layered structure. Thus, syntactic intergrowth and defects such as stacking faults occur during synthesis and it becomes difficult to isolate

2576-441: A very important role in getting good high- T c superconducting materials. The YBa 2 Cu 3 O 7− x compound is prepared by calcination and sintering of a homogeneous mixture of Y 2 O 3 , BaCO 3 and CuO in the appropriate atomic ratio. Calcination is done at 1,070 to 1,220 K (800 to 950 °C), whereas sintering is done at 1,220 K (950 °C) in an oxygen atmosphere. The oxygen stoichiometry in this material

2688-497: A week at 1,140 K (870 °C). Although the substitution of Pb in the Bi–Sr–Ca–Cu–O compound has been found to promote the growth of the high- T c phase, a long sintering time is still required. 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

2800-412: Is a fermion and at very low temperatures, they form two-atom Cooper pairs which are bosonic and condense into a superfluid . These Cooper pairs are substantially larger than the interatomic separation. The temperature required to produce liquid helium is low because of the weakness of the attractions between the helium atoms. These interatomic forces in helium are weak to begin with because helium

2912-474: Is a noble gas , but the interatomic attractions are reduced even more by the effects of quantum mechanics . These are significant in helium because of its low atomic mass of about four atomic mass units . The zero point energy of liquid helium is less if its atoms are less confined by their neighbors. Hence in liquid helium, its ground state energy can decrease by a naturally occurring increase in its average interatomic distance. However at greater distances,

3024-403: Is an alternating multi-layer of CuO 2 planes with superconductivity taking place between these layers. The more layers of CuO 2 , the higher T c . This structure causes a large anisotropy in normal conducting and superconducting properties, since electrical currents are carried by holes induced in the oxygen sites of the CuO 2 sheets. The electrical conduction is highly anisotropic, with

3136-414: Is assumed to be a point particle and the nucleus and electrons move in step ( adiabatic theorem ): ···o++++++o++++++o++++++o++++++o++++++o++++++o++++++o++++++o++++++o··· where n labels the n th atom out of a total of N , a is the distance between atoms when the chain is in equilibrium, and u n the displacement of the n th atom from its equilibrium position. If C is the elastic constant of

3248-438: Is at its equilibrium position.) In two or more dimensions, the x i {\displaystyle x_{i}} are vector quantities. The Hamiltonian for this system is where m is the mass of each atom (assuming it is equal for all), and x i and p i are the position and momentum operators, respectively, for the i th atom and the sum is made over the nearest neighbors (nn). However one expects that in

3360-453: Is currently BSCCO , a compound of Bi–Sr–Ca–Cu–O . The content of bismuth and strontium creates some chemical issues. It has three superconducting phases forming a homologous series as Bi 2 Sr 2 Ca n −1 Cu n O 4+2 n + x ( n =1, 2 and 3). These three phases are Bi-2201, Bi-2212 and Bi-2223, having transition temperatures of 20 K (−253.2 °C), 85 K (−188.2 °C) and 110 K (−163 °C), respectively, where

3472-476: 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

High-temperature superconductivity - Misplaced Pages Continue

3584-529: Is found to increase with the increase in CuO 2 layers. However, the value of T c decreases after four CuO 2 layers in TlBa 2 Ca n −1 Cu n O 2 n +3 , and in the Tl 2 Ba 2 Ca n −1 Cu n O 2 n +4 compound, it decreases after three CuO 2 layers. Cuprate of Hg–Ba–Ca The crystal structure of HgBa 2 CuO 4 (Hg-1201), HgBa 2 CaCu 2 O 6 (Hg-1212) and HgBa 2 Ca 2 Cu 3 O 8 (Hg-1223)

3696-442: Is further to extract access hydrogen from the reduction with CaH 2 , otherwise topotactic hydrogen may prevent superconductivity. The structure of cuprates which are superconductors are often closely related to perovskite structure, and the structure of these compounds has been described as a distorted, oxygen deficient multi-layered perovskite structure. One of the properties of the crystal structure of oxide superconductors

3808-571: Is known as a normal mode . The second equation, for ω k , is known as the dispersion relation between the angular frequency and the wavenumber . In the continuum limit , a →0, N →∞, with Na held fixed, u n → φ ( x ) , a scalar field, and ω ( k ) ∝ k a {\displaystyle \omega (k)\propto ka} . This amounts to classical free scalar field theory , an assembly of independent oscillators. A one-dimensional quantum mechanical harmonic chain consists of N identical atoms. This

3920-401: Is more difficult than the YBCO preparation. They also have a different crystal structure: they are tetragonal where YBCO is orthorhombic . Problems in these superconductors arise because of the existence of three or more phases having a similar layered structure. Moreover, the crystal structure of other tested cuprate superconductors are very similar. Like YBCO, the perovskite-type feature and

4032-495: 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 . In 1991 Hebard et al. discovered Fulleride superconductors, where alkali-metal atoms are intercalated into C 60 molecules. In 2008 Ganin et al. demonstrated superconductivity at temperatures of up to 38 K (−235.2 °C) for Cs 3 C 60 . P-doped Graphane

4144-419: 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

4256-460: Is not restricted to the direction of propagation, and can also occur in the perpendicular planes, like transverse waves . This gives rise to the additional normal coordinates, which, as the form of the Hamiltonian indicates, we may view as independent species of phonons. For a one-dimensional alternating array of two types of ion or atom of mass m 1 , m 2 repeated periodically at a distance

4368-399: Is present: the common isotope helium-4 or the rare isotope helium-3 . These are the only two stable isotopes of helium. See the table below for the values of these physical quantities. The density of liquid helium-4 at its boiling point and a pressure of one atmosphere (101.3 kilopascals ) is about 125 g/L (0.125 g/ml), or about one-eighth the density of liquid water . Helium

4480-650: Is pseudocubic, nearly orthorhombic . The other superconducting cuprates have another structure: they have a tetragonal cell. Each perovskite cell contains a Y or Ba atom at the center: Ba in the bottom unit cell, Y in the middle one, and Ba in the top unit cell. Thus, Y and Ba are stacked in the sequence [Ba–Y–Ba] along the c-axis. All corner sites of the unit cell are occupied by Cu, which has two different coordinations, Cu(1) and Cu(2), with respect to oxygen. There are four possible crystallographic sites for oxygen: O(1), O(2), O(3) and O(4). The coordination polyhedra of Y and Ba with respect to oxygen are different. The tripling of

4592-529: Is similar to that of Tl-1201, Tl-1212 and Tl-1223, with Hg in place of Tl. It is noteworthy that the T c of the Hg compound (Hg-1201) containing one CuO 2 layer is much larger as compared to the one-CuO 2 -layer compound of thallium (Tl-1201). In the Hg-based superconductor, T c is also found to increase as the CuO 2 layer increases. For Hg-1201, Hg-1212 and Hg-1223, the values of T c are 94, 128, and

High-temperature superconductivity - Misplaced Pages Continue

4704-417: Is sometimes included in high-temperature superconductors: It is relatively simple to manufacture, but it superconducts only below 39 K (−234.2 °C), which makes it unsuitable for liquid nitrogen cooling. Superconductivity was discovered by Kamerlingh Onnes in 1911, in a metal solid. Ever since, researchers have attempted to observe superconductivity at increasing temperatures with the goal of finding

4816-433: 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 conventional, purely s-wave pairing, more exotic pairing symmetries are thought to be involved ( d -wave in the case of the cuprates; primarily extended s -wave, but occasionally d -wave, in

4928-523: Is still valid because the fields produced by distant atoms are effectively screened . Secondly, the potentials V are treated as harmonic potentials . This is permissible as long as the atoms remain close to their equilibrium positions. Formally, this is accomplished by Taylor expanding V about its equilibrium value to quadratic order, giving V proportional to the displacement x and the elastic force simply proportional to x . The error in ignoring higher order terms remains small if x remains close to

5040-415: Is the position of the i th atom, and V is the potential energy between two atoms. It is difficult to solve this many-body problem explicitly in either classical or quantum mechanics. In order to simplify the task, two important approximations are usually imposed. First, the sum is only performed over neighboring atoms. Although the electric forces in real solids extend to infinity, this approximation

5152-633: Is the simplest quantum mechanical model of a lattice that allows phonons to arise from it. The formalism for this model is readily generalizable to two and three dimensions. In contrast to the previous section, the positions of the masses are not denoted by u i {\displaystyle u_{i}} , but instead by x 1 , x 2 , … {\displaystyle x_{1},x_{2},\dots } as measured from their equilibrium positions. (I.e. x i = 0 {\displaystyle x_{i}=0} if particle i {\displaystyle i}

5264-404: Is the subject of considerable research, and progress is ongoing. The main class of high-temperature superconductors is copper oxides combined with other metals, especially the rare-earth barium copper oxides (REBCOs) such as yttrium barium copper oxide (YBCO). The second class of high-temperature superconductors in the practical classification is the iron-based compounds . Magnesium diboride

5376-501: Is then reduced to Nd 0.8 Sr 0.2 NiO 2 via annealing the thin films at 533–553 K (260–280 °C) in the presence of CaH 2 . 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 0.8 Sr 0.2 NiO 2 thin film changes the phase space to allow for superconductivity. Of important

5488-537: Is very crucial for obtaining a superconducting YBa 2 Cu 3 O 7− x compound. At the time of sintering, the semiconducting tetragonal YBa 2 Cu 3 O 6 compound is formed, which, on slow cooling in oxygen atmosphere, turns into superconducting YBa 2 Cu 3 O 7− x . The uptake and loss of oxygen are reversible in YBa 2 Cu 3 O 7 −x . A fully oxygenated orthorhombic YBa 2 Cu 3 O 7− x sample can be transformed into tetragonal YBa 2 Cu 3 O 6 by heating in

5600-485: The discrete Fourier transforms of the x k and N "conjugate momenta" Π k defined as the Fourier transforms of the p k : The quantity k turns out to be the wavenumber of the phonon, i.e. 2 π divided by the wavelength . This choice retains the desired commutation relations in either real space or wavevector space From the general result The potential energy term is where The Hamiltonian may be written in wavevector space as The couplings between

5712-408: The electric force. Magnetic and gravitational forces are generally negligible. The forces between each pair of atoms may be characterized by a potential energy function V that depends on the distance of separation of the atoms. The potential energy of the entire lattice is the sum of all pairwise potential energies multiplied by a factor of 1/2 to compensate for double counting: where r i

SECTION 50

#1732859281012

5824-400: The normal coordinates for continuum field modes ϕ k = e i k n a {\displaystyle \phi _{k}=e^{ikna}} with k = 2 π j / ( N a ) {\displaystyle k=2\pi j/(Na)} for j = 1 … N {\displaystyle j=1\dots N} . Substitution into

5936-430: The normal modes do possess well-defined wavelengths and frequencies . In order to simplify the analysis needed for a 3-dimensional lattice of atoms, it is convenient to model a 1-dimensional lattice or linear chain. This model is complex enough to display the salient features of phonons. The forces between the atoms are assumed to be linear and nearest-neighbour, and they are represented by an elastic spring. Each atom

6048-535: The quantum mechanical quantization of the modes of vibrations for elastic structures of interacting particles. Phonons can be thought of as quantized sound waves , similar to photons as quantized light waves . The study of phonons is an important part of condensed matter physics. They play a major role in many of the physical properties of condensed matter systems, such as thermal conductivity and electrical conductivity , as well as in models of neutron scattering and related effects. The concept of phonons

6160-714: The resonating valence bond (RVB) theory , but a full understanding of these materials is still developing today. These superconductors are now known to possess a d -wave pair symmetry. The first proposal that high-temperature cuprate superconductivity involves d -wave pairing was made in 1987 by N. E. Bickers, Douglas James Scalapino and R. T. Scalettar, followed by three subsequent theories in 1988 by Masahiko Inui, Sebastian Doniach, Peter J. Hirschfeld and Andrei E. Ruckenstein, using spin-fluctuation theory, and by Claudius Gros , Didier Poilblanc, Maurice T. Rice and FC. Zhang, and by Gabriel Kotliar and Jialin Liu identifying d -wave pairing as

6272-577: The Canadian physicist John Cunningham McLennan , who was the first to produce quantities of liquid helium almost on demand. In 1932 Einstein reported that the liquid helium could help in creating an atomic bomb. Important early work on the characteristics of liquid helium was done by the Soviet physicist Lev Landau , later extended by the American physicist Richard Feynman . In 1961, Vignos and Fairbank reported

6384-530: 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. Examples of high- T c cuprate superconductors include YBCO and BSCCO , which are

6496-530: The CuO 2 lattice. The typical Fermi surface within the first CuO 2 Brillouin zone is sketched in Fig. 1 (left). It can be derived from the band structure calculations or measured by angle resolved photoemission spectroscopy ( ARPES ). Fig. 1 (right) shows the Fermi surface of BSCCO measured by ARPES. In a wide range of charge carrier concentration (doping level), in which the hole-doped HTSC are superconducting,

6608-508: The CuO 2 layers in both Bi-2212 and Bi-2223; there is no Ca layer in the Bi-2201 phase. The three phases differ with each other in the number of cuprate planes; Bi-2201, Bi-2212 and Bi-2223 phases have one, two and three CuO 2 planes, respectively. The c axis lattice constants of these phases increases with the number of cuprate planes (see table below). The coordination of the Cu atom is different in

6720-509: The CuO 2 planes which 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 reason for the high transition temperature is then argued to be due to the percolating behaviour of the carriers – the carriers follow zig-zag percolative paths, largely in metallic domains in the CuO 2 planes, until blocked by charge density wave domain walls , where they use dopant bridges to cross over to

6832-414: The Fermi surface is hole-like ( i.e. open, as shown in Fig. 1). This results in an inherent in-plane anisotropy of the electronic properties of HTSC. In 2018, the full three dimensional Fermi surface structure was derived from soft x-ray ARPES. Iron-based superconductors contain layers of iron and a pnictogen  – such as arsenic or phosphorus  – or a chalcogen . This

SECTION 60

#1732859281012

6944-471: The Y plane is to serve as a spacer between two CuO 2 planes. In YBCO, the Cu–O chains are known to play an important role for superconductivity. T c is maximal near 92 K (−181.2 °C) when x  ≈ 0.15 and the structure is orthorhombic. Superconductivity disappears at x  ≈ 0.6, where the structural transformation of YBCO occurs from orthorhombic to tetragonal. The preparation of other cuprates

7056-490: 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

7168-427: 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

7280-476: The case of the iron-based superconductors). In 2014, evidence showing that fractional particles can happen in quasi two-dimensional magnetic materials, was found by École Polytechnique Fédérale de Lausanne (EPFL) scientists lending support for Anderson's theory of high-temperature superconductivity. The "high-temperature" superconductor class has had many definitions. The label high- T c should be reserved for materials with critical temperatures greater than

7392-449: The chain at its ends. The resulting quantization is The upper bound to n comes from the minimum wavelength, which is twice the lattice spacing a , as discussed above. The harmonic oscillator eigenvalues or energy levels for the mode ω k are: The levels are evenly spaced at: where ⁠ 1 / 2 ⁠ ħω is the zero-point energy of a quantum harmonic oscillator . An exact amount of energy ħω must be supplied to

7504-420: The connections between atoms, the displacement of one or more atoms from their equilibrium positions gives rise to a set of vibration waves propagating through the lattice. One such wave is shown in the figure to the right. The amplitude of the wave is given by the displacements of the atoms from their equilibrium positions. The wavelength λ is marked. There is a minimum possible wavelength, given by twice

7616-473: 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

7728-408: The cuprate superconductors. Superconductivity in an infinite-layer nickelate, Nd 0.8 Sr 0.2 NiO 2 , 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 0.8 Sr 0.2 NiO 3 onto SrTiO 3 substrates that

7840-484: The cuprates continue to be the subject of considerable debate and further research. Certain aspects common to all materials have been identified. Similarities between the antiferromagnetic the low-temperature state of undoped materials and the superconducting state that emerges upon doping, primarily the d x−y orbital state of the Cu ions, suggest that electron–electron interactions are more significant than electron–phonon interactions in cuprates – making

7952-400: 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

8064-490: The effects of the interatomic forces in helium are even weaker. Because of the very weak interatomic forces in helium, the element remains a liquid at atmospheric pressure all the way from its liquefaction point down to absolute zero . At temperatures below their liquefaction points, both helium-4 and helium-3 undergo transitions to superfluids . (See the table below.) Liquid helium can be solidified only under very low temperatures and high pressures . Liquid helium-4 and

8176-485: The electronic properties. The cuprate superconductors adopt a perovskite structure. The copper-oxide planes are checkerboard lattices with squares of O ions with a Cu 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

8288-501: 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

8400-405: The equation of motion produces the following decoupled equations (this requires a significant manipulation using the orthonormality and completeness relations of the discrete Fourier transform), These are the equations for decoupled harmonic oscillators which have the solution Each normal coordinate Q k represents an independent vibrational mode of the lattice with wavenumber k , which

8512-411: The equilibrium position. The resulting lattice may be visualized as a system of balls connected by springs. The following figure shows a cubic lattice, which is a good model for many types of crystalline solid. Other lattices include a linear chain, which is a very simple lattice which we will shortly use for modeling phonons. (For other common lattices, see crystal structure .) The potential energy of

8624-479: The equilibrium separation a between atoms. Any wavelength shorter than this can be mapped onto a wavelength longer than 2 a , due to the periodicity of the lattice. This can be thought of as a consequence of the Nyquist–Shannon sampling theorem , the lattice points being viewed as the "sampling points" of a continuous wave. Not every possible lattice vibration has a well-defined wavelength and frequency. However,

8736-412: The existence of a different phase of solid helium-4, designated the gamma-phase. It exists for a narrow range of pressure between 1.45 and 1.78 K. Phonon A phonon is a collective excitation in a periodic, elastic arrangement of atoms or molecules in condensed matter , specifically in solids and some liquids . A type of quasiparticle in physics , a phonon is an excited state in

8848-506: The expression for the total potential energy of the crystal. These assumptions are that (i) the total potential energy can be written as a sum of pairwise interactions, and (ii) each atom interacts with only its nearest neighbors. These are used only sparingly in modern lattice dynamics. A more general approach is to express the potential energy in terms of force constants. See, for example, the Wiki article on multiscale Green's functions. Due to

8960-459: The harmonic oscillator lattice to push it to the next energy level. By analogy to the photon case when the electromagnetic field is quantized, the quantum of vibrational energy is called a phonon. All quantum systems show wavelike and particlelike properties simultaneously. The particle-like properties of the phonon are best understood using the methods of second quantization and operator techniques described later. This may be generalized to

9072-402: The indirect nature of the experimental evidence, as well as experimental issues such as sample quality, impurity scattering, twinning, etc. This summary makes an implicit assumption : superconductive properties can be treated by mean-field theory . It also fails to mention that in addition to the superconductive gap, there is a second gap, the pseudogap . The cuprate layers are insulating, and

9184-415: 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: Most undoped iron-based superconductors show a tetragonal-orthorhombic structural phase transition followed at lower temperature by magnetic ordering, similar to

9296-530: The lattice may now be written as Here, ω is the natural frequency of the harmonic potentials, which are assumed to be the same since the lattice is regular. R i is the position coordinate of the i th atom, which we now measure from its equilibrium position. The sum over nearest neighbors is denoted (nn). It is important to mention that the mathematical treatment given here is highly simplified in order to make it accessible to non-experts. The simplification has been achieved by making two basic assumptions in

9408-526: The most known materials that achieve superconductivity above the boiling point of liquid nitrogen. Liquid helium Liquid helium is a physical state of helium at very low temperatures at standard atmospheric pressures . Liquid helium may show superfluidity . At standard pressure, the chemical element helium exists in a liquid form only at the extremely low temperature of −269 °C (−452.20 °F; 4.15 K). Its boiling point and critical point depend on which isotope of helium

9520-445: The numbering system represent number of atoms for Bi Sr, Ca and Cu respectively. The two phases have a tetragonal structure which consists of two sheared crystallographic unit cells. The unit cell of these phases has double Bi–O planes which are stacked in a way that the Bi atom of one plane sits below the oxygen atom of the next consecutive plane. The Ca atom forms a layer within the interior of

9632-402: The occurrence of the Meissner effect . LK-99 , copper - doped lead-apatite, has also been proposed as a room-temperature superconductor. There have been two representative theories for high-temperature or unconventional superconductivity . Firstly, weak coupling theory suggests superconductivity emerges from antiferromagnetic spin fluctuations in a doped system. According to this theory,

9744-420: The optimal T c value is obtained with undistorted FeAs 4 tetrahedra. The symmetry of the pairing wavefunction is still widely debated, but an extended s -wave scenario is currently favoured. 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

9856-401: 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 spectroscopy , NMR , specific heat measurements, etc. Up to date 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

9968-477: 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

10080-443: The pairing mechanism for these systems. The qualitative explanation is as follows: In a superconductor, the flow of electrons cannot be resolved into individual electrons, but instead consists of many 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 in turn attracts another electron and forms

10192-531: The pairing wave function of the cuprate HTS should have a d x-y 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 like 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

10304-494: The penetration depth, specific heat and thermal conductivity. As of 2021, the superconductor with the highest transition temperature at ambient pressure is the cuprate of mercury, barium, and calcium, at around 133 K (−140 °C). There are other superconductors with higher recorded transition temperatures – for example lanthanum superhydride at 250 K (−23 °C), but these only occur at very high pressures. The origin of high-temperature superconductivity

10416-405: The perovskite unit cell leads to nine oxygen atoms, whereas YBa 2 Cu 3 O 7 has seven oxygen atoms and, therefore, is referred to as an oxygen-deficient perovskite structure. The structure has a stacking of different layers: (CuO)(BaO)(CuO 2 )(Y)(CuO 2 )(BaO)(CuO). One of the key feature of the unit cell of YBa 2 Cu 3 O 7−x (YBCO) is the presence of two layers of CuO 2 . The role of

10528-435: 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 . Metallic hydrogen has been proposed as a room-temperature superconductor, some experimental observations have detected

10640-437: The position variables have been transformed away; if the Q and Π were Hermitian (which they are not), the transformed Hamiltonian would describe N uncoupled harmonic oscillators. The form of the quantization depends on the choice of boundary conditions; for simplicity, periodic boundary conditions are imposed, defining the ( N  + 1)th atom as equivalent to the first atom. Physically, this corresponds to joining

10752-454: The presence of simple copper oxide (CuO 2 ) layers also exist in these superconductors. However, unlike YBCO, Cu–O chains are not present in these superconductors. The YBCO superconductor has an orthorhombic structure, whereas the other high- T c superconductors have a tetragonal structure. There are three main classes of superconducting cuprates: bismuth-based, thallium-based and mercury-based. The second cuprate by practical importance

10864-409: The properties of hole-doped and electron doped cuprates: The electronic structure of superconducting cuprates is highly anisotropic (see the crystal structure of YBCO or BSCCO ). Therefore, the Fermi surface of HTSC is very close to the Fermi surface of the doped CuO 2 plane (or multi-planes, in case of multi-layer cuprates) and can be presented on the 2‑D reciprocal space (or momentum space) of

10976-433: The rare helium-3 are not completely miscible . Below 0.9 kelvin at their saturated vapor pressure , a mixture of the two isotopes undergoes a phase separation into a normal fluid (mostly helium-3) that floats on a denser superfluid consisting mostly of helium-4. This phase separation happens because the overall mass of liquid helium can reduce its thermodynamic enthalpy by separating. At extremely low temperatures,

11088-558: The record value at ambient pressure 134 K (−139 °C), respectively, as shown in table below. The observation that the T c of Hg-1223 increases to 153 K (−120 °C) under high pressure indicates that the T c of this compound is very sensitive to the structure of the compound. The simplest method for preparing ceramic superconductors is a solid-state thermochemical reaction involving mixing, calcination and sintering . The appropriate amounts of precursor powders, usually oxides and carbonates, are mixed thoroughly using

11200-405: The sample metallic. The Sr impurities also act as electronic bridges, enabling interlayer coupling. Proceeding from this picture, some theories argue that the basic pairing interaction is still interaction with phonons , as in the conventional superconductors with Cooper pairs . While the undoped materials are antiferromagnetic, even a few percent of impurity dopants introduce a smaller pseudogap in

11312-412: The smallest unit cell exhibit both acoustic and optical phonons. A phonon is the quantum mechanical description of an elementary vibrational motion in which a lattice of atoms or molecules uniformly oscillates at a single frequency . In classical mechanics this designates a normal mode of vibration. Normal modes are important because any arbitrary lattice vibration can be considered to be

11424-401: The spring and m the mass of the atom, then the equation of motion of the n th atom is This is a set of coupled equations. Since the solutions are expected to be oscillatory, new coordinates are defined by a discrete Fourier transform , in order to decouple them. Put Here, na corresponds and devolves to the continuous variable x of scalar field theory. The Q k are known as

11536-476: The stacking sequence (Tl–O) (Tl–O) (Ba–O) (Cu–O) (Ba–O) (Tl–O) (Tl–O). In Tl 2 Ba 2 CaCu 2 O 8 (Tl-2212), there are two Cu–O layers with a Ca layer in between. Similar to the Tl 2 Ba 2 CuO 6 structure, Tl–O layers are present outside the Ba–O layers. In Tl 2 Ba 2 Ca 2 Cu 3 O 10 (Tl-2223), there are three CuO 2 layers enclosing Ca layers between each of these. In Tl-based superconductors, T c

11648-417: 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

11760-467: The superconductors are doped with interlayer impurities to make them metallic. The superconductive transition temperature can be maximized by varying the dopant concentration. The simplest example is La 2 CuO 4 , which consist of alternating CuO 2 and LaO layers which are insulating when pure. When 8% of the La is replaced by Sr, the latter act as dopants, contributing holes to the CuO 2 layers, and making

11872-426: The superfluid phase, rich in helium-4, can contain up to 6% helium-3 in solution. This makes the small-scale use of the dilution refrigerator possible, which is capable of reaching temperatures of a few millikelvins . Superfluid helium-4 has substantially different properties from ordinary liquid helium. In 1908, Kamerlingh-Onnes succeeded in liquifying a small quantity of helium. In 1923, he provided advice to

11984-411: The three phases. The Cu atom forms an octahedral coordination with respect to oxygen atoms in the 2201 phase, whereas in 2212, the Cu atom is surrounded by five oxygen atoms in a pyramidal arrangement. In the 2223 structure, Cu has two coordinations with respect to oxygen: one Cu atom is bonded with four oxygen atoms in square planar configuration and another Cu atom is coordinated with five oxygen atoms in

12096-527: Was an admixture of s symmetry in YBCO within about 3%. Also, they found that there was a pure d x−y order parameter symmetry in the tetragonal Tl 2 Ba 2 CuO 6 . Despite all these years, the mechanism of high- T c superconductivity is still highly controversial, mostly due to the lack of exact theoretical computations on such strongly interacting electron systems. However, most rigorous theoretical calculations, including phenomenological and diagrammatic approaches, converge on magnetic fluctuations as

12208-868: Was first liquefied on July 10, 1908, by the Dutch physicist Heike Kamerlingh Onnes at the University of Leiden in the Netherlands . At that time, helium-3 was unknown because the mass spectrometer had not yet been invented. In more recent decades, liquid helium has been used as a cryogenic refrigerant (which is used in cryocoolers ), and liquid helium is produced commercially for use in superconducting magnets such as those used in magnetic resonance imaging (MRI), nuclear magnetic resonance (NMR), magnetoencephalography (MEG), and experiments in physics , such as low temperature Mössbauer spectroscopy . The Large Hadron Collider contains superconducting magnets that are cooled with 120 tonnes of liquid helium. A helium-3 atom

12320-541: Was introduced in 1930 by Soviet physicist Igor Tamm . The name phonon was suggested by Yakov Frenkel . It comes from the Greek word φωνή ( phonē ), which translates to sound or voice , because long-wavelength phonons give rise to sound . The name emphasizes the analogy to the word photon , in that phonons represent wave-particle duality for sound waves in the same way that photons represent wave-particle duality for light waves . Solids with more than one atom in

12432-618: Was proposed in 2010 to be capable of sustaining high-temperature superconductivity. On 31st of 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. In 1999, Anisimov et al. conjectured superconductivity in nickelates, proposing nickel oxides as direct analogs to

12544-481: Was the first superconductor found above liquid nitrogen boiling point. There are two atoms of Barium for each atom of Yttrium. The proportions of the three different metals in the YBa 2 Cu 3 O 7 superconductor are in the mole ratio of 1 to 2 to 3 for yttrium to barium to copper, respectively: this particular superconductor has also often been referred to as the 123 superconductor. The unit cell of YBa 2 Cu 3 O 7 consists of three perovskite unit cells, which

#11988