Type-II superconductor

Last updated
Superconductive behavior under varying magnetic field and temperature. The graph shows magnetic flux B as a function of absolute temperature T. Critical magnetic flux densities BC1 and BC2 and the critical temperature TC are labeled. In the lower region of this graph, both type-I and type-II superconductors display the Meissner effect (a). A mixed state (b), in which some field lines are captured in magnetic field vortices, occurs only in Type-II superconductors within a limited region of the graph. Beyond this region, the superconductive property breaks down, and the material behaves as a normal conductor (c). Superconductor interactions with magnetic field.png
Superconductive behavior under varying magnetic field and temperature. The graph shows magnetic flux B as a function of absolute temperature T. Critical magnetic flux densities BC1 and BC2 and the critical temperature TC are labeled. In the lower region of this graph, both type-I and type-II superconductors display the Meissner effect (a). A mixed state (b), in which some field lines are captured in magnetic field vortices, occurs only in Type-II superconductors within a limited region of the graph. Beyond this region, the superconductive property breaks down, and the material behaves as a normal conductor (c).
Vortices in a 200-nm-thick YBCO film imaged by scanning SQUID microscopy YBCO vortices.jpg
Vortices in a 200-nm-thick YBCO film imaged by scanning SQUID microscopy

In superconductivity, a type-II superconductor is a superconductor that exhibits an intermediate phase of mixed ordinary and superconducting properties at intermediate temperature and fields above the superconducting phases. It also features the formation of magnetic field vortices with an applied external magnetic field. This occurs above a certain critical field strength Hc1. The vortex density increases with increasing field strength. At a higher critical field Hc2, superconductivity is destroyed. Type-II superconductors do not exhibit a complete Meissner effect. [2]

Contents

History

In 1935, J.N. Rjabinin and Lev Shubnikov [3] [4] experimentally discovered the type-II superconductors. In 1950, the theory of the two types of superconductors was further developed by Lev Landau and Vitaly Ginzburg in their paper on Ginzburg–Landau theory. [5] In their argument, a type-I superconductor had positive free energy of the superconductor-normal metal boundary. Ginzburg and Landau pointed out the possibility of type-II superconductors that should form inhomogeneous state in strong magnetic fields. However, at that time, all known superconductors were type-I, and they commented that there was no experimental motivation to consider precise structure of type-II superconducting state. The theory for the behavior of the type-II superconducting state in magnetic field was greatly improved by Alexei Alexeyevich Abrikosov, [6] who was elaborating on the ideas by Lars Onsager and Richard Feynman of quantum vortices in superfluids. Quantum vortex solution in a superconductor is also very closely related to Fritz London's work on magnetic flux quantization in superconductors. The Nobel Prize in Physics was awarded for the theory of type-II superconductivity in 2003. [7]

Vortex state

Ginzburg–Landau theory introduced the superconducting coherence length ξ in addition to London magnetic field penetration depth λ. According to Ginzburg–Landau theory, in a type-II superconductor . Ginzburg and Landau showed that this leads to negative energy of the interface between superconducting and normal phases. The existence of the negative interface energy was also known since the mid-1930s from the early works by the London brothers. A negative interface energy suggests that the system should be unstable against maximizing the number of such interfaces. This instability was not observed until the experiments of Shubnikov in 1936 where two critical fields were found.

In 1952 an observation of type-II superconductivity was also reported by Zavaritskii. Fritz London demonstrated [8] [9] that a magnetic flux can penetrate a superconductor via a topological defect that has integer phase winding and carries quantized magnetic flux. Onsager and Feynman demonstrated that quantum vortices should form in superfluids. [10] [11]

A 1957 paper by A. A. Abrikosov [12] generalizes these ideas. In the limit of very short coherence length the vortex solution is identical to London's fluxoid, [9] where the vortex core is approximated by a sharp cutoff rather than a gradual vanishing of superconducting condensate near the vortex center. Abrikosov found that the vortices arrange themselves into a regular array known as a vortex lattice. [7] Near a so-called upper critical magnetic field, the problem of a superconductor in an external field is equivalent to the problem of vortex state in a rotating superfluid, discussed by Lars Onsager and Richard Feynman.

Flux pinning

Position memory due to vortex pinning in a high temperature superconductor

In the vortex state, a phenomenon known as flux pinning becomes possible. This is not possible with type-I superconductors, since they cannot be penetrated by magnetic fields. [13]

If a superconductor is cooled in a field, the field can be trapped, which can allow the superconductor to be suspended over a magnet, with the potential for a frictionless joint or bearing. The worth of flux pinning is seen through many implementations such as lifts, frictionless joints, and transportation. The thinner the superconducting layer, the stronger the pinning that occurs when exposed to magnetic fields.

Materials

Type-II superconductors are usually made of metal alloys or complex oxide ceramics. All high-temperature superconductors are type-II superconductors. While most elemental superconductors are type-I, niobium, vanadium, and technetium are elemental type-II superconductors. Boron-doped diamond and silicon are also type-II superconductors. Metal alloy superconductors can also exhibit type-II behavior (e.g., niobium–titanium, one of the most common superconductors in applied superconductivity), as well as intermetallic compounds like niobium–tin.

Other type-II examples are the cuprate-perovskite ceramic materials which have achieved the highest superconducting critical temperatures. These include La1.85Ba0.15CuO4, BSCCO, and YBCO (Yttrium-Barium-Copper-Oxide), which is famous as the first material to achieve superconductivity above the boiling point of liquid nitrogen (77 K). Due to strong vortex pinning, the cuprates are close to ideally hard superconductors.

Important uses

Strong superconducting electromagnets (used in MRI scanners, NMR machines, and particle accelerators) often use coils wound of niobium-titanium wires or, for higher fields, niobium-tin wires. These materials are type-II superconductors with substantial upper critical field Hc2, and in contrast to, for example, the cuprate superconductors with even higher Hc2, they can be easily machined into wires. Recently, however, 2nd generation superconducting tapes are allowing replacement of cheaper niobium-based wires with much more expensive, but superconductive at much higher temperatures and magnetic fields "2nd generation" tapes.

Related Research Articles

<span class="mw-page-title-main">Superconductivity</span> Electrical conductivity with exactly zero resistance

Superconductivity is a set of physical properties observed in certain materials where electrical resistance vanishes and magnetic fields are expelled from the material. Any material exhibiting these properties is a superconductor. Unlike an ordinary metallic conductor, whose resistance decreases gradually as its temperature is lowered, even down to near absolute zero, a superconductor has a characteristic critical temperature below which the resistance drops abruptly to zero. An electric current through a loop of superconducting wire can persist indefinitely with no power source.

Superfluid helium-4 is the superfluid form of helium-4, an isotope of the element helium. A superfluid is a state of matter in which matter behaves like a fluid with zero viscosity. The substance, which looks like a normal liquid, flows without friction past any surface, which allows it to continue to circulate over obstructions and through pores in containers which hold it, subject only to its own inertia.

<span class="mw-page-title-main">Meissner effect</span> Expulsion of a magnetic field from a superconductor

The Meissner effect is the expulsion of a magnetic field from a superconductor during its transition to the superconducting state when it is cooled below the critical temperature. This expulsion will repel a nearby magnet.

The magnetic flux, represented by the symbol Φ, threading some contour or loop is defined as the magnetic field B multiplied by the loop area S, i.e. Φ = B ⋅ S. Both B and S can be arbitrary, meaning Φ can be as well. However, if one deals with the superconducting loop or a hole in a bulk superconductor, the magnetic flux threading such a hole/loop is quantized. The (superconducting) magnetic flux quantumΦ0 = h/(2e) ≈ 2.067833848...×10−15 Wb is a combination of fundamental physical constants: the Planck constant h and the electron charge e. Its value is, therefore, the same for any superconductor. The phenomenon of flux quantization was discovered experimentally by B. S. Deaver and W. M. Fairbank and, independently, by R. Doll and M. Näbauer, in 1961. The quantization of magnetic flux is closely related to the Little–Parks effect, but was predicted earlier by Fritz London in 1948 using a phenomenological model.

<span class="mw-page-title-main">Alexei Abrikosov (physicist)</span> Soviet, Russian and American theoretical physicist

Alexei Alexeyevich Abrikosov was a Soviet, Russian and American theoretical physicist whose main contributions are in the field of condensed matter physics. He was the co-recipient of the 2003 Nobel Prize in Physics, with Vitaly Ginzburg and Anthony James Leggett, for theories about how matter can behave at extremely low temperatures.

In physics, Ginzburg–Landau theory, often called Landau–Ginzburg theory, named after Vitaly Ginzburg and Lev Landau, is a mathematical physical theory used to describe superconductivity. In its initial form, it was postulated as a phenomenological model which could describe type-I superconductors without examining their microscopic properties. One GL-type superconductor is the famous YBCO, and generally all Cuprates.

<span class="mw-page-title-main">Magnesium diboride</span> Chemical compound

Magnesium diboride is the inorganic compound with the formula MgB2. It is a dark gray, water-insoluble solid. The compound has attracted attention because it becomes superconducting at 39 K (−234 °C). In terms of its composition, MgB2 differs strikingly from most low-temperature superconductors, which feature mainly transition metals. Its superconducting mechanism is primarily described by BCS theory.

<span class="mw-page-title-main">History of superconductivity</span>

Superconductivity is the phenomenon of certain materials exhibiting zero electrical resistance and the expulsion of magnetic fields below a characteristic temperature. The history of superconductivity began with Dutch physicist Heike Kamerlingh Onnes's discovery of superconductivity in mercury in 1911. Since then, many other superconducting materials have been discovered and the theory of superconductivity has been developed. These subjects remain active areas of study in the field of condensed matter physics.

In physics, a fluxon is a quantum of electromagnetic flux. The term may have any of several related meanings.

In superconductivity, a Josephson vortex is a quantum vortex of supercurrents in a Josephson junction. The supercurrents circulate around the vortex center which is situated inside the Josephson barrier, unlike Abrikosov vortices in type-II superconductors, which are located in the superconducting condensate.

<span class="mw-page-title-main">Abrikosov vortex</span>

In superconductivity, a fluxon is a vortex of supercurrent in a type-II superconductor, used by Alexei Abrikosov to explain magnetic behavior of type-II superconductors. Abrikosov vortices occur generically in the Ginzburg–Landau theory of superconductivity.

The superconductor–insulator transition is an example of a quantum phase transition, whereupon tuning some parameter in the Hamiltonian, a dramatic change in the behavior of the electrons occurs. The nature of how this transition occurs is disputed, and many studies seek to understand how the order parameter, , changes. Here is the amplitude of the order parameter, and is the phase. Most theories involve either the destruction of the amplitude of the order parameter - by a reduction in the density of states at the Fermi surface, or by destruction of the phase coherence; which results from the proliferation of vortices.

<span class="mw-page-title-main">Type-I superconductor</span> Type of superconductor with a single critical magnetic field

The interior of a bulk superconductor cannot be penetrated by a weak magnetic field, a phenomenon known as the Meissner effect. When the applied magnetic field becomes too large, superconductivity breaks down. Superconductors can be divided into two types according to how this breakdown occurs. In type-I superconductors, superconductivity is abruptly destroyed via a first order phase transition when the strength of the applied field rises above a critical value Hc. This type of superconductivity is normally exhibited by pure metals, e.g. aluminium, lead, and mercury. The only alloy known up to now which exhibits type I superconductivity is tantalum silicide (TaSi2). The covalent superconductor SiC:B, silicon carbide heavily doped with boron, is also type-I.

<span class="mw-page-title-main">Quantum vortex</span> Quantized flux circulation of some physical quantity

In physics, a quantum vortex represents a quantized flux circulation of some physical quantity. In most cases, quantum vortices are a type of topological defect exhibited in superfluids and superconductors. The existence of quantum vortices was first predicted by Lars Onsager in 1949 in connection with superfluid helium. Onsager reasoned that quantisation of vorticity is a direct consequence of the existence of a superfluid order parameter as a spatially continuous wavefunction. Onsager also pointed out that quantum vortices describe the circulation of superfluid and conjectured that their excitations are responsible for superfluid phase transitions. These ideas of Onsager were further developed by Richard Feynman in 1955 and in 1957 were applied to describe the magnetic phase diagram of type-II superconductors by Alexei Alexeyevich Abrikosov. In 1935 Fritz London published a very closely related work on magnetic flux quantization in superconductors. London's fluxoid can also be viewed as a quantum vortex.

In a standard superconductor, described by a complex field fermionic condensate wave function, vortices carry quantized magnetic fields because the condensate wave function is invariant to increments of the phase by . There a winding of the phase by creates a vortex which carries one flux quantum. See quantum vortex.

Superconductors can be classified in accordance with several criteria that depend on physical properties, current understanding, and the expense of cooling them or their material.

For a given temperature, the critical field refers to the maximum magnetic field strength below which a material remains superconducting. Superconductivity is characterized both by perfect conductivity and by the complete expulsion of magnetic fields. Changes in either temperature or magnetic flux density can cause the phase transition between normal and superconducting states. The highest temperature under which the superconducting state is seen is known as the critical temperature. At that temperature even the weakest external magnetic field will destroy the superconducting state, so the strength of the critical field is zero. As temperature decreases, the critical field increases generally to a maximum at absolute zero.

Type-1.5 superconductors are multicomponent superconductors characterized by two or more coherence lengths, at least one of which is shorter than the magnetic field penetration length , and at least one of which is longer. This is in contrast to single-component superconductors, where there is only one coherence length and the superconductor is necessarily either type 1 or type 2. When placed in magnetic field, type-1.5 superconductors should form quantum vortices: magnetic-flux-carrying excitations. They allow magnetic field to pass through superconductors due to a vortex-like circulation of superconducting particles. In type-1.5 superconductors these vortices have long-range attractive, short-range repulsive interaction. As a consequence a type-1.5 superconductor in a magnetic field can form a phase separation into domains with expelled magnetic field and clusters of quantum vortices which are bound together by attractive intervortex forces. The domains of the Meissner state retain the two-component superconductivity, while in the vortex clusters one of the superconducting components is suppressed. Thus such materials should allow coexistence of various properties of type-I and type-II superconductors.

Macroscopic quantum phenomena are processes showing quantum behavior at the macroscopic scale, rather than at the atomic scale where quantum effects are prevalent. The best-known examples of macroscopic quantum phenomena are superfluidity and superconductivity; other examples include the quantum Hall effect and topological order. Since 2000 there has been extensive experimental work on quantum gases, particularly Bose–Einstein condensates.

References

  1. ↑ Wells, Frederick S.; Pan, Alexey V.; Wang, X. Renshaw; Fedoseev, Sergey A.; Hilgenkamp, Hans (2015). "Analysis of low-field isotropic vortex glass containing vortex groups in YBa2Cu3O7−x thin films visualized by scanning SQUID microscopy". Scientific Reports. 5: 8677. arXiv: 1807.06746 . Bibcode:2015NatSR...5E8677W. doi:10.1038/srep08677. PMC   4345321 . PMID   25728772.
  2. ↑ Tinkham, M. (1996). Introduction to Superconductivity, Second Edition. New York, NY: McGraw-Hill. ISBN   0486435032.
  3. ↑ Rjabinin, J. N. and Schubnikow, L.W. (1935) "Magnetic properties and critical currents of superconducting alloys", Physikalische Zeitschrift der Sowjetunion, vol. 7, no.1, pp. 122–125.
  4. ↑ Rjabinin, J. N.; Shubnikow, L. W. (1935). "Magnetic Properties and Critical Currents of Supra-conducting Alloys". Nature. 135 (3415): 581. Bibcode:1935Natur.135..581R. doi:10.1038/135581a0. S2CID   4113840.
  5. ↑ Ginzburg, V.L. and Landau, L.D. (1950) Zh. Eksp. Teor. Fiz.20, 1064
  6. ↑ Abrikosov, A. A. (1957). On the magnetic properties of superconductors of the second group. Soviet Physics-JETP, 5, 1174-1182.
  7. 1 2 A. A. Abrikosov, "Type II superconductors and the vortex lattice", Nobel Lecture, December 8, 2003
  8. ↑ London, F. (1948-09-01). "On the Problem of the Molecular Theory of Superconductivity". Physical Review. 74 (5): 562–573. Bibcode:1948PhRv...74..562L. doi:10.1103/PhysRev.74.562.
  9. 1 2 London, Fritz (1961). Superfluids (2nd ed.). New York: Dover.
  10. ↑ Onsager, L. (March 1949). "Statistical hydrodynamics". Il Nuovo Cimento. 6 (S2): 279–287. Bibcode:1949NCim....6S.279O. doi:10.1007/BF02780991. ISSN   0029-6341. S2CID   186224016.
  11. ↑ Feynman, R.P. (1955), "Application of Quantum Mechanics to Liquid Helium", in WP Halperin (ed.), Progress in Low Temperature Physics, vol. 1, Elsevier, pp. 17–53, doi:10.1016/s0079-6417(08)60077-3, ISBN   978-0-444-53307-4
  12. ↑ "Journal of Experimental and Theoretical Physics". www.jetp.ac.ru. Retrieved 2021-04-11.
  13. ↑ Rosen, J., Ph.D., & Quinn, L. "Superconductivity". In K. Cullen (ed.), Encyclopedia of physical science.
This page is based on this Wikipedia article
Text is available under the CC BY-SA 4.0 license; additional terms may apply.
Images, videos and audio are available under their respective licenses.