Review on Superconductivity: The Phenomenon occurred at Low Temperature

M. J. Patel, M. E. (Cryogenics), Mechanical Engineering Department,

L. D. College of Engineering, Ahmedabad (INDIA),

mjpatel_328@yahoo.co.in

D. H. Agrawal, M. E. (Cryogenics), A. M. Pathan, M. E. (Cryogenics),Mechanical Engineering Department,

L. D. College of Engineering, Ahmedabad (INDIA),

Abstract—Superconductivity is a phenomenon at nano-scopic level that does not exist in nature (although very recently the first known superconducting mineral, ‘covellite’, was surprisingly discovered). A superconductor shows no electrical resistance to the flow of an electrical current (up to a value named critical current) if cooled below a given temperature (its critical temperature) and in presence of a magnetic field not exceeding a certain critical value. Since 1911, a huge number of superconductors have been synthesized, with constantly increasing critical temperature, whose record value currently exceeds 150 K (-120 °C). This paper gives an overview on history of superconductivity and fundamental properties of superconductors. It also focuses on classification of superconductors, certain superconducting materials and high temperature superconductivity. Finally, it shows certain basic technological applications of superconductivity.

Keywords—Superconductivity, Cryogenics, HTS, LTS, Tc, Hc, Cuprates

I. INTRODUCTION

Superconductivity is an electrical resistance of exactly zero which occurs in certain materials below a characteristic temperature. It was discovered by Heike Kamerlingh Onnes in 1911 [3]. Like ferromagnetism and atomic spectral lines, superconductivity is a quantum mechanical phenomenon. It is also characterized by a phenomenon called the Meissner effect, the ejection of any sufficiently weak magnetic field from the interior of the superconductor as it transitions into the superconducting state. The occurrence of the Meissner effect indicates that superconductivity cannot be understood simply as the idealization of perfect conductivity in classical physics.

The electrical Resistivity of a metallic conductor decreases gradually as the temperature is lowered. However, in ordinary conductors such as copper and silver, this decrease is limited by impurities and other defects. Even near absolute zero, a real sample of copper shows some resistance. Despite these imperfections, in a superconductor the resistance drops abruptly to zero when the material is cooled below its critical temperature. An electric current flowing in a loop of superconducting wire can persist indefinitely with no power source [2]. In 1986, it was discovered that some cuprateceramic materials have critical temperatures above 90 K (−183 °C). These high-temperature superconductors renewed

interest in the topic because of the prospects for improvement and potential room-temperature superconductivity. From a practical perspective, even 90 K is relatively easy to reach with readily available liquid nitrogen (which has a boiling point of 77 K), resulting in more experiments and applications [1].

Figure 1. Dependence of resistance on temperature, found for a Superconductor.

II. HISTORY OF SUPERCONDUCTIVITY

Superconductivity was discovered in 1911 by Heike Kamerlingh Onnes, who was studying the resistance of solid mercury at cryogenic temperatures using the recently discovered liquid helium as a refrigerant. At the temperature of 4.2 K, he observed that the resistance abruptly disappeared [3]. He initially thought that his apparatus had shorted out. Only later did he realize that the effect was real. In subsequent decades, superconductivity was found in several other materials. In 1913, lead was found to superconduct at 7 K, and in 1941 niobium nitride was found to superconduct at 16 K. The next important step in understanding superconductivity occurred in 1933, when Meissner and Ochsenfeld discovered that superconductors expelled applied magnetic fields, a phenomenon which has come to be known as the Meissner effect. In 1935, F. and H. London showed that the Meissner effect was a consequence of the minimization of the electromagnetic free energy carried by superconducting current [4].

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In 1950, the phenomenological Ginzburg-Landau theory of superconductivity was devised by Landau and Ginzburg [5]. This theory, which combined Landau's theory of second-order phase transitions with a Schrödinger-like wave equation, had great success in explaining the macroscopic properties of superconductors. In particular, Abrikosov showed that Ginzburg-Landau theory predicts the division of superconductors into the two categories now referred to as Type I and Type II. Abrikosov and Ginzburg were awarded the 2003 Nobel Prize for their work (Landau had received the 1962 Nobel Prize for other work, and died in 1968) [5].Also in 1950, Maxwell and Reynolds et al. found that the critical temperature of a superconductor depends on the isotopic mass of the constituent element [6][7]. This important discovery pointed to the electron-phonon interaction as the microscopic mechanism responsible for superconductivity. The complete microscopic theory of superconductivity was finally proposed in 1957 by Bardeen, Cooper and Schrieffer. Independently, the superconductivity phenomenon was explained by Nikolay Bogolyubov. This BCS theory explained the superconducting current as a superfluid of Cooper pairs, pairs of electrons interacting through the exchange of phonons. For this work, the authors were awarded the Nobel Prize in 1972. The BCS theory was set on a firmer footing in 1958, when Bogoliubov showed that the BCS wave unction, which had originally been derived from a variational argument, could be obtained using a canonical transformation of the electronic Hamiltonian. In 1959, Lev Gor'kov showed that the BCS theory reduced to the Ginzburg-Landau theory close to the critical temperature.

In 1962, the first commercial superconducting wire, a niobium-titanium alloy, was developed by researchers at Westinghouse, allowing the construction of the first practical superconducting magnets. In the same year, Josephson made the important theoretical prediction that a supercurrent can flow between two pieces of superconductor separated by a thin layer of insulator. This phenomenon, now called the Josephson Effect, is exploited by superconducting devices such as SQUIDs. It is used in the most accurate available measurements of the magnetic flux quantum Фo = h/2e, and thus (coupled with the quantum Hall Resistivity) for Planck's constant h. Josephson was awarded the Nobel Prize for this work in 1973. In 2008, it was discovered that the same mechanism that produces superconductivity could produce a super insulator state in some materials, with almost infinite electrical resistance.

III. FUNDAMENTAL PROPERTIES OFSUPERCONDUCTOR

A. Zero Resistance

In ideal cases, the Resistivity (ρ) of any pure metal should decrease to zero smoothly as the temperature approaches the absolute zero. In Practice however, ρ can never become zero, first due to unattainably of absolute zero and secondly, because of presence of other scattering centers, besides the lattice

vibration such as the impurity and lattice defects in real materials. The situation is quite different in superconductors. The material which looses the resistance at particular temperature above 0 K (at 0 K the material loosing its resistance is known as perfect/ideal conductor) is termed as superconductor and the temperature at which this phenomenon of disappearance of resistance occurs is known as transition temperature or Critical Temperature Tc. This state of zero resistance in material above 0 K is believed to be due the formation of cooper pairs in the material. Bardeen, Cooper and Schrieffee showed in 1957 that at 0 K, an electron with a momentum moving the lattice can collide with the intermediate temperature 0<T<Tc, the material contains copper pairs as well as the normal electrons.

B. Meissner Effect

Another property of a superconductor is that once the transition from the normal state to the superconducting state occurs, external magnetic fields can not penetrate it. This effect is called the Meissner Effect and has implications for making high speed, magnetically-levitated trains. It also has implications for making powerful, small, superconducting magnets for Nuclear Magnetic Resonance (NMR).

Figure 2. Meissner Effect.

C. Josephson Effect [2]

One final property of superconductors is that when two of them are joined by a thin, insulating layer, it is easier for the electron pairs to pass from one superconductor to another without resistance is called as Josephson Effect. This effect has implications for super fast electrical switches that can be used to make small, high-speed computers.

Figure 3. Josephson Effect.

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IV. CLASSIFICATION OF SUPERCONDUCTOR

A. By their physical properties:

Type I Superconductor: There is a single value of the critical field at which the transition from superconducting to normal behavior is abrupt called soft superconductor. Examples: Mercury, Lead, Tin

Type II Superconductor: There is a lower Critical field HC1 at which transition begins and an upper critical field HC2 at which transition is completed.Examples: Niobium, vanadium

Critical Field (Hc): The magnetic field required to destroy the superconductivity is called critical field (HC). The unit of critical field is Tesla.

B. Based on Critical Temperature (Tc):

Low Temperature Superconductor: Become superconductor below the boiling point of LN2 at 77K.

High Temperature superconductor: Become superconductor above the boiling point of LN2 at 77K.

This criterion is used when we want to emphasize whether or not we can cool the sample with liquid nitrogen (whose boiling point is 77 K), which is much more feasible than liquid helium (the alternative to achieve the temperatures needed to get low temperature superconductors).

C. Based on BCS Theory (John Bardeen, Leon Cooper & John Schrieffer):

Conventional superconductors: These are the superconductors which can be fully explained with the BCS theory or related theories.

Unconventional superconductors: These are the superconductors which are failed to be explained using such theories.

This criterion is important, as the BCS theory is explaining the properties of conventional superconductors since 1957, but on the other hand there have been no satisfactory theory to explain fully unconventional superconductors. In most of cases type I superconductors are conventional, but there are several exceptions as niobium, which is both conventional and type II.

D. Based on Materials:

Pure elements:Lead and mercury. But not all pure elements are superconductors, as some never reach the superconducting phase. Most superconductors made of pure elements are type I except niobium, technetium, vanadium, silicon.

Allotropes of carbon: Fullerenes, nano-tubes, diamond etc...

Alloys: Niobium-Titanium (NbTi) (discovered in1962), NbN, Nb3Ge etc…

Ceramics: Several Yttrium Barium Copper Oxides (YBa2Cu3O7 -YBCO family) which are the most famous high temperature superconductors. And Magnesium diboride (MgB2), whose critical temperature is 39K, being the conventional superconductor with the highest known temperature.

V. LIST OF SUPERCONDUCTING MATERIALS

TABLE I. LIST OF SUPERCONDUCTING MATERIALS [1]

Pure Metals:Material Tc (K) Hc (T) Year

Al 1.2 105 1933Ln 3.4 280Sn 3.7 305Pb 7.2 803 1913Nb 9.2 2060 1930

Alloys:Material Tc (K) Hc (T) Year

NbN 15 1.4 X 105 1940Nb3Ge 23 3.7 X 105 1971

Ceramics:Material Tc (K) Year

La1.85Ba0.15CuO4 35 1986YBa2Cu3O7 93 1987Bi2Sr2CaCu2O8+x 94 1988Ta2Ba2Ca2Cu3O10+x 125 1988HgBa2Ca2Cu3O8+x 150* 1993

* Under pressure

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VI. HIGH TEMPERATURE SUPERCONDUCTIVITY

High temperature superconductors (abbreviated high Tc or HTS) are materials that have a superconducting transition temperature (Tc) above 30 K (−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 Muller and Johannes Bednorz, for which they were awarded the Nobel Prize in Physics in 1987 [8]. Until Fe-based superconductors were discovered in 2008 [9], 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) [10]. Examples of high-Tc cuprate superconductors include La1.85Ba0.15CuO4, and YBCO (Yttrium-Barium-Copper-Oxide), which is famous as the first material to achieve superconductivity above the boiling point of liquid nitrogen.

"High temperature" has three common definitions in the context of superconductivity:

1) Above the temperature of 30 K that had historically been taken as the upper limit allowed by BCS theory. This is also above the 1973 record of 23 K that had lasted until copper-oxide materials were discovered in 1986.

2) Having a transition temperature that is a larger fraction of the Fermi temperature than for conventional superconductors such as elemental mercury or lead. This definition encompasses a wider variety of unconventional superconductors and is used in the context of theoretical models.

3) Greater than the boiling point of liquid nitrogen (77 K or −196 °C). This is significant for technological applications of superconductivity because liquid nitrogen is a relatively inexpensive and easily handled coolant.

Figure 4. A small sample of the High Temperature Superconductor BSCCO-2223.

TABLE II. TRANSITION TEMPERATURES OF WELL KNOWN SUPERCONDUCTORS (BOILING POINT OF LIQUID NITROGEN FOR

COMPARISON) [10]

Material Transition temperature

(K)

Class

HgBa2Ca2Cu3Ox 133

Bi2Sr2Ca2Cu3O10

(BSCCO-2223)110

YBa2Cu3O7

(YBCO-123)90

Copper oxide superconductors

Boiling point of LN2

77

SmFeAs (O,F) 55

CeFeAs (O,F) 41

LaFeAs (O,F) 26

Iron based superconductors

Boiling point of LH2

20

Nb3Sn 18

NbTi 10

Nb 9.2

Hg (mercury) 4.2

Metallic low temperature

superconductors

A. Copper Oxide Superconductors (Cuprates):

Cuprate 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 on to the copper oxide layers. The undoped 'parent' or 'mother' compounds are Mott insulators with long range anti-ferromagnetic order at low enough temperature.

B. Iron based superconductors:

Iron-based superconductors contain layers of iron and a pnictogen, such as arsenic, phosphorus, or chalcogens. 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 super conduct at up to 43 K under pressure.

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VII. APPLICATIONS OF SUPERCONDUCTIVITY

TABLE III. LARGE SCALE APPLICATIONS OF SUPERCONDUCTIVITY

Application Major Technical FeaturesPower Cables Higher current densities,

smaller cable diameters, lower transmission losses

Current Limiters Highly non-linear super-normal conductor transition, self controlled current limitation

Transformers Higher current densities, smaller size, lower weight, lower losses

Motors/Generators Higher current densities, higher magnetic fields, smaller size, low weight & losses

Magnets for RTD (Research & Technology Development ), Magnetic Energy Storage, Magnetic Separation, NMR (Nuclear Magnetic Resonance) Spectroscopy, MRI (Magnetic Resonance Imaging), Magnetic Levitation

Higher current densities, higher and ultra higher magnetic fields, higher magnetic field gradients, smaller size, lower weight, lower losses, persistent currents, ultra high temporal field stabilities, stronger levitation forces, larger air gaps

Cavities for Accelerators Lower surface resistance, higher quality factors, higher microwave-power handling

Magnetic Bearings (based on HTS bulk materials)

Higher current densities, lower losses, stronger levitation forces, self controlled auto stable levitation

CONCLUSION:

The basic facts about Superconductivity are: Resistivity goes to zero below the critical temperature Tc

(the most sensitive measurements imply R < 10-25 Ω). Many different materials show superconductivity. Critical Temperature (Tc) values range from a few mK up

to 160 K. Superconductors expel flux (the Meissner effect) and act

as perfect diamagnets. Superconductivity is destroyed by a critical magnetic field

Bc. Specific heat, infrared absorption, tunneling etc... all

imply that there is an energy gap associated with superconductivity

Superconducting materials have wide applications in different field like nuclear magnetic resonance, plasma research, levitation train and electrical power transmission. There has been a growing interest in the High temperature superconductors (HTS) due to their applications as lossless current leads for magnets, levitation etc. For meaningful applications of HTS, easy fabrication techniques for its large scale production are required. The future trend of superconductivity research is to find materials that can become superconductors at room temperature. Once this happens, the whole world of electronics, power and transmission will be revolutionized.

REFERENCES

[1] T. V. Ramakrishnan, C N R Rao, “Superconductivity Today – An Elementary Introduction”, Second Edition, Uiversities Press.

[2] John C. Gallop (1990). SQUIDS, the Josephson Effects and Superconducting Electronics. CRC Press. pp. 3, 20. ISBN 0750300515.

[3] H. K. Onnes (1911). "The resistance of pure mercury at helium temperatures". Commun. Phys. Lab. Univ. Leiden 12: 120.

[4] F. London and H. London (1935). "The Electromagnetic Equations of the Supraconductor". Proc. R. Soc. London A 149 (866): 71–88.

[5] V. L. Ginzburg and L.D. Landau (1950). "On the theory of superconductivity". Zh. Eksp. Teor. Fiz. 20 (1064).

[6] E. Maxwell (1950). "Isotope Effect in the Superconductivity of Mercury". Phys. Rev. 78 (4): 477.

[7] C. A. Reynolds, B. Serin, W. H. Wright and L. B. Nesbitt (1950). "Superconductivity of Isotopes of Mercury". Phys. Rev. 78 (4): 487.

[8] J. G. Bednorz and K.A. Mueller (1986). "Possible high TC

superconductivity in the Ba-La-Cu-O system". Z. Phys. B64 (2): 189–193.

[9] Ren, Zhi-An; Che, Guang-Can; Dong, Xiao-Li; Yang, Jie; Lu, Wei; Yi, Wei; Shen, Xiao-Li; Li, Zheng-Cai et al. (2008). "Superconductivity and phase diagram in iron-based arsenic-oxides ReFeAsO1−δ (Re = rare-earth metal) without fluorine doping". EPL (Europhysics Letters)83: 17002.

[10] Anthony Leggett (2006). "What DO we know about high Tc?”, Nature Physics 2: 134.

[11] L. R. Lawrence et al: "High Temperature Superconductivity: The Products and their Benefits" (2002) Bob Lawrence & Associates, Inc.

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