Superconductors are materials whose electrical resistance tends to zero (abruptly) when the temperature falls below the so-called transition temperature (becomes immeasurably small, less than 1 ⋅ 10 −20 Ω ). The superconductivity in 1911 from Heike Kamerlingh Onnes , a pioneer of Low Temperature Physics , discovered. It is a macroscopic quantum state .
Many metals, but also other materials, are superconductors. The transition temperature - also known as the “critical temperature” T c - is very low for most superconductors; To achieve superconductivity, the material generally has to be cooled with liquefied helium (boiling temperature −269 ° C). Only in the case of high-temperature superconductors is liquefied nitrogen sufficient for cooling (boiling temperature −196 ° C).
In the superconducting state, the “ Meißner-Ochsenfeld effect ” occurs, i. H. the interior of the material remains or becomes free of electrical and magnetic fields. An electric field would be broken down immediately by the charge carriers moving without resistance. Magnetic fields are displaced by the build-up of appropriate shielding currents on the surface, which compensate for the external magnetic field with their own magnetic field. A magnetic field that is not too strong penetrates the material only about 100 nm; this thin layer carries the shielding and conduction currents.
The current flow through the superconductor lowers the transition temperature. The transition temperature also drops when there is an external magnetic field. If the magnetic field exceeds a critical value, different effects can be observed depending on the material. Breaks the superconductivity suddenly, it is called a superconductor of the first kind or the type I . Superconductors of the second type, on the other hand ( Type II ), have two critical field strengths, from the lower the field begins to penetrate, at the higher the superconductivity breaks down. In the area in between, the magnetic field increasingly penetrates the conductor in the form of microscopic tubes. The magnetic flux in these flux tubes is quantized. Type II superconductors are interesting for technical applications due to their high current carrying capacity.
Technical applications of superconductivity are the generation of strong magnetic fields - for particle accelerators , nuclear fusion reactors , magnetic resonance tomography , levitation - as well as measurement and energy technology.
Of the great variety of different superconductors that z. B. divided into 32 different classes, the first discovered metallic superconductors and the technically important A15 phases as well as the ceramic high-temperature superconductors are important.
Superconductivity was discovered in 1911 by Heike Kamerlingh Onnes shortly after his discovery of helium liquefaction when taking measurements on the metal mercury . This effect, which was generally unknown at the time, was initially only observed at extremely low temperatures below 4.2 Kelvin . At 39 K, magnesium diboride has the highest transition temperature among the metallic superconductors at atmospheric pressure. This limits the use of metallic superconductivity to relatively few applications, because the cooling requires liquid helium and is therefore very complex and expensive.
Metallic superconductors, however, have the great advantage over the following classes that they can easily be used to form wires, such as those required for the construction of coils for the generation of very strong magnetic fields. The properties of metallic superconductors are explained by the BCS theory .
In 2015 it was reported by Mikhail Eremets and colleagues that hydrogen sulfide H 2 S becomes a metallic conductor under high pressures (100–300 GPa ) with a transition temperature of −70 ° C (= 203 K). In 2019, the Eremets group measured a transition temperature of about 250 K (≈ −23 ° C) for the lanthanum hydride LaH 10 under high pressure (170 GPa); it is therefore the material with the highest known transition temperature.
Ceramic high temperature superconductors
High-temperature superconductors (HTSC) are materials whose transition temperature is above 23 K, the highest transition temperature of conventional, metallic (alloy) superconductors. This class of ceramic superconductors ( cuprates ) with particularly high transition temperatures was only discovered in 1986 by Bednorz and Müller , who were awarded the Nobel Prize in Physics in 1987 .
Particularly interesting for the technology are HTSC, which with a transition temperature of over 77 K ( boiling point of nitrogen ) enable cost-effective cooling. The best known representative is the yttrium barium copper oxide of the formula YBa 2 Cu 3 O δ 7 , also known as YBaCuO , YBCO or 123-oxide is referred to. Superconductivity is observed for δ = 0.05 to 0.65.
The current conduction of these materials takes place in separate current paths and is direction-dependent. So far it has not been clarified on which physical principles the power line in the HTSL is based.
Technical use is difficult because of the brittleness of the ceramic material. Nevertheless, it was possible to produce a flexible conductor material from it by filling the ceramic material into tubes made of silver, which were then rolled out into flexible strips.
|in K||in ° C|
|YBa 2 Cu 3 O 7||93||−180|
|Bi 2 Sr 2 Ca 2 Cu 3 O 10||110||−163|
|HgBa 2 Ca 2 Cu 3 O 8||133||−140|
|Hg 0.8 Tl 0.2 Ba 2 Ca 2 Cu 3 O 8.33 (current record holder at standard pressure
, not yet reproduced and published by a second independent research group)
Ferrous high temperature superconductors
|in K||in ° C|
|LaO 0.89 F 0.11 FeAs||26th||−247|
|LaO 0.9 F 0.2 FeAs||28.5||−244.6|
|CeFeAsO 0.84 F 0.16||41||−232|
|SmFeAsO 0.9 F 0.1||43||−230|
|NdFeAsO 0.89 F 0.11||52||−221|
|SmFeAsO ≈ 0.85||55||−218|
The Japanese Hideo Hosono and colleagues discovered a completely new and unexpected class of high-temperature superconductors in 2008: compounds made from iron, lanthanum, phosphorus and oxygen can be superconducting. By choosing other admixtures, such as arsenic, the transition temperature can be increased from originally 4 K to currently (2011) 56 K. After the pnictogens phosphorus and arsenic, these superconductors are called iron pnictides .
The proportion of iron atoms was surprising, because every known superconducting material becomes normally conductive through sufficiently strong magnetic fields. These strong internal magnetic fields could even be a prerequisite for superconductivity. The guesswork about the basics of physics just got bigger. So far it is only certain that the current flow is carried by pairs of electrons, as described in the BCS theory . It is unclear what effect connects these Cooper pairs . It seems certain that it is not an electron- phonon interaction, as is the case with metallic superconductors .
In 2017, a research team led by Pablo Jarillo-Herrero at the Massachusetts Institute of Technology demonstrated the superconducting ability of graphene , whereby two honeycomb-like monolayers of carbon atoms were superimposed at an angle of 1.1 degrees, strongly cooled and provided with a small electrical voltage. The effect was previously predicted by Allan H. MacDonald and Rafi Bistritzer . Jarillo-Herrero, MacDonald and Bistritzer received the Wolf Prize in Physics in 2020 .
Metallic superconductors at extremely low temperatures
|in K||in ° C|
|PbMo 6 S 8||15th||−258.15|
|K 3 C 60||19th||−254.15|
|Nb 3 Ge||23||−250.15|
|metallic H 2 S||203||-70.15|
Depending on their behavior in the magnetic field, a distinction is made between type I and type II superconductors, also known as first and second type superconductors.
Superconductor type 1
In superconductors type I, a magnetic field is completely displaced from the interior, except for a thin layer on the surface. The magnetic field decreases exponentially very quickly on the surface of the superconductor; the characteristic dimension of about 100 nm of the surface layer is the so-called (London) penetration depth . This condition is also known as the Meissner phase . A superconductor of the first type also becomes normally conductive for temperatures when either the external magnetic field exceeds a critical value or the current density through the superconductor exceeds a critical value . Most metallic elements show this behavior and have very low transition temperatures in the range of a few Kelvin . Exceptions are the non-superconducting alkali and alkaline earth metals as well as copper , silver and gold . The occurrence of a critical current density can be understood by realizing that energy is required to start a shielding current. This energy must be supplied by the condensation energy during the phase transition from normal to superconductive. As soon as the required energy exceeds the condensation energy, there can be no more superconductivity.
In type I superconductors, superconductivity is explained by the formation of pairs of electrons ( Cooper pairs ) in the conductor. In normal electrical conduction, the electrical resistance arises from the interaction of electrons with lattice defects in the crystal lattice and with lattice vibrations . In addition, scattering processes between the electrons can also play an important role. The quantum physical theory for describing type I superconductors is called the BCS theory after its authors Bardeen, Cooper and Schriefer : electrons are fermions which, according to BCS, combine under certain conditions to form bosonic pairs, so-called Cooper pairs. The set of these bosons then takes on a macroscopic quantum state, which the fermions are denied (cf. also superfluidity ). The coupling of the electrons to Cooper pairs and their delocalization in the common quantum state suppresses the transfer of energy to the crystal lattice and thus enables the resistance-free flow of electrical current.
Superconductor type 2
Superconductors of the 2nd type are in the Meißner phase up to the so-called "lower critical magnetic field" , so they behave like type I. At higher magnetic fields, magnetic field lines in the form of so-called flux tubes can penetrate the material ( Schubnikow - or mixed phase, also vortex or flow tube state) before the superconducting state is completely destroyed in the event of an "upper critical magnetic field" . The magnetic flux in a flux hose is always equal to the magnetic flux quantum:
If a current with density J flows through the superconductor, it exerts a Lorentz force on the flow tubes
- ( = Length of the river hose)
perpendicular to J and the magnetic field B from. As a result, the flow hoses move across the material at the speed v . The tubes disappear at one edge and form anew at the opposite edge. This field movement in turn causes a Lorentz force which, according to Lenz's rule , is directed against the current. This counterforce causes a voltage drop, so there is an electrical resistance in the superconductor.
To prevent this, impurities (pinning centers) can be built into the crystal lattice, which hold the flow tubes up to a certain limit force. Only when the Lorentz force exceeds this limit does drift occur and with it the so-called flux flow resistance. Superconductors with a large limit force are called hard superconductors .
The superconductors of the second type are theoretically not as well understood as the superconductors of the first type. Although the formation of Cooper pairs is also assumed in these superconductors, a generally accepted model for their complete description does not yet exist.
Examples of type II superconductors are the ceramic high-temperature superconductors . Two important groups are YBaCuO (yttrium-barium-copper oxide) and BiSrCaCuO (bismuth-strontium-calcium-copper oxide). Furthermore, most superconducting alloys belong to type II, such as the niobium-aluminum alloys used for MR magnets. Since around 2008 a new class of materials has gained in importance; the so-called iron pniktide . The basic building block of these superconductors is arsenic and iron and usually occurs in combination with a rare earth , oxygen and fluorine .
Superconductors, with slight differences between the 1st and 2nd types, show other special properties in addition to the practical loss of electrical resistance and the displacement of magnetic fields from their structure. Most of them can be explained with the BCS theory or consideration of the free enthalpy (“Gibbs function”). The free enthalpy of the respective phase can be calculated using various observation parameters (e.g. pressure, temperature, magnetic field). The Gibbs function in this case is determined by a minimum, i.e. That is, the superconducting phase becomes unstable compared to the normally conducting phase if the free enthalpy of the superconducting phase is greater than that of the normally conducting phase (and vice versa). A rotating superconductor generates a magnetic field, the orientation of which coincides with the axis of rotation of the superconductor, which is known as the London moment .
A so-called critical magnetic field at which superconductivity breaks down, can as a function of ambient temperature T are considered. In the vicinity of the absolute zero point, expenditure has to be made to destroy the superconducting phase. When the transition temperature is reached , the superconducting phase collapses even without an external magnetic field. The function of the external critical magnetic field can be approximated by
to be discribed. The explanation for the breakdown of superconductivity at sufficiently high magnetic fields lies in the binding energy of the Cooper pairs; if energy is supplied to them above their binding energy, they break open and the normally conductive phase arises. The ambient temperature must be correspondingly lower in order to compensate for this process with the condensation of Cooper pairs. The critical energy cannot only be generated by magnetic fields. Functions with pressure (1.) and electric fields (2.) were also found for the ambient temperature. Since the breaking of Cooper pairs is endothermic, a magnetic field and a substance in it in the superconducting state can cool the area around the superconductor. As a technical application, however, this cooling process using demagnetization is of no interest.
- The critical temperature generally drops at very high pressure. However, there are also some reverse dependencies. This anomaly of some substances is caused by a structural transformation of the conductor due to the high pressure. The critical temperature of the substance can first drop with increasing pressure, then at a certain pressure a modification occurs, which suddenly has higher transition temperatures. These high-pressure superconductors also include substances in which a transition into the superconducting phase has previously only been observed at high pressure.
- If current flows through a superconductor, the magnetic field generated by the current destroys the superconductivity from a certain strength.
The volume of a substance in the normally conducting phase (at temperatures ) is smaller than the volume in the superconducting phase ( ). If so, both values roughly correspond to each other ( ). This is interesting because during the transition phase both phases S and N exist side by side in the conductor . In order to explain this phenomenon, however, more intensive considerations are necessary.
The specific heat capacity of the electrons increases by leaps and bounds during the transition from normal to superconducting state for type I / II superconductors ( Rutgers formula ). In classical superconductors, it decreases exponentially with temperature in the superconducting state, since Cooper pairs cannot absorb any heat and so only electrons contribute to the heat capacity that are excited via the energy gap (see also Boltzmann factor ). The heat capacity of the phonons (lattice vibrations) remains unchanged during the transition to the superconducting state.
The superconducting state has little influence on the thermal conductivity . One has to consider this influence for two types of substances. On the one hand, substances in which heat is mainly transmitted via the grid, which is what makes up a large part of conductors. This heat conduction is hindered in the vicinity by the strong interferences at the transitions between S- and N-conducting layers, but better by the lack of interaction with the electrons compared to the normally conducting phase. In the case of substances in which the electrons play a large part in the conduction of heat, this naturally deteriorates. In this regard, thought has been given to using superconductors as switches for heat flows that can be controlled via a critical field.
The London equations
Without going into the carriers of the supercurrent, Fritz and Heinz London derived a description of superconductivity in 1935. The London equations describe the resistance-free transport and the Meißner-Ochsenfeld effect .
Witali Ginsburg and Lew Landau achieved a phenomenological description of superconductivity in 1950. They described the transition from normally conducting to superconducting state by means of a “ second order phase transition ”. In the Ginsburg-Landau theory , the macroscopic wave function of the superconducting state is used as the order parameter . (From this theory there are cross-references to high-energy physics, namely to the so-called Higgs mechanism , which is about the generation of the mass of certain elementary particles, which - similar to superconductivity - are subject to special gauge symmetries .)
The fundamental, microscopic description of superconductivity, which in contrast to the previous theories "explained everything", was presented in 1957 by John Bardeen , Leon Neil Cooper and John Robert Schrieffer . Conventional superconductors can be described very well with this BCS theory . The BCS theory emerged about 50 years after the phenomenon was discovered. There is currently (as of 2019) no generally accepted theory for high-temperature superconductivity .
Generation of strong magnetic fields
An important field of application is the generation of strong, constant or only slowly changing magnetic fields. The ohmic resistance of the coil windings of conventional electromagnets generates large amounts of heat and thus a large loss of energy.
So far (2014) only classic superconductors (SL) have been used for this application, especially alloys of niobium . For strong superconducting coils kilometers long and only a few micrometers thin conductor threads are necessary; these cannot yet be made from high-temperature superconductors (HTSC).
A superconducting coil through which current flows can be closed, whereupon the current in principle remains in the coil for an infinite amount of time without loss. To “charge” the self-contained coil, a short section of the coil is heated above the transition temperature. This opens the coil and can be supplied with power via supply lines. When the desired amperage is reached, the heater is switched off. As a result, the coil is closed again. In the case of continuous operation, the electrical connections can be mechanically removed after the coil has been charged and the container of the coil can be closed. To maintain the field, only regular refilling of the cooling media liquid helium and liquid nitrogen is necessary. A good example of this is an NMR device.
The biggest fault is the so-called quenching (Engl. To quench = delete), a local exposure of superconductivity. The now normally conducting point acts as an electrical resistance. It heats up, which increases the resistance. The normally conductive area is enlarged by heat conduction. In this way, the current collapses and with it the magnetic field. Since the energy stored in the magnetic field is quite large, this process can destroy the coil.
Superconductors are ideally diamagnetic . A current can therefore only flow on its surface, and for large currents without exceeding the limit current density, many thin SL filaments have to be connected in parallel. By embedding these threads in copper it is achieved that the current is absorbed by the normally conducting copper during quenching and the heating remains low, so that the normally conducting area does not grow too quickly ( stabilized superconductor). This prevents the conductor from being destroyed. Such coils made from stabilized superconductors are used, for example, in magnetic resonance tomographs , particle accelerators and nuclear fusion reactors .
Microwaves in superconducting cavities
Superconductors are also used for cavity resonators ( cavities ) in particle accelerators, although the critical field strength drops significantly at high frequencies. Above a critical frequency, the Cooper pairs are broken up directly by photon absorption. Then the critical field strength drops to zero. The only way to push this limit further is through deeper cooling.
For example, in the TESLA project, superconducting cavities made of pure niobium were developed, which are now (2014) in use in various electron accelerators (see linear accelerators ). An advantage and at the same time disadvantage of the system is the low attenuation: the efficiency is particularly high, but at the same time parasitic modes are not attenuated.
The Josephson effect and SQUIDs allow the highly accurate measurement of magnetic fields, e.g. B. to determine brain and heart magnetic fields , in non-destructive material testing or geomagnetic prospecting .
Planned and beginning applications
The previously known superconducting materials either have to be cooled to extremely low temperatures, which is very expensive, or they are difficult to process. The following applications will only become economical when material combinations are found whose usability does not cause any more problems than advantages due to none of these disadvantages. A superconductor at ambient temperature would be ideal.
Energy transport and conversion
In the case of superconductors of the second type for transporting higher electrical currents, there is the problem that these materials do not become normal, good electrical conductors like metals when they transition to normal, but rather - to a good approximation - become insulators. If such a current-carrying superconductor changes to the normal state (for example by exceeding the maximum current density), the current flowing briefly through the line inductance will heat the material according to Joule's law , which can lead to the complete destruction of the superconductor. It is therefore necessary to embed such materials, for example as microscopically thin threads, in a normal conductor. The difficulty of drawing thin threads from these ceramic-like materials is one of the main obstacles to use at higher currents.
The first systems have already been built in power distribution networks in which high-temperature superconductors are used as short-circuit current limiters. In the event of a short circuit, an increased current density means that the superconductor first merges into the mixed area and then into the normally conducting area. The advantage over short-circuit current limiting reactors is that there is only a greatly reduced voltage drop during normal operation. Compared to conventional fuses and short-circuit limiters with detonators, such a current limiter has the advantage that the superconducting state can be achieved again without having to exchange equipment and normal operation is possible again a short time after the failure.
Superconductors are hardly competitive for long-distance lines, because electrical power can be efficiently transmitted even on traditional lines at high voltages. However, due to their higher achievable current density, more electrical power can be transmitted in the same space in superconductors. Therefore, superconducting cables can be used where expansions are necessary due to increased demand and limited structural space. A 1 km long high-temperature superconductor cable for three-phase alternating current with 10 kV , cooled only with liquid nitrogen , has been used in the power supply of the city of Essen since May 2014 as part of a pilot project and replaces a conventional 110 kV line. A station at one end of the cable is sufficient to operate the cooling. An aluminum plant in Voerde is planning superconductors for a 200 kA power line and cites lower space requirements and material costs as advantages.
With superconductors, low-loss transformers can be produced, which have smaller dimensions and mass for the same power and thus bring advantages in mobile operation ( locomotives ), for example . There is no need for environmentally hazardous oil cooling. With good thermal insulation, refrigeration machines should be sufficient for cooling .
Virtually loss-free electric motors with high-temperature superconductors could bring significant volume and weight savings compared to classic motors. A possible increase in the already very good efficiency of 98% (for large engines), on the other hand, would be almost meaningless.
The construction of generators based on superconductors has also been the focus of research for several years. Generators can be made much lighter and more compact with superconductors. Such generators would, for example in wind power plants, bring about lower tower head masses and thus reduce costs. With a 10 MW machine, the generator weight could be halved compared to a conventional permanent magnet generator , with a 5 MW system the generator weight could be reduced to only approx. 34 tons. A prototype of a 3.6 MW generator was tested on a test stand in Bremerhaven and installed in an existing wind turbine in Denmark for practical testing in November 2018. There the generator worked for 700 hours without problems before the wind turbine was shut down as scheduled after the test was completed. The commercial application of this technology is believed to be possible around 2020.
With the use of superconducting bearings , flywheels can be stored without friction, which can serve as short-term storage of electrical energy, e.g. B. to compensate for rapid load fluctuations in the interconnected networks .
Magnetic energy storage
In a superconducting magnetic energy store (SMES), coils store energy in the magnetic field. The energy can be called up very quickly and could therefore be used to compensate for rapid load fluctuations in power grids (flicker compensator) or to generate short pulses of high power.
There have been attempts to develop superconducting electronics since the 1970s. Among other things, research projects were carried out by IBM. In these projects, attempts were made to apply the methods of voltage level-based semiconductor electronics to superconductivity. For physical reasons, the clock frequency that can be achieved with this is limited to a few GHz and therefore not faster than current semiconductor processors.
In 1985, a research group at Moscow University proposed an alternative approach that uses special properties of superconductivity, the Josephson effect and flux quantization in superconducting loops. It is based on the exchange of individual flux quanta between superconducting loops and is therefore referred to as rapid single flux quantum electronics (RSFQ electronics, from Rapid Single Flux Quantum ). This electronics family is characterized by very low power losses and clock frequencies above 100 GHz.
Niobium is used in RSFQ electronics. The operating temperature of 4.2 K is usually reached using liquid helium. Unlike the previously mentioned applications, superconducting electronics could not benefit from the development of a room temperature superconductor. The superconducting electronics are based on extremely low signal levels. With increasing temperatures, the power of the thermal noise increases linearly, so that at temperatures above 30 K the low signal-to-noise ratio prevents the function of a complex circuit.
Before experiments could be carried out at temperatures close to absolute zero , there were various theories as to how the electrical resistance would behave in this temperature range, e.g. B. that the resistance would increase sharply or that it would not fall below a certain level.
The effect of superconductivity was first discovered on April 8, 1911 by the Dutchman Heike Kamerlingh Onnes during experiments with liquid helium. He observed that below 4.19 Kelvin , mercury suddenly lost its electrical resistance. Although quantum mechanics was still new at the time, he already postulated that superconductivity could only be explained quantum mechanically.
In 1950 the successful phenomenological Ginsburg-Landau theory emerged . A quantum mechanical theory of superconductivity was first given in 1957 by the American physicists John Bardeen , Leon Neil Cooper and John Robert Schrieffer ( BCS theory ), for which they were awarded the Nobel Prize in Physics in 1972 .
In 1986 the German physicist Johannes Georg Bednorz and the Swiss Karl Alex Müller (both worked at the IBM research center near Zurich ) published their discovery of high-temperature superconductivity, for which they received the Nobel Prize in 1987. A theory about how this type of superconductivity came about is still pending. Their discovery sparked great scientific research activities around the world.
The Russian physicists Vitali Lasarewitsch Ginsburg and Alexei Alexejewitsch Abrikossow received the Nobel Prize in 2003 for their research on the various types of superconductors (superconductors 1st and 2nd type).
From the 2000s, there were also applications of high-temperature superconductors in electrical power supply as generators and motors. In 2014, the world's longest superconductor cable was integrated into city operations for the first time on a test basis. The 1 km long high-temperature superconductor cable designed for 40 MW was manufactured by Nexans in Hanover.
Organic superconductors were predicted in 1965 by William A. Little and discovered in 1979 by Klaus Bechgaard and Denis Jérome . The first were quasi-one-dimensional, later two-dimensional organic superconductors (such as fullerenes , carbon nanotubes ) were also found.
- Kryotron , a switching element for superconducting devices.
- List of critical temperatures of chemical elements
- James F. Annett: Superconductivity, superfluids, and condensates . Oxford Univ. Press, Oxford 2005, ISBN 978-0-19-850756-7 .
- Peter J. Ford: The rise of the superconductors . CRC Pr., Boca Raton 2005, ISBN 0-7484-0772-3 .
- Werner Buckel, Reinhold Kleiner: Superconductivity - Basics and Applications . 6th edition. Wiley-VCH, 2004, ISBN 978-3-527-40348-6 .
- AV Narlikar: Frontiers in superconducting materials . Springer, Berlin 2005, ISBN 3-540-24513-8 .
- Gernot Goll: Unconventional superconductors . Springer, Berlin 2006, ISBN 3-540-28985-2 .
- Andrei G. Lebed: The physics of organic superconductors and conductors. Springer, Berlin 2008, ISBN 978-3-540-76667-4 .
- Gernot Krabbes: High temperature superconductor bulk materials: fundamentals - processing - properties control - application aspects. Wiley-VCH, Weinheim 2006, ISBN 3-527-40383-3 .
- David A. Cardwell, David S. Ginley: Handbook of superconducting materials. Institute of Physics, Bristol 2003, ISBN 0-7503-0898-2 .
- JR Schrieffer, M. Tinkham: Superconductivity . In: Reviews of modern physics . No. 71 , 1999, p. 313-317 , doi : 10.1103 / RevModPhys.71.S313 .
- Superconductors and superfluids at World of Physics.
- Michael Schreiner: Why does the hovering magnet rock until it turns continuously?
- Superconductivity (PDF; 42 kB). On: technorama.ch , accessed on Feb. 24, 2009 (high-quality popular science explanation of the superconductor effects)
- Ilka Flegel: The challenge of superconductivity . On: Welt der Physik , accessed November 26, 2015.
- Hubertus Luetkens: Isn't superconductivity created quite differently? . TU Dresden, Feb. 23, 2009, accessed on Sept. 16, 2009 (press release).
- Michael Kathke: Superconductivity, an introduction. (PDF; 365 kB) Aachen, June 7, 1999, accessed on October 27, 2010 (an elaboration on the seminar lecture in the seminar Solid State Physics WS 1997/98).
- Hermann Rietschel †, Karlsruhe: https://www.spektrum.de/lexikon/physik/hoch Temperatur-supraleiter / 6805 , accessed on November 8, 2019
- Joe Eck: Superconductor Information for the Beginner . Retrieved on Feb. 24, 2009 (extensive link list, transition temperatures for type 1 and type 2 superconductors and much more).
- What is superconductivity? from the alpha-Centauri television series(approx. 15 minutes). First broadcast on July 20, 2005.
- Michael Schreiner: Why does a floating magnet start to rotate? . Retrieved on Feb. 24, 2009 (video, inter alia, on the temperature distribution in the floating magnet).
- Less loss is gain (superconductivity) (multimedia show in Shockwave format).
- Lectures on Superconductivity, University of Cambridge (English)
- Saturday lecture on November 14, 2006 at the University of Jena, Paul Seidel, Superconductivity - a balance 95 years after its discovery
- Quantum Superconductivity Levitation Video from the Superconductivity Group at Tel Aviv University
- Siegfried Hunklinger: Solid State Physics . 5th, act. Ed. De Gruyter Oldenbourg, Berlin / Boston 2017, ISBN 978-3-11-056775-5 , p. 482-484 .
- JE Hirsch, MB Maple F. Marsiglio: Superconducting materials classes: Introduction and overview . In: Physica C . Superconductivity and its Applications. tape 514 , July 15, 2015, ISSN 0921-4534 , p. 1–8 , doi : 10.1016 / j.physc.2015.03.002 , arxiv : 1504.03318 .
- F. Steglich et al .: Superconductivity in the Presence of Strong Pauli Paramagnetism: CeCu 2 Si 2 . In: Physical Review Letters . tape 43 , no. 25 , 1979, pp. 1892–1896 , doi : 10.1103 / PhysRevLett.43.1892 , bibcode : 1979PhRvL..43.1892S .
- Andrea Naica-Loebell: New superconductor magnesium diboride . Telepolis, February 27, 2001, accessed July 15, 2014.
- A. P. Drozdov, MI Eremets, IA Troyan, V. Ksenofontov, SI Shylin: Conventional superconductivity at 203 kelvin at high pressures in the sulfur hydride system . In: Nature . August 17, 2015, doi : 10.1038 / nature14964 .
- AP Drozdov, PP Kong, VS Minkov, SP Besedin, MA Kuzovnikov: Superconductivity at 250 K in lanthanum hydride under high pressures . In: Nature . tape 569 , no. 7757 , May 2019, ISSN 0028-0836 , p. 528-531 , doi : 10.1038 / s41586-019-1201-8 .
- A. Pawlak: Superconductivity in the city center. Physik-Journal Volume 13 (2014), Issue 6, p. 6.
- F. Schwaigerer, B. Sailer, J. Glaser, HJ Meyer: Electricity served ice cold: superconductivity . In: Chemistry in Our Time . 2nd Edition. tape 36 , 2002, p. 108-124 , doi : 10.1002 / 1521-3781 (200204) 36: 2 <108 :: AID-CIUZ108> 3.0.CO; 2-Y .
- Björn Gojdka: The new gold rush: iron-containing superconductors ( Memento from August 27, 2009 in the Internet Archive ). DESY - World of Physics, Hamburg, July 22, 2009, accessed on November 24, 2009.
- Rainer Scharf: Arsenide superconductor with that certain something . pro-physik.de, January 29, 2009, accessed November 24, 2009.
- From alchemy to quantum dynamics: On the trail of superconductivity, magnetism and structural instability in the iron picnics . Max Planck Society, Research Report 2011 - Max Planck Institute for Chemical Physics of Solids, accessed on July 29, 2011.
- Yuan Cao, Valla Fatemi, Ahmet Demir, Shiang Fang, Spencer L. Tomarken, Pablo Jarillo-Herrero and others: Correlated insulator behavior at half-filling in magic-angle graphene superlattices . In: Nature . March 5, 2018, ISSN 1476-4687 , doi : 10.1038 / nature26154 ( nature.com [accessed March 11, 2018]).
- Charles Kittel: Introduction to Solid State Physics . 7th edition. Wiley, New York 1996, ISBN 978-0-471-11181-8 .
- Joachim Grehn, Joachim Krause: Metzler Physik. Westermann Schroedel Diesterweg Schönihg Winklers GmbH, Braunschweig 2007, ISBN 978-3-507-10710-6 , p. 465.
- Siegfried Hunklinger: Solid State Physics . 5th, act. Ed. De Gruyter Oldenbourg, 2017, ISBN 978-3-11-056775-5 , p. 488 .
- Michael Pekeler, Peter Schmüser: Superconductors in Particle Accelerators, Physik Journal, 2006, No. 3, Online
- Geophysics Airborne Tensor ( Memento of February 2, 2010 in the Internet Archive ). Institute for Photonic Technologies , Jena, accessed on February 6, 2010.
- World premiere: superconducting current limiter protects self-sufficiency in a power plant. (PDF; 218 kB) Nexans, November 6, 2009, accessed on September 14, 2013 .
- RWE Germany - AmpaCity - technological world premiere in Essen. (No longer available online.) In: rwe.com. April 30, 2014, archived from the original on January 24, 2015 ; accessed on February 11, 2015 .
- dpa: RWE is testing superconductor cables in Essen. In: handelsblatt.com . April 9, 2013, accessed February 11, 2015 .
- Superconductivity instead of high-voltage cables - length record in Essen. In: Wissenschaft-aktuell.de. Retrieved February 11, 2015 .
- Trimet in Voerde relies on sustainable superconductor technology. February 4, 2020, accessed March 7, 2020 .
- Islam et al., A review of offshore wind turbine nacelle: Technical challenges, and research and developmental trends. In: Renewable and Sustainable Energy Reviews 33, 2014, pp. 161–176, doi: 10.1016 / j.rser.2014.01.085
- World first as wind turbine upgraded with high temperature superconductor . In: Chemistry World . November 22, 2018. Retrieved November 23, 2018.
- Premiere for the superconducting generator . In: ingenieur.de , May 10, 2019. Retrieved November 9, 2019.
- Superconducting generators: industrial production from 2020 . In: Energy and Technology. May 12, 2015. Retrieved September 13, 2015.
- Dirk van Delft, Peter Kes: The discovery of superconductivity (PDF; 576 kB). In: Physics Today. Vol. 63, Issue 9, September 2010, pp. 38-43.
- Siegfried Hunklinger: Solid State Physics . 5th, act. Ed. De Gruyter Oldenbourg, 2017, ISBN 978-3-11-056775-5 , p. 497 .
- Walther Meißner, Robert Ochsenfeld: A new effect when superconductivity occurs. In: Naturwissenschaften, Volume 21, No. 44, 1933, pp. 787-788.
- SS Kalsi, Applications of High Temperature Supraconductors to Electric Power Equipment, Wiley 2011th
- RWE press release http://www.rwe.com/web/cms/de/1301026/rwe-deutschland-ag/energiewende/intelligente-netze/ampacity/ ( Memento of January 24, 2015 in the Internet Archive ) , accessed on June 18, 2014.
- When electricity no longer has any resistance one day welt.de, accessed on March 20, 2013.