For verification of this paper, please visit on http://www.socialresearchfoundation.com/anthology.php#8

There are numerous applications of superconductivity and these applications can change our civilization far into the future in the same way that electricity did in the 20th century. The important present and future applications of superconductivity are in the field of nuclear fusion (ITER), Quantum Train (High Temperature Superconducting MAGLEV), Magnetic Resonance Imaging MRI and Nuclear magnetic resonance (NMR) machines, Elevators (Superconducting elevators will allow Megacities to flourish and will allow for theoretical Mega Structures to reach well over a mile high into the atmosphere), The Large Hadron Collider (LHC), Transmission through the use of HTS power cables (which provides 0% loss of electrical current during transmission), Evacuated Tube Transport Technology ET3.

A lot of work is going into developing superconductors to raise their critical temperature (Tc). High-temperature superconductors (abbreviated high-Tc or HTS) are materials that behave as superconductors at unusually high temperatures. Several theories have been proposed to explain the pairing mechanism responsible for the phenomenon of superconductivity in highTc superconductors. Still there exist lots of discrepancies and the research continues for the quest of actual mechanism responsible for superconductivity in these materials. Main challenge is to prepare flexible superconductors with high critical current densities in higher magnetic fields on long length.

The discovery of superconductivity by KammerlinghOnnes in 1911 in mercury below 4 K (−269.15 °C) [1] led to the search of new materials with higher transition temperatures. Later many other superconducting metals, alloys and compounds were also discovered. In 1913, lead was found to superconduct at 7 K, in 1941 niobium-nitride was found to superconduct at 16 K, in 1953 vanadium-silicon displayed superconductive properties at 17.5 K. The metallic superconductors usually have transition temperatures below 30 K.Ever since, researchers have attempted to observe superconductivity at increasing temperatures [2] with the goal of finding a room-temperature superconductor [3]. In 1986, J. Georg Bednorz and K. Alex Müller and Georg Bednorz created a brittle ceramic compound (the lanthanum, barium, copper and oxygen compound) that superconducted at the highest temperature 30 K. In 1986-87 Bednorz encountered a barium-doped compound of lanthanum and copper oxide whose resistance dropped to zero at a temperature around 35 K (−238.2 °C) [4,5]. Later in 1987, Yttrium was substituted for lanthanum in the Müller and Bednorz molecule and other copper oxide compound was synthesized such as yttrium barium copper oxide (YBCO) with an incredible Tc of 92 K [6]. For the first time a material (YBCO) had been found that would superconduct at temperatures warmer than liquid Nitrogen, a commonly available coolant.  Further in 1988, bismuth strontium calcium copper oxide (BSCCO) [7] and Thallium-barium-calcium-copper-oxygen (TBCCO) [8] with transition temperatures as high as 138 K, well above the boiling point of liquid nitrogen (77K). Until 2015 the superconductor with the highest transition temperature that had been confirmed by multiple independent research groups was mercury barium calcium copper oxide (HgBa2Ca2Cu3O8) at around 133 K [9].

Until 2008, only certain compounds of copper and oxygen (also called cuprates) were believed to have HTS properties, and the term high-temperature superconductor was used for superconducting compounds of cuprates such as bismuth strontium calcium copper oxide (BSCCO) and yttrium barium copper oxide (YBCO). Several iron-based compounds (the iron pnictides) are now known to be superconducting at high temperatures. In 2015, hydrogen sulfide (H2S) under extremely high pressure (around 150 gigapascals) was found to undergo superconducting transition near 203 K, the highest temperature superconductor known to date

After more than twenty years of intensive research, the origin of high-temperature superconductivity is still not clear, but it seems that instead of electron-phonon attraction mechanisms, as in conventional superconductivity, one is dealing with genuine electronic mechanisms (e.g. by antiferromagnetic correlations), and instead of 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 the case of the iron-based superconductors).[10,11].

Crystalstructures of high-temperature ceramic superconductors

Most of the cuprate superconductors may be viewed as intergrowth of perovskite and rock salt blocks. One of the properties of the crystal structure of oxide superconductors is an alternating multi-layer of CuO₂ planes. The superconductivity is believed to occur by the doping of charge carriers into the CuO₂ planes. The more layers of CuO₂, the higher theT_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 CuO₂ sheets. The electrical conduction is highly anisotropic, with a much higher conductivity parallel to the CuO₂ plane than in the perpendicular direction. Generally, critical temperatures depend on the chemical compositions,cations substitutions and oxygen content.

Table 1: Critical temperature (Tc), crystal structure of some high-Tc superconductors Formula Notation Tc (K) No. of Cu-O planes in unit cell Crystal structure YBa2Cu3O7 123 92 2 Orthorhombic Bi2Sr2CuO6 Bi-2201 20 1 Tetragonal Bi2Sr2CaCu2O8 Bi-2212 85 2 Tetragonal Bi2Sr2Ca2Cu3O10 Bi-2223 110 3 Tetragonal Tl2Ba2CuO6 Tl-2201 80 1 Tetragonal Tl2Ba2CaCu2O8 Tl-2212 108 2 Tetragonal Tl2Ba2Ca2Cu3O10 Tl-2223 125 3 Tetragonal TlBa2Ca3Cu4O11 Tl-1234 122 4 Tetragonal HgBa2CuO4 Hg-1201 94 1 Tetragonal HgBa2CaCu2O6 Hg-1212 128 2 Tetragonal HgBa2Ca2Cu3O8 Hg-1223 134 3 Tetragonal

Figure 1 :YBCO unit cell

Preparation of high-T_c superconductors

The simplest method for preparing high-T_c superconductors is a solid-state reaction method involving mixing, calcination and sintering. These powders are calcined in the temperature range from 800 °C 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 a very important role in getting good high-T_c superconducting materials. In YBa₂Cu₃O_7−x ,sintering is done at 950 °C in an oxygen atmosphere since the oxygen stoichiometry in this material is very crucial for obtaining a superconducting YBa₂Cu₃O_7−x compound.The preparation of Bi-, Tl- and Hg-based high-T_c superconductors is difficult compared to YBCO superconductor because of the existence of three or more phases having a similar layered structure in these compounds. Thus, syntactic intergrowth and defects such as stacking faults occur during synthesis and it becomes difficult to isolate a single superconducting phase.

Cuprates

The superconducting properties of cuprate superconductors are highly dependent on the doping concentration. Figure 2 shows the doping dependent phase diagram of cuprate superconductors for both electron (n) and hole (p) doping. The phases shown are the antiferromagnetic (AF) phase, the superconducting phase, and the pseudogap phase. The antiferromagnetic phase exists close to zero doping and the superconducting phase exists aound optimal doping. Doping ranges possible for some common compounds are also shown [12].

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 onto the copper-oxide layers. The undoped parent compounds are Mott insulators with long-range antiferromagnetic order at low enough temperature. Single band models are generally considered to be sufficient to describe the electronic properties.

Figure 2 : Doping dependent phase diagram of cuprate superconductors

Possible mechanisms for superconductivity in the cuprates are still the subject of considerable debate and further research. Certain aspects common to all materials have been identified.Similarities between the antiferromagnetic low-temperature state of the undoped materials and the superconducting state that emerges upon doping, primarily the d_x²_-y² orbital state of the Cu²⁺ ions, suggest that electron-electron interactions are more significant than electron-phonon interactions in cuprates – making the superconductivity unconventional. Recent work on the Fermi Surface has shown that nesting occurs at four points in the antiferromagnetic Brillouin zone where spin waves exist and that the superconducting energy gap is larger at these points. The weak isotope effects observed for mostcuprates contrast with conventional superconductors that are well described by BCS theory.

Iron-based superconductors

Iron-based superconductors contain layers of iron and a pnictogen- such as arsenic or phosphorus - or a chalcogen. This is currently the family with the second highest critical temperature, behind the cuprates. Interest in their superconducting properties began in 2006 with the discovery of superconductivity in LaFePO at 4 K [13] and gained much greater attention in 2008 after the analogous material LaFeAs(O,F) [14] was found to superconduct at up to 43 K under pressure [15]. The highest critical temperatures in the iron-based superconductor family exist in thin films of FeSe, where a critical temperature in excess of 100 K has recently been reported [16]. Most undoped iron-based superconductors show a tetragonal-orthorhombic structural phase transition followed at lower temperature by magnetic ordering, similar to the cuprate superconductors. However, they are poor metals rather than Mott insulators.

Figure 3 shows the simplified doping dependent phase diagrams of iron-based superconductors for both Ln-1111 [17] and Ba-122 materials [18]. The phases shown are the antiferromagnetic/ spin density wave (AF/SDW) phase close to zero doping and the superconducting phase around optimal doping.

Figure 3: Doping dependent phase diagrams of iron-based superconductors

Hydrogen sulfide

At pressures above 90 GPa, hydrogen sulfide becomes a metallic conductor of electricity. When cooled below acritical temperature this high-pressure phase exhibits superconductivity. The critical temperature increases with pressure, ranging from 23 K at 100 GPa to 150 K at 200 GPa [19]. If hydrogen sulfide is pressurized at higher temperatures, then cooled, the critical temperature reaches 203 K (−70 °C), the highest accepted superconducting critical temperature as of 2015 [20]. It has been predicted that by substituting a small part of sulfur with phosphorus and using even higher pressures it may be possible to raise the critical temperature to above 0 °C (273 K) and achieve room-temperature superconductivity[20,21].

Other materials sometimes referred to as high-temperature superconductors

The label high-Tc may be reserved for materials with critical temperature greater than the boiling point of liquid nitrogen (77 K or −196 °C). However, a number of materials had critical temperatures below 77 K but are commonly referred to in publication as being in the high-Tc class.Magnesium diboride (MgB2) is occasionally referred to as a high-temperature superconductor [22] because its Tc value of 39 K is above that historically expected for BCS superconductors. While 39 K is still well below the Tc's of the "warm" ceramic superconductors, subsequent refinements in the way MgB2 is fabricated have paved the way for its use in industrial applications. Laboratory testing has found MgB2 will outperform NbTi and Nb3Sn wires in high magnetic field applications like MRI.However, it is more generally regarded as the highest-Tc conventional superconductor, the increased Tc resulting from two separate bands being present at the Fermi level.

Fulleride superconductors where alkali-metal atoms are intercalated into C60 molecules show superconductivity at temperatures up to 38 K for Cs3C60. [23]. Someorganic superconductors and heavy fermion compounds are considered to be high-temperature superconductors because of their high Tc values relative to their Fermi energy, despite the Tc values being lower than for many conventional superconductors. This description may relate better to common aspects of the superconducting mechanism than the superconducting properties.

Metallic hydrogen

Theoretical work by Neil Ashcroft in 1968 predicted that solid metallic hydrogen at extremely high pressure should become superconducting at approximately room-temperature because of its extremely high speed of sound and expected strong coupling between the conduction electrons and the lattice vibrations [24].This prediction is yet to be experimentally verified.

Table 2: Transition temperatures of well-known superconductors (Boiling point of liquid nitrogen for comparison)

Transition temperature (in K)	Transition temperature (in oC)	Material	Class
203	−70	H2S(at 150 GPa pressure)[9]	Hydrogen-based superconductor
195	−78	Sublimation point of dry ice
184	−89.2	Lowest Tempreture recorded on Earth
145	-128	Boiling point of tetrafluoro methane
133	−140	HgBa2Ca2Cu3Ox(HBCCO)	Copper-oxide superconductors
110	−163	Bi2Sr2Ca2Cu3O10(BSCCO)
93	−180	YBa2Cu3O7(YBCO)
90	−183	Boiling point of liquid oxygen
77	−196	Boiling point of liquid nitrogen
55	−218	SmFeAs(O,F)	Iron-based superconductors
41	−232	CeFeAs(O,F)
26	−247	LaFeAs(O,F)
20	−253	Boiling point of liquid hydrogen
18	−255	Nb3Sn	Metallic low-temperature superconductors Iron-based superconductors
10	−263	NbTi
9.2	−263.8	Nb
4.2	−268.8	Boiling point of liquid helium
4.2	−268.8	Hg (mercury)	Metallic low-temperature superconductors

 

2.8Magnetic properties of high T_csuperconductors

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-Tc superconductors can sustain much higher magnetic fields.

Figure 4 :Superconductor timeline

Theories of high temperature superconductivity

The mathematically-complex BCS theory explains superconductivity within the realms of classical mechanics, only applicable for the superconductivity of TYPE I superconductors. Further BCS theory explains the superconductivity of  elements and simple alloys and discovered that electrons in a superconductor are grouped in pairs, called Cooper pairs, and the motion of all of the Cooper pairs within a single superconductor are correlated. Cooper pairs are formed from an interaction between electrons and phonons. The identification of the primary mechanism responsible for the superconductivity in high Tc superconductors is one of the most challenging problems of theoretical condensed matter physics. The mechanism that causes the electrons in these crystals to form pairs is not known [25]. Since the materials are generally very complex, multi-layered crystals (for example, BSCCO), making theoretical modelling is very difficult.Several theories have been proposed to understand the pairing mechanism responsible for superconductivity but still there are lots of discrepancies.

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 [26]. According to this theory, the pairing wave function of the cuprate HTS should have a dx²-y² symmetry. Thus, determining whether the pairing wave function has d-wave symmetry is essential to test the spin fluctuation mechanism. That is, if the HTS order parameter (pairing wave function) does not have d-wave symmetry, then a pairing mechanism related to spin fluctuations can be ruled out. (Similar arguments can be made for iron-based superconductors but the different material properties allow a different pairing symmetry.) Secondly, there was the interlayer coupling model, according to which a layered structure consisting of BCS-type (s-wave symmetry) superconductors can enhance the superconductivity by itself [27].

By introducing an additional tunnelling interaction between each layer, this model successfully explained the anisotropic symmetry of the order parameter as well as the emergence of the HTS. Thus, in order to solve this unsettled problem, there have been numerous experiments such as photoemission 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.

Another theory which is currently on debate by many researchers is Anderson’s Superexchange theory [28]. This is a quantum phenomenon called superexchange i.e. a force arising from electrons’ ability to hop. When electrons can hop between multiple locations, their position at any one moment becomes uncertain, while their momentum becomes precisely defined. A sharper momentum can be a lower momentum, and therefore a lower-energy state, which particles naturally seek out.These charge-transfer superexchange interactions between electrons on adjacent Cu sites have been hypothesized to generate the intense spin-singlet electron-pair formation in cuprate superconductors. [29,30].

Technological applications could benefit from both the higher critical temperature being above the boiling point of liquid nitrogen and also the higher critical magnetic field (and critical current density) at which superconductivity is destroyed. In magnet applications, the high critical magnetic field may 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 which are expensive to manufacture and not easily turned into wires or other useful shapes. Also, high-temperature superconductors do not form large, continuous superconducting domains, but only clusters of micro-domains within which superconductivity occurs.

Improving the quality and variety of samples also gives rise to considerable research, both with the aim of improved characterization of the physical properties of existing compounds, and synthesizing new materials, often with the hope of increasing Tc. Main challenge is to prepare flexible conductors with high critical current densities in higher magnetic fields on long length. Technological research focuses on making HTS materials in sufficient quantities to make their use economically viable and optimizing their properties in relation to application such as motors, generators, transmission cables and in medical and electronics industry. A tremendous progress has been achieved in this direction as we have now developed high temperature superconducting filters in mobile phone base stations, high temperature superconducting SQUID operation in regular technical environment, high temperature superconducting magnets generating a 5T field in addition to a 18T background, 100 m long high temperature superconducting power cables are more than what could be expected on realistic grounds in such a short period of time. Steady improvement of the high temperature superconducting materials basis will surely widen this spectrum of applications within near future [31]. The feasibility of superconducting power cables, magnetic energy-storage devices, transformers, fault current limiters and motors, largely using (Bi,Pb)₂Sr₂Ca₂Cu₃Ox conductor, is proven. Widespread applications now depend significantly on cost-effective resolution of fundamental materials and fabrication issues, which control the production of low-cost, high-performance conductors of these remarkable compounds [32,33].

Significant progress has been made in the development of high temperature superconductors in respect of their transition temperatures and critical current densities and critical magnetic fields so that they can be used for many practical applications. The economic benefits associated with superconducting wires, magnets and motors are remarkable.

1. KamerlinghOnnes, H. (1911) Commun. Leiden 120b, 3-5. 2. Timmer, John (May 2011). "25 years on, the search for higher-temp superconductors continues". ArsTechnica. Retrieved 2 March 2012. 3. Nisbett, Alec (Producer) (1988). Superconductor: The race for the prize (Television Episode). Mourachkine, A. (2004). Room-Temperature Superconductivity.Cambridge International Science Publishing. 4. Bednorz, J. G.; Müller, K. A. (1986). "Possible high TC superconductivity in the Ba-La-Cu-O system". ZeitschriftfürPhysik B. 64 (2): 189–193. 5. The Nobel Prize in Physics 1987: J. Georg Bednorz, K. Alex Müller. Nobelprize.org. Retrieved 2012-04-19. 6. M.K. Wu, J.R. Ashburn, C.J. Torng, P.H. Hor, R.L. Meng, L. Gao, Z.J. Huang, Y.Q. Wang and C.W. Chu, Phys. Rev. Letter 58 (1987), 908. 7. H. Maeda, Y. Tanaka, M. Fukutomi and T. Asano, Jpn. J. of Appl. Phys. 27 (1988) L209. 8. Z.Z. Sheng and A.M. Hermann, Nature 332 (1988) 138. 9. Schilling, A.; Cantoni, M.; Guo, J. D.; Ott, H. R. (1993). "Superconductivity in the Hg-Ba-Ca-Cu-O system". Nature. 363 (6424): 56–58. 10. Dalla Piazza, B.; Mourigal, M.; Christensen, N. B.; Nilsen, G. J.; Tregenna-Piggott, P.; Perring, T. G.; Enderle, M.; McMorrow, D. F.; Ivanov, D. A.; Rønnow, H. M. (15 December 2014). "Fractional excitations in the square-lattice quantum antiferromagnet". Nature Physics. 11 (1): 62–68. 11. "How electrons split: New evidence of exotic behaviors". Nanowerk. ÉcolePolytechniqueFédérale de Lausanne. Dec 23, 2014. 12. C. Hartinger. "DFG FG 538 – Doping Dependence of Phase transitions and Ordering Phenomena in Cuprate Superconductors". Retrieved 2009-10-29. 13. Kamihara, Y; Hiramatsu, H; Hirano, M; Kawamura, R; Yanagi, H; Kamiya, T; Hosono, H (2006). "Iron-Based Layered Superconductor: LaOFeP". Journal of the American Chemical Society. 128 (31): 10012–10013. 14. Kamihara, Y; Watanabe, T; Hirano, M; Hosono, H (2008). "Iron-Based Layered Superconductor La[O1−xFx]FeAs (x=0.05–0.12) with Tc =26 K". Journal of the American Chemical Society. 130 (11): 3296–3297. 15. Takahashi, H; Igawa, K; Arii, K; Kamihara, Y; Hirano, M; Hosono, H (2008). "Superconductivity at 43 K in an iron-based layered compound LaO1-xFxFeAs". Nature. 453 (7193): 376–378. 16. Jian-FengGe; et al. (2014). "Superconductivity in single-layer films of FeSe with a transition temperature above 100 K". Nature Materials. 1406: 3435. 17. Luetkens, H; Klauss, H. H.; Kraken, M; Litterst, F. J.; Dellmann, T; Klingeler, R; Hess, C; Khasanov, R; Amato, A; Baines, C; Kosmala, M; Schumann, O. J.; Braden, M; Hamann-Borrero, J; Leps, N; Kondrat, A; Behr, G; Werner, J; Büchner, B (2009). "Electronic phase diagram of the LaO1−xFxFeAs superconductor". Nature Materials. 8 (4): 305–9. 18. Chu, Jiun-Haw; Analytis, James; Kucharczyk, Chris; Fisher, Ian (2008). "Determination of the phase diagram of the electron doped superconductor Ba(Fe1−xCox)2As2". Physical Review B. 79: 014506. 19. Drozdov, A.P.; Eremets, M. I.; Troyan, I. A. (2014). "Conventional superconductivity at 190 K at high pressures". 20. Cartlidge, Edwin (18 August 2015). "Superconductivity record sparks wave of follow-up physics". Nature News. Retrieved 18 August 2015’ 21. Ge, Y. F.; Zhang, F.; Yao, Y. G. (2016). "First-principles demonstration of superconductivity at 280 K in hydrogen sulfide with low phosphorus substitution". Phys. Rev. B. 93 (22): 224513. 22. Preuss, Paul. "A Most Unusual Superconductor and How It Works". Berkeley Lab. Retrieved 12 March 2012. 23. Ganin, A. Y.; Takabayashi, Y; Khimyak, Y. Z.; Margadonna, S; Tamai, A; Rosseinsky, M. J.; Prassides, K (2008). "Bulk superconductivity at 38 K in a molecular system". Nature Materials. 7 (5): 367–71. 24. Ashcroft, N. W. (1968). "Metallic Hydrogen: A High-Temperature Superconductor?".Physical Review Letters. 21 (26): 1748–1749. 25. A. Leggett (2006). "What do we know about high Tc?".Nature Physics. 2 (3): 134–136. 26. Monthoux, P.; Balatsky, A.; Pines, D. (1992). "Weak-coupling theory of high-temperature superconductivity in the antiferromagnetically correlated copper oxides". Physical Review B. 46 (22): 14803–14817. 27. Chakravarty, S; Sudbø, A; Anderson, P. W.; Strong, S (1993). "Interlayer Tunneling and Gap Anisotropy in High-Temperature Superconductors". Science. 261 (5119): 337–340. 28. P. W. Anderson, Antiferromagnetism. Theory of superexchange interaction. Phys. Rev. 79, 350 (1950). 29. Shane M. O’Mahony, WangpingRen, Weijiong Chen, and J. C. Séamus Davis. “On the electron pairing mechanism of copper-oxide high temperature superconductivity” September 6, 2022, 119 (37) e2207449119 30. High-Temperature Superconductivity Understood at Last, Quanta Magazine, September 21, 2022. 31. Narlikar, A.V; High Temperature Superconductivity, 2 -Engineering Applications, Springer, Berlin, 2004; p.35. 32. High Tc superconducting materials for electric power applications, DavidLarbalestier, Alex Gurevich, D. Matthew Feldmann, and Anatoly Polyanskii,Nature 414, 368–377, 2001. 33. High-Performance High-Tc Superconducting Wires, S. Kang, A. Goyal, J. Li, A. A. Gapud, P. M. Martin, L. Heatherly, J. R. Thompson, D. K. Christen, F. A. List, M. Paranthaman, D.F.Lee;Science 311(5769):1911-4, 2006.