Superconductivity

Superconductivity refers to a collection of physical properties exhibited by superconductors: materials that demonstrate zero electrical resistance and expel magnetic fields. In contrast to conventional metallic conductors, which experience a gradual reduction in resistance as temperature approaches absolute zero, superconductors possess a distinct critical temperature below which their electrical resistance instantaneously disappears. Consequently, an electrical current circulating within a superconducting wire loop can sustain itself indefinitely without requiring an external power source.

The phenomenon of superconductivity was first identified in 1911 by the Dutch physicist Heike Kamerlingh Onnes. Similar to ferromagnetism and atomic spectral lines, superconductivity is a phenomenon explicable solely through the principles of quantum mechanics. A defining characteristic is the Meissner effect, which involves the complete expulsion of magnetic fields from the superconductor's interior as it transitions into the superconducting state. The presence of the Meissner effect demonstrates that superconductivity transcends a mere idealization of perfect conductivity within classical physics.

In 1986, researchers discovered that certain cuprate-perovskite ceramic materials exhibited critical temperatures exceeding 35 K (−238 °C). Shortly thereafter, Ching-Wu Chu demonstrated that substituting lanthanum with yttrium to form YBCO elevated the critical temperature to 92 K (−181 °C), a significant advancement as it allowed for the use of liquid nitrogen as a refrigerant. This exceptionally high transition temperature is theoretically unattainable for conventional superconductors, leading to these materials being designated as high-temperature superconductors. The availability of inexpensive liquid nitrogen, which boils at 77 K (−196 °C), makes superconductivity at these higher temperatures particularly advantageous, enabling numerous experiments and applications that would be impractical at significantly lower temperatures.

History

Heike Kamerlingh Onnes discovered superconductivity on April 8, 1911, while investigating the electrical resistance of solid mercury at cryogenic temperatures, utilizing recently synthesized liquid helium as a refrigerant. At 4.2 K, he noted an abrupt disappearance of resistance. During the same experimental series, he also observed the superfluid transition of helium at 2.2 K, though its importance was not immediately recognized. The exact date and context of this discovery were only fully reconstructed a century later, following the retrieval of Onnes's laboratory notebook. Over the ensuing decades, superconductivity was identified in various other materials. For instance, lead was found to superconduct at 7 K in 1913, and niobium nitride at 16 K in 1941.

Substantial research efforts were dedicated to elucidating the mechanisms of superconductivity; a pivotal breakthrough occurred in 1933 when Meissner and Ochsenfeld observed that superconductors expelled applied magnetic fields, a phenomenon subsequently termed the Meissner effect. By 1935, Fritz and Heinz London demonstrated that the Meissner effect resulted from the minimization of electromagnetic free energy associated with superconducting currents.

London constitutive equations

The initial theoretical framework developed for superconductivity was entirely classical, encapsulated by the London constitutive equations. These equations were proposed by Fritz and Heinz London in 1935, soon after the observation of magnetic field expulsion from superconductors. A significant achievement of this theoretical model is its capacity to explain the Meissner effect, describing how a material exponentially expels all internal magnetic fields upon transitioning into the superconducting state. Application of the London equation allows for the determination of the magnetic field's dependence on the distance from the superconductor's surface.

The two London constitutive equations for a superconductor are as follows:

$${\displaystyle {\frac {\partial \mathbf {j} }{\partial t}}={\frac {ne^{2}}{m}}\mathbf {E} ,\qquad \mathbf {\nabla } \times \mathbf {j} =-{\frac {ne^{2}}{m}}\mathbf {B} .}$$

This initial equation is derived directly from Newton's second law, specifically applied to superconducting electrons.

Conventional Superconductivity Theories (1950s)

In the 1950s, theoretical condensed matter physicists developed a comprehensive understanding of "conventional" superconductivity, primarily through two significant and influential theories: the phenomenological Ginzburg–Landau theory (1950) and the microscopic BCS theory (1957).

The phenomenological Ginzburg–Landau theory of superconductivity was formulated by Landau and Ginzburg in 1950. This theoretical framework, which integrated Landau's theory of second-order phase transitions with a Schrödinger-like wave equation, proved highly effective in elucidating the macroscopic characteristics of superconductors. Notably, Abrikosov demonstrated that the Ginzburg–Landau theory accurately predicts the classification of superconductors into the two distinct categories currently known as Type I and Type II. Abrikosov and Ginzburg received the 2003 Nobel Prize for their contributions; Landau had previously been awarded the 1962 Nobel Prize for unrelated research and passed away in 1968. Furthermore, the Coleman-Weinberg model, a four-dimensional extension of the Ginzburg–Landau theory, holds significant relevance in quantum field theory and cosmology.

Concurrently in 1950, Maxwell and Reynolds, among others, independently observed that a superconductor's critical temperature is contingent upon the isotopic mass of its constituent elements. This pivotal finding strongly suggested that the electron–phonon interaction serves as the underlying microscopic mechanism driving superconductivity.

The comprehensive microscopic theory of superconductivity was ultimately introduced in 1957 by Bardeen, Cooper, and Schrieffer. This seminal BCS theory elucidated the superconducting current as a superfluid composed of Cooper pairs, which are electron pairs that interact via the exchange of phonons. The authors were collectively honored with the Nobel Prize in 1972 for this groundbreaking research.

The theoretical foundation of BCS theory was significantly strengthened in 1958 when N. N. Bogolyubov demonstrated that the BCS wavefunction, initially derived through a variational argument, could also be obtained via a canonical transformation of the electronic Hamiltonian. Subsequently, in 1959, Lev Gor'kov established that BCS theory converges with Ginzburg–Landau theory when approaching the critical temperature.

Generalizations of BCS theory, when applied to conventional superconductors, provide the fundamental framework for comprehending the phenomenon of superfluidity, as these systems belong to the lambda transition universality class. However, the applicability of these generalizations to unconventional superconductors remains a subject of ongoing debate.

Niobium

The initial practical application of superconductivity emerged in 1954 with Dudley Allen Buck's development of the cryotron. This device utilizes two superconductors possessing significantly disparate critical magnetic field values, integrated to create a rapid and straightforward switching mechanism for computer components.

Following the 1911 discovery of superconductivity, Kamerlingh Onnes attempted to construct an electromagnet with superconducting windings; however, he observed that relatively low magnetic fields abolished superconductivity in the materials under investigation. Decades later, in 1955, G. B. Yntema successfully developed a compact 0.7-tesla iron-core electromagnet utilizing superconducting niobium wire windings. A significant breakthrough occurred in 1961 when J. E. Kunzler, E. Buehler, F. S. L. Hsu, and J. H. Wernick reported the remarkable finding that niobium–tin, a compound comprising three parts niobium and one part tin, could sustain a current density exceeding 100,000 amperes per square centimeter within an 8.8-tesla magnetic field at 4.2 Kelvin. Despite its inherent brittleness and fabrication challenges, niobium–tin proved instrumental in generating magnetic fields up to 20 tesla.

In 1962, T. G. Berlincourt and R. R. Hake identified that more ductile alloys of niobium and titanium were suitable for applications requiring magnetic fields up to 10 tesla. This discovery promptly led to the commercial manufacturing of niobium–titanium supermagnet wire by Westinghouse Electric Corporation and Wah Chang Corporation. While niobium–titanium exhibits less potent superconducting characteristics compared to niobium–tin, its superior ductility and ease of fabrication established it as the predominant "workhorse" material for supermagnets. Both niobium–tin and niobium–titanium have been extensively utilized in medical MRI systems, bending and focusing magnets for large high-energy-particle accelerators, and various other technological applications. A 2014 assessment by Conectus, a European superconductivity consortium, estimated that global economic activity critically dependent on superconductivity reached approximately five billion euros, with MRI systems constituting about 80% of this sum.

The Josephson Effect

In 1962, Josephson advanced a significant theoretical prediction: a supercurrent could traverse two superconducting materials separated by a thin insulating layer. This phenomenon, subsequently termed the Josephson effect, is fundamental to the operation of superconducting devices like SQUIDs. It facilitates the most precise current measurements of the magnetic flux quantum, Φ§23§ = h/(2e), where h represents the Planck constant. When combined with quantum Hall resistivity, this effect enables highly accurate determinations of the Planck constant. Josephson received the Nobel Prize in 1973 for his seminal contributions.

In 2008, a hypothesis emerged suggesting that the underlying mechanism responsible for superconductivity might also induce a superinsulator state in certain materials, characterized by nearly infinite electrical resistance. Subsequent research in 2020, involving the initial development and investigation of superconducting Bose–Einstein condensate (BEC), indicated a "smooth transition" between BEC and Bardeen-Cooper-Shrieffer regimes.

Two-Dimensional Materials

Devices fabricated from single-layer materials have exhibited various forms of superconductivity. Furthermore, some of these materials demonstrate the capacity to transition between conductive, insulating, and other distinct behavioral states.

The process of twisting materials imparts a "moiré" pattern, characterized by tiled hexagonal cells that emulate atomic structures and accommodate electrons. Within this specific environment, electrons exhibit sufficiently slow movement, allowing their collective interactions to dictate their behavior. When each cell contains a single electron, the electrons adopt an antiferromagnetic configuration, where each electron possesses a preferred spatial position and magnetic orientation, resulting in intrinsic magnetic fields that typically alternate in direction. The introduction of additional electrons facilitates superconductivity through the formation of Cooper pairs. Fu and Schrade posited that electron-on-electron interactions enable the coexistence of both antiferromagnetic and superconducting states.

The initial successful demonstration of superconductivity in two-dimensional materials involved a twisted bilayer graphene sheet, reported in 2018, exhibiting a critical temperature (Tc) of approximately 1.7 K with a 1.1° twist angle. Subsequently, in 2021, a twisted three-layer graphene device was shown to superconduct at a Tc of approximately 2.8 K. A further advancement in 2022 documented superconductivity in an untwisted trilayer graphene device, with a Tc ranging from 1 to 2 K. This untwisted configuration later proved to be highly tunable, capable of readily replicating behaviors observed across numerous other material arrangements. The ability to directly monitor the effects of electron addition or slight electric field attenuation in a material facilitates rapid experimentation with an unparalleled array of material compositions to identify those conducive to superconductivity.

Recent observations have identified a form of superconductivity, termed "chiral superconductivity," in four- and five-layer rhombohedral graphene. This phenomenon is characterized by spontaneously broken time-reversal symmetry. Notably, these systems exhibited no superlattice effects and demonstrated the ability to transition between two distinct magnetic states without losing their superconducting properties. This behavior significantly diverges from other documented instances of superconductivity in the presence of magnetic fields.

Such devices hold potential applications within the field of quantum computing.

Beyond graphene, other two-dimensional (2D) materials have also been engineered to exhibit superconductivity. For instance, transition metal dichalcogenide (TMD) sheets, when twisted at a 5-degree angle, intermittently achieved superconductivity through the formation of a Josephson junction. The experimental setup involved thin palladium layers for electrical connection to a tungsten telluride layer, which was encapsulated and protected by boron nitride. Separately, another research collective successfully demonstrated superconductivity in molybdenum telluride (MoTe₂) within 2D van der Waals materials, leveraging ferroelectric domain walls. The critical temperature (Tc) for this observation was suggested to exceed that of typical TMDs, which generally range from approximately 5 to 10 Kelvin.

Researchers at Cornell introduced a 3.5-degree twist into an insulating material, a modification that facilitated the deceleration and strong interaction of electrons, resulting in a configuration of one electron per cell and subsequent superconductivity. This observed behavior is not adequately explained by current theoretical frameworks.

Fu and colleagues have posited a mechanism wherein electrons self-organize into a repeating crystalline structure. This arrangement permits the electron lattice to exist independently of the underlying atomic nuclei and to undergo relaxation. It is hypothesized that ripples within this electron lattice facilitate electron pairing, analogous to the role of phonons, though this theory remains unconfirmed.

Classification

Superconductors are categorized based on various criteria, with the most prevalent classifications including:

Response to a magnetic field

Superconductors can be categorized as either Type I or Type II. A Type I superconductor is characterized by a single critical magnetic field; above this field, superconductivity ceases, while below it, the magnetic field is entirely expelled. Conversely, a Type II superconductor possesses two critical fields, allowing for partial magnetic field penetration via localized points known as vortices within this intermediate range. Moreover, in multicomponent superconductors, a hybrid behavior can emerge, classifying them as Type-1.5.

Theory of operation

A superconductor is designated as conventional if its mechanism is primarily governed by electron–phonon interactions and can be elucidated by the Bardeen–Cooper–Schrieffer (BCS) theory or its advanced form, the Eliashberg theory. Conversely, if these conditions are not met, it is classified as unconventional. An alternative definition for an unconventional superconductor is one where the superconducting order parameter transforms according to a non-trivial irreducible representation of the material's point group or space group.

Critical temperature

A superconductor is typically classified as high-temperature if it achieves a superconducting state above 30 Kelvin (−243.15 °C), a threshold exemplified by the initial discovery by Georg Bednorz and K. Alex Müller. This designation can also refer to materials that become superconducting when cooled with liquid nitrogen, specifically those with a critical temperature (T_c) exceeding 77 Kelvin, primarily highlighting the sufficiency of liquid nitrogen as a coolant. In contrast, low-temperature superconductors are materials with a critical temperature below 30 Kelvin, predominantly requiring cooling by liquid helium (T_c > 4.2 Kelvin). A notable exception to this classification involves certain iron pnictide superconductors, which exhibit characteristics typical of high-temperature superconductors despite having critical temperatures below 30 Kelvin.

Material

Superconducting materials encompass diverse classes, including elemental substances (e.g., mercury or lead), various alloys (such as niobium–titanium, germanium–niobium, and niobium nitride), ceramic compounds (e.g., YBCO and magnesium diboride), superconducting pnictides (e.g., fluorine-doped LaOFeAs), single-layer materials like graphene and transition metal dichalcogenides, and organic superconductors (e.g., fullerenes and carbon nanotubes). It is worth noting that fullerenes and carbon nanotubes, being composed solely of carbon, could also be considered within the category of chemical elements.

Elementary properties

Superconductors exhibit a range of physical properties that vary across different materials, including critical temperature, the superconducting gap value, the critical magnetic field, and the critical current density at which superconductivity ceases. Conversely, a distinct set of properties remains independent of the specific material. Key examples of these include the Meissner effect, magnetic flux quantization, and persistent currents, which signify a state of zero electrical resistance. These "universal" characteristics stem from the broken symmetry inherent in superconductors and the manifestation of off-diagonal long-range order. As a thermodynamic phase, superconductivity possesses unique distinguishing attributes that are largely unaffected by microscopic structural details. The formation of Cooper pairs is intrinsically linked to off-diagonal long-range order.

Zero Electrical DC Resistance

The most straightforward approach to determine a material's electrical resistance involves integrating a sample into an electrical circuit in series with a current source I and subsequently measuring the voltage V across the sample. According to Ohm's law, the sample's resistance is calculated as R = V / I. Consequently, a zero voltage drop across the sample indicates the absence of electrical resistance.

Superconductors possess the unique ability to sustain an electrical current without any applied voltage, a characteristic leveraged in superconducting electromagnets, such as those utilized in MRI systems. Experimental observations confirm that currents within superconducting coils can endure for extended periods without detectable degradation, with evidence suggesting a minimum lifetime of 100,000 years. Theoretical projections for persistent current lifetimes, contingent on wire geometry and temperature, can even surpass the estimated age of the universe. Practically, currents introduced into superconducting coils within a gravimeter in Belgium persisted for 28 years, 7 months, and 27 days, specifically from August 4, 1995, to March 31, 2024. In these instruments, measurements rely on monitoring the levitation of a four-gram superconducting niobium sphere.

Within a normal conductor, an electric current can be conceptualized as an electron fluid traversing a dense ionic lattice. These electrons continuously collide with the lattice ions, transferring a portion of the current's energy to the lattice during each collision. This absorbed energy is subsequently converted into heat, fundamentally representing the vibrational kinetic energy of the lattice ions. Consequently, the energy conveyed by the current undergoes continuous dissipation, a phenomenon known as electrical resistance and Joule heating.

The dynamics within a superconductor diverge significantly. In a conventional superconductor, the electronic fluid does not comprise individual electrons but rather consists of bound pairs of electrons, termed Cooper pairs. This pairing arises from an attractive interaction between electrons mediated by the exchange of phonons. Despite its inherent weakness, rendering it susceptible to disruption by minor thermal vibrations, the energy spectrum of this Cooper pair fluid exhibits an energy gap due to quantum mechanical principles. This gap signifies a minimum energy threshold, ΔE, required to excite the fluid. Consequently, if ΔE exceeds the lattice's thermal energy, represented by kT (where k is the Boltzmann constant and T is the temperature), the fluid will not undergo scattering by the lattice. This characteristic establishes the Cooper pair fluid as a superfluid, enabling its flow without energy dissipation.

Type II superconductors, a category encompassing all known high-temperature superconductors, exhibit a very low but measurable resistivity when an electric current is applied in the presence of a strong magnetic field, potentially generated by the current itself, at temperatures just below the nominal superconducting transition. This phenomenon arises from the movement of magnetic vortices within the electronic superfluid, leading to the dissipation of a portion of the current's energy. However, if the applied current is sufficiently weak, these vortices remain static, and the material's resistivity disappears. While the resistance resulting from this effect is negligible compared to that of non-superconducting substances, it necessitates consideration in precise experimental contexts. Furthermore, upon a substantial reduction in temperature below the nominal superconducting transition, these vortices can solidify into a disordered yet immobile state termed a "vortex glass". Below the critical temperature for this vortex glass transition, the material's electrical resistance genuinely reaches zero.

Phase Transition

Superconductivity manifests in materials when their temperature T is reduced below a specific critical temperature, denoted as T_c. This critical temperature is material-dependent. Typically, conventional superconductors exhibit critical temperatures ranging from below 1 K to approximately 20 K. For instance, solid mercury possesses a critical temperature of 4.2 K. As of 2015, the highest critical temperature recorded for a conventional superconductor was 203 K for H§67§S, albeit requiring extreme pressures of approximately 90 gigapascals. Cuprate superconductors, however, can achieve significantly higher critical temperatures; YBa§89§Cu§1011§O§1213§, an early discovered cuprate, has a critical temperature exceeding 90 K, and mercury-based cuprates have been observed with critical temperatures surpassing 130 K. The fundamental physical mechanism underlying these elevated critical temperatures is not yet fully elucidated. Nevertheless, it is established that a two-electron pairing phenomenon is involved, although the precise nature of this pairing (${\displaystyle s}$-wave versus ${\displaystyle d}$-wave) remains a subject of ongoing debate.

Analogously, at a constant temperature below the critical temperature, superconducting materials lose their superconducting properties when subjected to an external magnetic field exceeding the critical magnetic field. This behavior is attributed to the quadratic increase in the Gibbs free energy of the superconducting phase with the magnetic field, whereas the free energy of the normal phase remains largely unaffected by it. If a material exhibits superconductivity in the absence of a magnetic field, its superconducting phase free energy is lower than that of the normal phase. Consequently, at a specific finite magnetic field strength (proportional to the square root of the free energy difference at zero magnetic field), the two free energies equalize, precipitating a phase transition to the normal state. More broadly, elevated temperatures and stronger magnetic fields result in a reduced proportion of superconducting electrons, thereby increasing the London penetration depth for external magnetic fields and currents. At the point of phase transition, this penetration depth becomes infinite.

The initiation of superconductivity is characterized by abrupt alterations in several physical properties, a definitive indicator of a phase transition. For instance, in the normal (non-superconducting) state, the electronic heat capacity exhibits a direct proportionality to temperature. However, at the superconducting transition, it undergoes a discontinuous increase and subsequently deviates from linear behavior. At cryogenic temperatures, the heat capacity instead follows an exponential relationship, expressed as e^−α/T, where α is a constant. This exponential dependence provides compelling evidence for the presence of an energy gap.

The order of the superconducting phase transition remained a subject of considerable discussion for an extended period. Empirical evidence suggests a second-order transition, characterized by the absence of latent heat. Conversely, an external magnetic field introduces latent heat, attributable to the superconducting phase exhibiting lower entropy than the normal phase below the critical temperature. Consequently, experimental observations have confirmed that increasing the magnetic field beyond its critical threshold during this phase transition results in a reduction of the superconducting material's temperature.

Theoretical computations conducted in the 1970s proposed that the transition might, in fact, be weakly first-order, influenced by long-range electromagnetic field fluctuations. By the 1980s, theoretical frameworks, specifically a disorder field theory emphasizing the critical role of superconductor vortex lines, demonstrated that the transition is second-order in the Type II regime and first-order (involving latent heat) in the Type I regime, with these two regions delineated by a tricritical point. These findings received substantial corroboration from Monte Carlo computer simulations.

Meissner Effect

Upon introducing a superconductor into a weak external magnetic field, denoted as B_a=H_a, and subsequently cooling it below its critical transition temperature, the magnetic field is expelled. However, the Meissner effect does not entail a complete expulsion; rather, the magnetic field permeates the superconductor only to a minimal extent, quantified by the parameter λ, known as the London penetration depth, which describes its exponential decay to zero within the material's interior. This phenomenon constitutes a fundamental characteristic of superconductivity. Typically, for the majority of superconductors, the London penetration depth approximates 100 nanometers.

The Meissner effect is occasionally conflated with the diamagnetic response anticipated in an ideal electrical conductor. As per Lenz's law, the application of a changing magnetic field to a conductor induces an electric current within it, generating an opposing magnetic field. Within a perfect conductor, an arbitrarily substantial current can be induced, leading to a resultant magnetic field that precisely nullifies the external applied field.

The Meissner effect fundamentally differs from this phenomenon, representing the spontaneous expulsion of magnetic flux that accompanies the transition to the superconducting state. Consider a material initially in its normal state, permeated by a constant internal magnetic field. Upon cooling this material below its critical temperature, an abrupt expulsion of the internal magnetic field would be observed, an outcome not predicted by Lenz's law.

A phenomenological explanation for the Meissner effect was advanced by the brothers Fritz and Heinz London, who demonstrated that the electromagnetic free energy within a superconductor is minimized under the condition: $${\displaystyle \nabla ^{2}\mathbf {B} =\lambda ^{-2}\mathbf {B} \,}$$, where B represents the magnetic field and λ denotes the London penetration depth.

This formulation, recognized as the London equation, posits that the magnetic field within a superconductor undergoes an exponential decay from its surface value.

A superconductor exhibiting minimal or no internal magnetic field is characterized as being in the Meissner state. This state ceases to exist when the applied magnetic field exceeds a specific threshold. Superconductors are categorized into two distinct classes based on the mechanism of this transition. For Type I superconductors, the superconducting property is abruptly abolished when the applied field's intensity surpasses a critical value, denoted as H_c. Depending on the sample's configuration, an intermediate state may emerge, characterized by an intricate arrangement of normal material regions permeated by a magnetic field interspersed with superconducting regions devoid of a field. Conversely, in Type II superconductors, increasing the applied field beyond a critical value, H_c1, results in a mixed state, also termed the vortex state. In this state, a progressively larger magnetic flux permeates the material, yet electrical current flow remains dissipationless, provided the current magnitude is not excessive. Superconductivity is ultimately extinguished at a second critical field strength, H_c2. The mixed state originates from vortices within the electronic superfluid, often referred to as fluxons due to the quantized nature of the flux they carry. Predominantly, pure elemental superconductors, with the exceptions of niobium and carbon nanotubes, are classified as Type I, whereas nearly all impure and compound superconductors fall under Type II.

London Moment

Conversely, a rotating superconductor produces a magnetic field that is precisely collinear with its axis of rotation. This phenomenon, known as the London moment, was effectively utilized in the Gravity Probe B mission. The experiment involved measuring the magnetic fields generated by four superconducting gyroscopes to ascertain their respective spin axes. This methodology was crucial for the experiment, as it represents one of the limited techniques available for precisely identifying the spin axis of an otherwise undifferentiated spherical object.

High-Temperature Superconductivity

Applications

Superconductors represent highly promising materials for the development of foundational circuit components across electronic, spintronic, and quantum technological domains. A notable illustration is the superconducting diode, which facilitates unidirectional supercurrent flow, thereby offering the potential for dissipationless superconducting and hybrid semiconducting-superconducting technologies.

Superconducting magnets constitute some of the most potent electromagnets currently recognized. Their applications span various fields, including MRI/NMR systems, mass spectrometers, beam-steering magnets in particle accelerators, and plasma confinement magnets within certain tokamaks. Furthermore, these magnets are employed in magnetic separation processes, enabling the extraction of weakly magnetic particles from a matrix of less magnetic or non-magnetic substances, as exemplified in the pigment manufacturing sector. Their utility also extends to large-scale wind turbines, where they mitigate limitations imposed by high electrical currents; a 3.6-megawatt industrial-grade superconducting windmill generator has been successfully trialed in Denmark.

During the mid-20th century (1950s and 1960s), superconductors were integral to the construction of experimental digital computers, employing cryotron switches. In contemporary applications, superconductors have been utilized in the fabrication of digital circuits based on rapid single flux quantum technology, as well as in RF and microwave filters for mobile telecommunication base stations.

Superconductors are fundamental to the construction of Josephson junctions, which serve as the constituent elements for Superconducting Quantum Interference Devices (SQUIDs)—recognized as the most sensitive magnetometers available. SQUIDs find application in scanning SQUID microscopes and magnetoencephalography. Furthermore, arrays of Josephson devices are employed to establish the SI unit of voltage. Superconducting photon detectors can be implemented in diverse device architectures. Specifically, a superconductor–insulator–superconductor Josephson junction can function either as a photon detector or as a mixer, contingent upon its operational mode. The substantial alteration in resistance observed during the transition from the normal to the superconducting state is exploited in the fabrication of thermometers for cryogenic micro-calorimeter photon detectors. This identical principle is also applied in the development of ultrasensitive bolometers constructed from superconducting materials. Superconducting nanowire single-photon detectors provide high-speed, low-noise single-photon detection capabilities and have been extensively adopted in sophisticated photon-counting applications.

Emerging markets are increasingly adopting high-temperature superconductivity devices, particularly where their superior efficiency, compact size, and reduced weight justify the associated higher initial expenditures. For instance, in wind turbine applications, the decreased mass and volume of superconducting generators can yield substantial reductions in construction and tower expenses, thereby mitigating the increased generator costs and ultimately diminishing the overall levelized cost of electricity (LCOE).

Future applications demonstrating significant promise encompass high-performance smart grids, advanced electric power transmission systems, transformers, energy storage units, compact fusion power reactors, electric motors (such as those for vehicle propulsion in vactrains or maglev trains), magnetic levitation systems, fault current limiters, the integration of superconducting materials to enhance spintronic devices, and superconducting magnetic refrigeration. A notable challenge, however, is superconductivity's susceptibility to dynamic magnetic fields, which complicates the development of alternating current (AC) applications like transformers, making direct current (DC) applications comparatively more straightforward. Superconducting transmission lines offer substantial advantages over conventional power lines, exhibiting greater efficiency and requiring considerably less physical space. This not only contributes to improved environmental sustainability but also has the potential to foster greater public acceptance for electric grid expansion. Furthermore, the capacity for high-power transmission at reduced voltages presents an appealing industrial benefit. Recent progress in cooling system efficiency and the utilization of economical refrigerants, such as liquid nitrogen, have also substantially lowered the operational costs associated with maintaining superconductivity.

Nobel Prizes

As of 2022, five Nobel Prizes in Physics have been awarded for research pertaining to superconductivity:

• Heike Kamerlingh Onnes (1913), recognized "for his investigations on the properties of matter at low temperatures which led, inter alia, to the production of liquid helium".
• John Bardeen, Leon N. Cooper, and J. Robert Schrieffer (1972), honored "for their jointly developed theory of superconductivity, usually called the BCS-theory".
• Leo Esaki, Ivar Giaever, and Brian D. Josephson (1973), awarded "for their experimental discoveries regarding tunneling phenomena in semiconductors and superconductors, respectively" and "for his theoretical predictions of the properties of a supercurrent through a tunnel barrier, in particular those phenomena which are generally known as the Josephson effects".
• Georg Bednorz and K. Alex Müller (1987), recognized "for their important break-through in the discovery of superconductivity in ceramic materials".
• Alexei A. Abrikosov, Vitaly L. Ginzburg, and Anthony J. Leggett (2003), honored "for pioneering contributions to the theory of superconductors and superfluids".

• BCS theory – Microscopic theory of superconductivity
• Hydrogen cryomagnetics – Use of cryogenic liquid hydrogen to cool an electromagnet
• MXenes – Class of two-dimensional inorganic compounds
• Superconducting magnetic energy storage – Energy storage technique

References

• IEC standard 60050-815:2000, International Electrotechnical Vocabulary (IEV) – Part 815: Superconductivity Archived 2020-03-07 at the Wayback Machine.
• Kleinert, Hagen (1989). "Superflow and Vortex Lines". Gauge Fields in Condensed Matter. Vol. 1. World Scientific. ISBN 978-9971-5-0210-2.Larkin, Anatoly; Varlamov, Andrei (2005). Theory of Fluctuations in Superconductors. Oxford University Press. ISBN 978-0-19-852815-9.Lebed, A. G. (2008). The Physics of Organic Superconductors and Conductors. Vol. 110 (1st ed.). Springer. ISBN 978-3-540-76667-4.Matricon, Jean; Waysand, Georges; Glashausser, Charles (2003). The Cold Wars: A History of Superconductivity. Rutgers University Press. ISBN 978-0-8135-3295-0."Physicist Discovers Exotic Superconductivity". ScienceDaily. 17 August 2006.Tinkham, Michael (2004). Introduction to Superconductivity (2nd ed.). Dover Books. ISBN 978-0-486-43503-9.Tipler, Paul; Llewellyn, Ralph (2002). Modern Physics (4th ed.). W. H. Freeman. ISBN 978-0-7167-4345-3.O'Mahony, Shane M.; University of Oxford (2022). "On the Electron Pairing Mechanism of Copper-Oxide High-Temperature Superconductivity." Proceedings of the National Academy of Sciences, 119 (37): e2207449119. arXiv:2108.03655. Bibcode:2022PNAS..11907449O. doi:10.1073/pnas.2207449119. PMC 9477408. PMID 36067325.

• Video about Type I Superconductors: R=0/transition temperatures/ B is a state variable/ Meissner effect/ Energy gap(Giaever)/ BCS model
• YouTube Video Levitating magnet
• The Schrödinger Equation in a Classical Context: A Seminar on Superconductivity – The Feynman Lectures on Physics.