Superconductors

• Type of physical science: Condensed matter physics
• Field of study: Solids

Superconductors have zero resistance to the flow of electrical current at temperatures below a critical point. Once a current is established in these large-scale quantum systems, it persists indefinitely.

Overview

In 1908, the Dutch physicist Heike Kamerlingh Onnes (1853–1926) liquefied the rare gas helium at 4 kelvins above absolute zero, or equivalent to –269 degrees Celsius. In 1913, he received the Nobel Prize in Physics for his pioneering work in low temperatures; earlier, Kamerlingh Onnes had discovered a remarkable occurrence that opened a new field of science. Shortly after his discovery of liquid helium, Kamerlingh Onnes used this cryogenic liquid to carry out low-temperature studies of the electrical resistance of metals. He was working with mercury, and, as is common to metals, the resistance of mercury decreased slowly as the temperature dropped. Below the temperature of 4.2 kelvins, the resistance plummeted, and Kamerlingh Onnes was unable to detect any resistance. Mercury turned into a superconductor of electricity below the critical temperature of 4.2 kelvins.

Many experiments by Kamerlingh Onnes and others convinced the scientific community that superconductors have not merely a low resistance but zero resistance to the flow of a steady electrical current. Once a current begins circulation within a superconductor, the current persists. This notable ability of superconductors does not fit the classical scientific model of electrons moving through a dense forest of atoms in a metal; it was not fully explained until 1957, when John Bardeen, Leon N. Cooper, and John Robert Schrieffer used quantum theory to describe the process. Bardeen, Cooper, and Schrieffer shared the 1972 Nobel Prize in Physics for their work on the so-called BCS theory.

In the years immediately following Kamerlingh Onnes’s discovery of superconductivity, the unbearably low critical temperatures rose in fits and starts. Within two years, the poor metallic conductor lead demonstrated a critical temperature of 7 kelvins; it was not until the mid-1930s that superconductivity appeared in niobium, another metal, at 9 kelvins. Within another few years, certain niobium-based compounds passed the 10-kelvin barrier. In the early 1950s, the commercially important intermetallic superconductor Nb₃Sn displayed a critical temperature of 18 kelvins. In 1973, scientists passed the 20-kelvin barrier. The superconductor was a combination of niobium and the semiconductor germanium, Nb₃Ge, which has a critical temperature of 23 kelvins for transition into the superconducting state.

In 1986, Karl Alexander Müller and J. Georg Bednorz discovered the class of high-temperature superconductors based on the copper oxides. Their initial breakthrough material was lanthanum-barium-copper oxide.

The initial La-Ba-Cu-O material had a transition temperature of about 30–35 kelvins, higher than the previous record of about 23 K for Nb₃Ge. As a result of their work, Muller and Bednorz shared the 1987 Nobel Prize in Physics. Within two years, the critical temperature tripled to more than 120 kelvins. In 1987, C. W. Chu, M. K. Wu, and their coworkers discovered superconductivity at 92 kelvins in yttrium-barium-copper oxide, YBa₂Cu₃O₇, often called YBCO or 1-2-3. This astounding increase in the critical temperature triggered the rapid discovery of other variants of the copper oxide superconductors. These copper oxides show conduction mainly in parallel layers formed by the copper and oxygen atoms. The new discoveries raised the critical temperature to 110 kelvins in a copper oxide of bismuth with strontium and calcium and 122 kelvins in TBCCO, a copper oxide of thallium with barium and calcium. For the first time, high-temperature superconductors, or HTSCs, existed that possessed critical temperatures above that of liquid nitrogen, a common, inexpensive commercial refrigerant obtained by cooling the nitrogen of the air.

The experimental progress in the discovery of higher-temperature superconductors emphasizes two facts about superconductors: The superconductors must be conductors; paradoxically, they should be poor conductors, and the poorer, the better. The search for high critical superconducting temperatures moved scientists inexorably away from good conductors and toward materials that are closer and closer to the edge of electrical conduction.

The three best conductors among the common metals are silver, copper, and gold, but superconductivity exists only below 0.3 kelvin in these metals and may even be absent. The base material for Muller and Bednorz’s copper oxide superconductor is La₂CuO₄, which is an insulator. In other words, it does not conduct electricity. Strontium must be added to the composition in place of lanthanum to provide conduction in a manner similar to dopants that provide conduction in semiconductor devices. YBCO is more akin to a normal conductor, like LSCO and the other copper oxide superconductors; however, it is only a two-dimensional, layered conductor. To understand why such unusual and poor conductors make good superconductors, it is necessary to study the mechanism that produces superconductivity.

Electrons are the basic carriers of electrical charge and provide electrical current in most common materials. Quantum mechanics, which was pioneered by Max Planck (1858-1947), explained much about the nature of electrons. First, electrons have an intrinsic quantum property called spin. The spin may be up or down, but the spin is 1/2, and the spin projection is ±ħ/2, where ħ = h/2π (with h being the Planck’s constant). Second, electrons and all particles with half-spin are exclusive. Called fermions for the Italian-born American physicist Enrico Fermi (1901–54), these particles occupy only one energy state at a time. The state describes the motion of a particular spinning electron in space. A maximum of two electrons, one with spin up and the other with spin down, can occupy a given state but not the same full quantum state. Two more electrons at the same velocity must move in a different direction. If more electrons are added, they must enter different energy states and directions, filling the energy states like water filling a jug.

Normal metals have twice as many electrons and act as half-filled jugs. If the jug is tipped, the water runs up the sides. If voltage is applied to a metal, the electrons run through the metal, producing the current. In contrast, insulators and semiconductors act like completely filled jugs. If the filled jug is tipped, the water has no place to move. Similarly, a voltage produces no appreciable current in an insulator or semiconductor. The strontium in the LSCO superconductor acts to absorb some of the electrons from the filled La₂CuO₄, leaving a hole in the electron sea, like a bubble in the filled jug. If the jug is turned over, the bubble moves up, opposite gravity. In fact, water is flowing down around the bubble. A voltage applied to LSCO causes the holes to move opposite to the electrons, producing a current as if the carriers were positive. This whole motion dominates the behavior of all the copper-oxide, high-temperature superconductors.

Quantum mechanics helps explain one more aspect of superconductors. Integral spin particles, such as light photons with spin 1, are not subject to the Pauli exclusion principle. Called bosons after the Indian scientist Satyendra Nath Bose (1894–1974), these particles may share one energy state. For example, a typical helium-neon laser has more than a hundred billion photons in one energy state, which shapes its narrow red beam. If electrons pair so that each pair behaves as a composite boson, many such pairs can occupy the same quantum state and move coherently through the material. When cooled below its critical temperature, a material can exhibit superconductivity; a persistent current can continue in a closed superconducting loop without an applied voltage.

Such paired electrons, or paired holes, do form below the critical temperature of a superconductor and are called Cooper pairs. A related pairing turns very cold liquid helium into a superfluid. In conventional superconductors, electron-phonon interactions are also present above the critical temperature and contribute to electrical resistance in the normal state. Thus, normal-state poor conductivity does not, by itself, imply stronger Cooper pairing or better superconductivity. In a conductor, any electron feels the repulsions of all the other electrons and the attractions of the bound positive ions that compose the fixed lattice of the conductor. The other electrons and ions are on all sides of the electron, and the net forces cancel. As a result, the electrons or holes in a conductor are, on average, free. There are two ways in which carriers of the same charge may attract each other when one looks beyond the average.

The first method considers the situation in which the carriers are electrons; this method equally applies to the analogous situation in which the carriers are holes. As an electron moves through the latticework, it attracts the opposite fixed charges, deforming the lattice slightly in the carrier’s wake. Another electron, which has opposite spin and, normally, is moving in a direction opposite to the first electron, will be attracted to the lattice deformation. Quantum physics allows electrons of opposite spin to pass easily through each other. Thus, both carriers will be attracted to the same region of the latticework and, effectively, to each other. The deformation of the lattice sets up sound waves, or phonons, in the conductor; thus, the pair attraction is the result of phonon interaction. Below the critical temperature, the phonon interaction binds Cooper pairs and yields superconductivity. The BCS theory fills in the details and describes traditional low-temperature superconductors in which phonon pairing predominates.

A second method that may yield pair binding takes place when an electron repels the bound negative electron cloud surrounding the positive ion lattice. The effect is to leave a positive wake that attracts the second electron in the Cooper pair. This binding has several variations under the heading of excitonic interaction. Conventional phonon binding is not strong enough to explain the high critical temperatures of the copper oxide superconductors. Whether excitonic binding can explain the superconductivity in these high-temperature superconductors is not clear. Superconductors are one of the few examples in nature where quantum effects dominate large-scale wonders.

Quantum mechanics produces further unusual effects in superconductors. A supercurrent carried by Cooper pairs can flow between two superconductors separated by a thin insulating barrier even with no applied voltage; an applied voltage produces the AC Josephson effect. Quantum theory states that particles can tunnel through thin barriers.

When a voltage V appears between two superconductors, Cooper pairs tunnel between the superconductors at the frequency f given by hf = (2e) V, where h is Planck’s constant, and e is the electron’s charge. The separation region between the two superconductors forms a Josephson junction; tunneling is known as the Josephson effect, which has been verified experimentally to an extraordinary degree. The presence of 2e rather than e in the detected frequency proves the existence of the Cooper pairs.

A superconductor expels any magnetic field present when it makes the transition from the normal conducting state to the superconducting state. Known as the Meissner effect, this process renders superconductors diamagnetic. Since any current present in the superconducting state generates a magnetic field, this field is also expelled from the superconductor’s interior and penetrates only through a thin layer of the superconductor. The thickness of this layer is known as the London penetration depth. In the Meissner state, screening current is concentrated mainly within about a London penetration depth of the surface, rather than uniformly throughout the bulk.

Many applications require only a thin thread or layer of superconductor to carry current. The layer may be deposited on another material for strength, while the thread, or threads, may be buried within a support material.

Superconductors vary in the manner in which they expel magnetic fields. Type I superconductors expel magnetic fields completely from their interior, whereas type II superconductors expel magnetic fields by segregating the fields into thin filaments that form a vortex pattern within the body of the superconductor. Type II superconductors are the more useful superconductors since they can withstand higher magnetic fields by increasing the number of vortex filaments, thereby multiplying their internal surface area as the magnetic field rises. High-temperature superconductors are of type II. Quantum physics dictates that magnetic flux is equal to the magnetic field times the area trapped in the vortices. The magnetic flux carried by superconducting vortices is quantized in unitsof h/2e.

Applications

The most important large-scale application for conventional low-temperature superconductors is the production of large magnetic fields. Superconducting magnets are used in laboratories that study high-energy physics or seek to imprison the sun’s energy in plasma fusion, in hospitals that use magnetic resonance imaging (MRI) for diagnosing patients, and in the removal of magnetic materials from garbage and waste.

Large currents that course through low-temperature, superconducting windings generate the large magnetic fields in these applications. Liquid helium is the conventional coolant for the low-temperature, type II superconductors. An important characteristic of any superconductor used to generate large magnetic fields is the maximum magnetic field that the superconductor can withstand at the coolant temperature before losing its superconductivity.

Common low-temperature superconductors are Ni-Ti, which can withstand modest magnetic fields of 7 to 10 teslas; Nb₃Sn, which can withstand fields 14 to 16 teslas; and V₃Ga, a high-field low-temperature superconductor that is no longer commonly used.

For strength, handling, and safety, the superconductors used for magnetic field generation are embedded within a metal matrix. For example, Nb₃Sn filaments are often encased in a bronze conductor and Nb-Ti filaments in copper. If cooling fails during operation, the metal stabilizer must assume the current carried by the superconductor. This helps prevent overheating and damage to the coils when the superconductor switches to its normal, resistive state.

The maximum magnetic field that a superconductor can withstand increases with the critical temperature of the superconductor. Thus, the maximum magnetic fields of the high-temperature superconductors are immense, up to 100 tesla at low temperatures. These maximum fields depend on the orientation of the copper oxide planes and on the actual current that the superconductor carries. High currents, as well as magnetic fields, act to suppress superconductivity.

In magnetic applications, bulk high-temperature superconductors must achieve sufficiently high current density under operating temperature and magnetic-field conditions to compete with copper, and the exact requirement depends on the application and conductor design. Good-quality, crystalline thin films of the new superconductors easily exceed this specification. Yet, bulk samples of these ceramic superconductors have minute crystal grains separated by disorganized boundaries. These grain boundaries lower the ability of the bulk superconductors to carry current. In addition, movement of the magnetic vortices trapped in these type II superconductors produces heating. The success of the low-temperature superconductor Nb-Ti depends on normally conducting titanium precipitates that pin the vortices in the superconducting composite. The new high-temperature materials require similar inventive techniques, which will come to eliminate grain boundary effects, pin magnetic vortices, and produce bulk samples that are easy to fabricate into useful and inexpensive superconducting coils.

A second application of low-temperature superconductors is to measure extremely small magnetic fields using SQUIDs, or superconducting quantum interference devices. The device consists of two Josephson junctions placed within a superconducting wire loop. As with magnetic vortices, the magnetic flux within the superconducting loop is quantized in multiples of h/2e. The current within the SQUID, along with the loop area, gives a precise measurement of the magnetic field. SQUIDs can measure extremely small magnetic fields (down to femtotesla levels) and very small voltage differences. This precision enables scientists to map the magnetic field generated by brain activity. The development of high-temperature superconductor SQUIDs would replace cooling with bulky liquid helium with more compact and portable liquid nitrogen or electrical cooling systems and would provide more widespread use of these precise quantum measurement devices. Research focuses on superconductors that operate at normal pressure, improving practical deployment, although low-temperature cooling is still required.

There are many possible uses for high-temperature superconductors when they are cooled to liquid nitrogen temperatures. Some materials have shown superconductivity near room temperature, but only under extremely high pressures (hundreds of gigapascals), making them impractical for current applications. In addition to magnetic field coils and SQUIDs, these uses include magnetic levitation of trains, magnetic energy storage, electrical transmission lines and their surge protectors, hybrid semiconductor-superconductor computers and computer interconnects, and low-loss, microwave circuits and lines. These possible uses depend strongly on the success of material scientists in fabricating, shaping, and processing the conductors that have resulted in the creation of a new area of science. Research has demonstrated superconductivity at about 151 kelvins under normal pressure, marking progress toward more practical superconducting materials, although cooling is still required. Research increasingly uses artificial intelligence and computational models to predict and design new superconducting materials more efficiently.

Context

In 1913, Kamerlingh Onnes described his 1911 experiments on mercury. “Mercury has passed into a new state which. . .may be called the superconductive state. . . The behavior of metals in this state gives rise to new fundamental questions.” The answers to these questions required quantum theory, initiated by Max Planck in 1900 and culminating with the BCS theory four decades later. The classical mechanics of Sir Isaac Newton and the electromagnetism of James Clerk Maxwell cannot describe the large-scale events involved with superconductivity. In a superconductor, no steady electric field exists; currents persist without resistance once established. Only quantum theory explains this seemingly unbelievable behavior.

The carriers of superconductors are Cooper pairs, bound together at temperatures below the critical temperature. In the superconducting state, all the bound pairs condense into the lowest energy state available, mimicking bosons, and cannot give up energy. Resistance heats a conductor when current flows, and the heat comes from energy lost by the carriers. Since the superconducting Cooper pairs have no energy to give, no heating is possible, and there is no resistance. Above the critical temperature, thermal energy breaks apart the Cooper pairs, spreads the electrons in energy, and generates the resistance of the normal conductor. Quantum mechanics explains how persistent currents in the superconducting state stay together while streaming through the atom maze.

Particles such as the Cooper pairs also behave like waves. Cooper pairs behave collectively like bosons, similar to how photons are bosons. A light beam moves through flat glass without spreading. The beam does experience the dense atoms in its path, but the wave phenomenon of constructive interference continually reforms the beam in the direction of motion, and only in that direction. The atoms slow the light beam and bend its path at the surface of the glass, but the light travels straight once it is inside the glass. When the beam exits the glass, it bends parallel to its original direction and resumes its original speed. If trapped inside a glass fiber in a phone network, the light travels at a reduced speed determined by the material’s refractive index. Like the light beam, persistent supercurrents are quantum beams of supercarriers that are guided within the superconductor, forever moving and never able to lose energy or rest.

Principal terms

CONDUCTIVITY: the measure of a material’s ability to carry electrical current

ELECTRICAL CONDUCTOR: a substance that permits the easy flow of electrical current

ELECTRICAL CURRENT: the flow of electrical charges through space or through a material

KELVIN TEMPERATURE SCALE: no temperature can be below 0 kelvin, classical thermal motion ceases; but quantum motion remains, water freezes at 273.15 kelvins, and boils at 373.15 kelvins

QUANTUM: one of the indivisible units into which energy and other physical quantities can be subdivided

RESISTANCE: a measure of the obstruction of flow of the electrical current in a material

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