Whenever we take the electrical properties of material into account, we classify it into three main categories: a conductor, a semiconductor, or an insulator. In general, the crucial difference between these three classifications is their degree of resistivity. Insulators, being highly resistive, do not allow electricity to pass through them, whereas semiconductors and conductors, having moderate and low resistivity, respectively, allow the current to pass through them. Nonetheless, the resistivity of a material is dependent on the temperature. In theory, the materials that behave like insulators at room temperature can conduct electricity when cooled down to a certain temperature. This idea later led to the discovery of a new class of materials called superconductors that offer zero resistance to the flow of current below a certain operating temperature. Superconductivity was first discovered by Dutch physicist Heike Kamerlingh Onnes on April 8, 1911, in Leiden. By using liquid helium as a refrigerant, Onnes observed that the resistivity of mercury disappeared abruptly at a temperature of 4.19 K. Onnes stated that the specific resistance became thousands of times less in amount relative to the best conductor at ordinary temperature. Onnes later reversed the process and found that at 4.2 K, the resistance returned to the material. Soon after this discovery, many other elemental metals were found to exhibit zero resistance below a specific characteristic temperature of the material, called the critical temperature, Tc; however, the phenomenon was purely observational and had no explanation at that time.
In 1933, while looking for an explanation for superconductivity, Walter Meissner and Robert Ochsenfeld discovered that superconductors also exhibit a magnetic phenomenon, which is now known as the Meissner effect. The discovery of the Meissner effect was also an experimental observation and lacked a theoretical explanation. In 1957, John Bardeen, Leon Cooper, and John Schrieffer proposed an adequate theoretical explanation for both the electrical and magnetic behavior of superconductors called the BCS theory. They received the Nobel Prize in Physics in 1972 for this theory. Let’s try to understand these phenomena in more detail.
Meissner Effect
The Meissner effect is another fundamental characteristic that distinguishes the superconductor from an ideal conductor. When a normal conductor is placed in a magnetic field, it produces current via electromagnetic induction, but a material under the transition from the normal to the superconducting state actively excludes magnetic fields from its interior; this is called the Meissner effect. In 1933, German physicists “Walther Meissner” and “Robert Ochsenfeld” discovered this phenomenon. During their experiment with superconducting Tin and Lead samples, they found that the value of the magnetic field outside the sample increases when the sample is cooled below the transition (critical) temperature in the presence of an external magnetic field. This increase in the magnetic field outside the sample reflects the magnetic field being ejected from the sample’s interior. This state of the superconductor is known as the Meissner state, and it breaks when the value of the magnetic field exceeds a certain point called Critical Magnetic Field.
This constraint to zero magnetic fields inside a superconductor is distinct from the perfect diamagnetism, which would arise from its zero electrical resistance. Zero resistance would imply that if you tried to magnetize a superconductor, current loops would be generated to exactly cancel the imposed field (Lenz’s law). One of the theoretical explanations of the Meissner effect comes from the London equation. It shows that the magnetic field decays exponentially inside the superconductor over a distance of 20-40 nm. It is described in terms of a parameter called the London penetration depth. The discovery of the Meissner effect has laid the foundation of MagLev (short for Magnetic Levitation), a transportation system that makes use of superconductivity for high speed.
Type-I Superconductors
The superconductors classified into this category are also known as “soft” superconductors. The identical characteristic for the classification of superconductors is how their Meissner states break down above the critical magnetic field. Type-I materials remain in the superconducting state only for relatively weak applied magnetic fields. Above a given threshold, the field abruptly penetrates the material, shattering the superconducting state. There are around 30 elements in the periodic table that fall under the category of type-I superconductors. They exhibit a very sharp transition to a superconducting state and “perfect” diamagnetism – the ability to repel a magnetic field completely. The common examples of type-I superconductors are pure metals, such as aluminum, lead, mercury, and some covalent aggregates such as heavily doped silicon carbide with boron, SiC:B.
Magnetic phase diagram for type-I and type-II superconductor
Type-II Superconductors
This category of superconductors is commonly referred to as “hard” superconductors or “high-temperature superconductors.” It mainly consists of compounds, including ceramics and alloys. They generally have higher critical temperatures than superconductors of the Type I variety, as high as 130 K ( ≈ -143 degrees C). Unlike Type I superconductors, Type II is penetrable by magnetic fields, and therefore, they are known to partially exhibit the Meissner effect. Although they not perfectly diamagnetic, Type II superconductors exist in a mixed state of normal regions surrounded by areas of superconducting current called the vortex state, which makes them more versatile. Type II can withstand much stronger magnetic fields and still retain its superconductive properties in comparison to Type I. Since current moving through a superconductor creates a magnetic field, Type II superconductors can carry larger amounts of current than those of Type I without losing their superconductivity. This behavior has made it possible to use superconductivity in high magnetic fields, leading to the development of magnets for particle accelerators. Along with certain metal alloys (e.g. niobium-titanium and niobium-tin), niobium, vanadium, and technetium are few examples of type-II superconductors.
BCS Theory
A commemorative plaque placed in the Bardeen Engineering Quad at the University of Illinois at Urbana-Champaign. It commemorates the Theory of Superconductivity developed here by John Bardeen and his students, for which they won a Nobel Prize for Physics in 1972.
A successful theory of superconductivity was developed in the 1950s by John Bardeen, Leon Cooper, and J. Robert Schrieffer, for which they received the Nobel Prize in 1972. This theory is known as the BCS theory, which is short of “Bardeen Cooper Schrieffer theory.” The resistance of a conductor is due to collisions between free electrons and phonons (the quantum mechanical description of an elementary vibrational motion in which a lattice of atoms or molecules uniformly oscillates at a single frequency). The BCS Theory is based on a very counterintuitive fact that an attractive interaction exists between two electrons (facilitated by phonons) at extremely low temperatures. In typical Type I superconductors, this interaction occurs due to Coulomb attraction between the electron and the crystal lattice. An electron moving randomly through the lattice will cause a slight increase in positive charges around it by pulling the positive ions. This increase in positive charge will, in turn, attract another electron. These two electrons are attracting each other via phonons, and they are known as a “Cooper pair.” If the energy required to bind these electrons together is less than the energy from the thermal vibrations of the lattice attempting to break them apart, the pair will remain bound. This explains why superconductivity requires low temperatures.
The thermal vibration of the lattice must be small enough to allow the formation of Cooper pairs. A current flowing in the superconductor just shifts the total moment slightly from zero so that, on average, one electron in a cooper pair has a slightly larger momentum magnitude than its pair. The interaction between a Cooper pair is transient. Each electron in the pair goes on to form a Cooper pair with other electrons, and this process continues with the newly formed Cooper pair so that each electron goes on to form a Cooper pair with other electrons. The result is that each electron in the solid is attracted to every other electron forming a large network of interactions. The collective behavior of all the electrons in the solid prevents any further collisions with the lattice, hence the zero resistivity. It is important to note that the description mentioned above is qualitative, whereas the formal treatment from the BCS theory is quantum mechanical. The electrons have wave-like behavior that is described by a wave function that extends throughout the solid and overlaps with other electron wave functions. As a result, the whole network of electrons behaves like one wave function whose collective motion is coherent. This BCS theory prediction of Cooper pair interaction with the crystal lattice has been verified experimentally by the isotope effect, i.e., the critical temperature of a material depends on the mass of the nucleus of the atoms. If an isotope is used (neutrons are added to make it more massive), the critical temperature decreases. This effect is most evident in Type I and appears only weakly in Type II.
Examples of Superconductors
1. Aluminum
It is a well-known fact that aluminum is a good conductor of electricity at room temperature, but do you know it can show superconductivity also? At 1.2 K, aluminum becomes a type-I superconductor whose resistivity abruptly drops to zero. Due to its ability to form a high-quality oxide, aluminum is one of the many potential superconducting materials that can be used to create Josephson Junctions for quantum computers. Josephson junctions form the heart of the superconducting qubit, a leading candidate for the creation of fault-tolerant quantum computation. The non-linear inductance of the Josephson Junction creates an anharmonicity in its energy level spectrum. This allows a quantum mechanical basis (1 or 0) to be established between discrete energy levels, which is essential for forming a quantum bit, or qubit.
2. Niobium-tin
Niobium–tin is an intermetallic compound of niobium (Nb) and tin (Sn) with the chemical formula {Nb}_{3}{Sn}. It is industrially used as a type II superconductor to create superconducting wires, solenoids, and electromagnets. Although Niobium-tin has a critical temperature of 18.3 K, it remains superconducting up to the magnetic flux density of 30 teslas. It is used in the form of cables to produce strong 11 T main dipole magnets and the inner triplet quadrupole magnets that are located at the ATLAS and CMS interaction points of the Large Hadron Collider at Cern. Another potential application of {Nb}_{3}{Sn} is to form solenoids and toroidal field superconducting magnets for ITER (International Thermonuclear Experimental Reactor) fusion reactors.
Many of the major components of one of the 15 m long superconducting dipole magnets for the LHC at CERN.
3. Niobium–titanium
Niobium-titanium is another type II superconductor that is used industrially to manufacture superconducting wires and magnets. The superior high-critical-magnetic-field and high-critical-supercurrent-density properties of Nb-Ti, together with affordability and easy workability, distinguish Nb-Ti alloys from thousands of other superconductors and justify their status as the most widely utilized (workhorse) superconductors. With a maximal critical magnetic field of about 15 teslas, Nb-Ti alloys are suitable for fabricating super magnets generating magnetic fields up to about 10 teslas. Although Niobium-titanium superconductors are more expensive than other superconducting materials, they are widely used because they are easy to fabricate. Around 80% of the worldwide production of Nb-Ti superconductors accounts for the manufacturing of superconducting coils that generate high magnetic fields in MRI (Magnetic Resonance Imaging) scanners.
4. Rare-Earth Barium Copper Oxide (ReBCO)
Rare-Earth Barium Copper Oxide (ReBCO) is a family of chemical compounds known for exhibiting high-temperature superconductivity. Superconductors made of ReBCO also have the ability to withstand higher magnetic fields than other superconductors. Due to their stronger magnetic field and relatively high superconducting critical temperature, these materials have been proposed for future magnetic confinement fusion reactors such as the ARC reactor, allowing a more compact and economical construction. Although any rare-earth element can be used in a ReBCO, popular choices include yttrium (YBCO), lanthanum (LBCO), samarium, neodymium, and gadolinium.
5. BSCOO
Bismuth strontium calcium copper oxide (BSCCO) is a type of cuprate superconductor having the generalized chemical formula {Bi}_{2}{Sr}_{2}{Ca}_{n−1}{Cu}_{n}{O}_{2n+4+x}, with n = 2 being the most commonly studied compound. BSCOO is classified as a class of high-temperature superconductors that do not contain any rare earth elements. It was first discovered in 1988 by Hiroshi Maeda and his colleagues at the National Research Institute for Metals in Japan, though at the time they were unable to determine its precise composition and structure. The potential applications of BSCOO superconductors include superconducting chips for quantum sensors, quantum computers, and SQUIDs (superconducting quantum interference devices).