# Superconductor

A superconductor is a substance which, below a certain temperature, will conduct electricity with zero resistance and repel magnetic fields. Original superconductors were metals needed very low temperatures to operate, but more recent superconductors have been ceramics needing relatively higher temperatures.

## Resistance and Lattice Structure

Theoretically electron flow in a metal or ceramic lattice (structure of a conductor made up of recurring base units) is unimpeded however in practice this is not the case. Resistance (opposition to the flow of electricity which converts it into heat) in conductors is caused by two main factors.

• Impurities in the lattice which disrupt the flow of electrons by causing collisions
• Vibrations of the lattice, atoms are slightly displaced from their original positions increasing the chance of a collision with an electron and hence reducing current

The former of these can only be fixed through industrial means. The latter of these is influenced by the temperature of the object, more heat means the lattice has more energy which means more vibrations. Hence by lowering the heat of the conductor resistance will be decreased. In many substance reducing the heat below a particular temperature (or critical temperature) will result in resistance being reduced to zero.

## Theories of Superconductivity

The main theory behind superconductivity was proposed by John Bardeen, Leon Cooper and John Schrieffer, and is commonly known as the BSC theory. The general principle is that electrons in the Band Theory are condensed into a quantum ground state.

In normal conductors electrons repel each other because of like charges, however in cases of superconductivity they travel in pairs known as "Cooper Pairs". When one electron moves through the lattice the positive charges of the ions in the lattice are attracted to it. This causes a distortion of the lattice, and because of the low temperature of the lattice the atoms do not immediately vibrate back to their original position. This causes an area of high density of positive ions, which in turn attracts a second electron. The two electrons effectively work as one unit to navigate through the lattice, reducing resistance to zero, because of the repulsion between the two any collision between the first electron and the lattice is repelled and hence all collisions are elastic (with no loss of kinetic energy). The Cooper pairs passing through any particular point are constantly changing, once the lead electron has moved onwards the second electron becomes the new lead electron and a third electron is attracted to it.

In order to overcome the electrostatic repulsion between electrons the BSC theory proposes the concept of phonons, inaudiable sound waves that mimick tiny vibrations in the lattice. These phonons correspond to the distortion of the lattice, and as such it is said the phonons maintain the Cooper Pairs. When the lead electron passes through the lattice it causes a distortion which in turn attracts a second electron, so in theory the lead electron has emitted a phonon which has been absorbed by the second electron.

The mathematics behind the BSC theory is modelled by the Ginzburg-Landau theory.

## Meissner Effect

When a superconductor is cooled below its critical temperature it will expel all magnetic fields passing through it. This does not occur uniformly for all superconductors, and the penetration depth (the point to which magnetic fields can pass into the material) varies depending on the substance. Once of the consequences of the meissner effect is magnetic levitation, in which a reasonably sized magnet placed over a superconductor will float because of the repulsive force on its field.

## Superconductor Materials

Superconductive materials are separated into two distinct categories.

Type I superconductors are those with pure metal lattices. They were the first discovered, and their critical temperature lies very close to absolute zero (–459.67 °F). Examples of Type I superconductors and their critical temperatures (in Kelvins) include aluminium (1.2K), lead (7K), mercury (4K), tin (4K), titanium (0.4K), tungsten (0.015K) and zinc (0.85K).

Type II semiconductors are those synthetically produced by scientists, and are typically metal based ceramics. Their critical temperatures range from -459.67 °F up to about -211.27 °F. These temperatures are more plausible than those exhibitted by Type I superconductors, and as such Type II superconductors have seen more extensive application.

## Application

### Transport

Superconductors are utilised in train systems to levitate the train above the tracks, reducing friction, allowing for speeds up to 300 mph. There are six train systems in the world which utilise maglev technology, with 2 under construction and six further proposals.

There are two main types of maglev transport.

Electromagnetic: utilises the meissner effect, electromagnets beneath the train extrapolate a field, nodes on the train are cooled to below the critical temperature. The field is expelled from the superconductive material, resulting in an upwards force on the train which causes it to levitate.

Electrodynamic: electromagnets are placed both on and below the train and are cooled to below their critical temperature, resulting in high currents and hence higher magnetic fields. These strong fields repel each other, causing the train to levitate.

### Medical

Electromagnets cooled to below their critical temperature can support high currents with no resistance. These currents in turn induce a larger magnetic field. As such superconductors are utilised in some areas of magnetic resonance imaging and magneto-encephalography to produce magnetic fields which can determine injury, disease and nerve signals.

### Scientific Research

The high magnetic fields afforded by superconductors are extensively harnessed in particle accelerators allowing for high speed acceleration of electrons and ions. The proton accelerator at Fermilab uses 774 superconducting magnets in a ring of circumference 6.2 km.

### Industrial Use

Once again the high magnetic fields of superconducting electromagnets are used in magnetic separation and accurate magnetic detection (the SQUID magnetometers quantitatively detect the magnetic properties of rocks by detecting the change in a field produced by an electromagnet. As the original field is so strong very precise measurements can be made). Superconductors are also used as shields from magnetic fields where desirable, and such an application is also used in the SQUID method (to avoid background magnetism).

### Electronics

Fast switching devices such as Josephson junctions use two superconductors separated by a thin insulating barrier to allow small, rapid changes in circuits (due to a very low current allowed by the zero resistance). These switches have seen constrained use in transistors.

Superconducting transformers allow close to zero power loss because of the lack of resistance offered to eddy currents which form in the iron core. This allows for significant increases in efficiency of electrical systems.

Some supercomputers have been built using superconductive circuits. The zero resistance to low currents theoretically can dramatically increase the speed of processing, although as of yet no superconducting computer has shown any significant advantage over conventional computers. The Jet Propulsion Laboratory is current researching with the aim of producing a computer with speeds of up to 250 times that of normal units.

### Potential Applications

Currently the main barrier to the potential of superconductors is due to the low temperatures at which they operate. However, as science develops materials with increasingly higher critical temperatures this obstacle will have less impact, and superconductions may have applications in several envisioned areas, including:

• Supercomputers (see electronics)
• Power transmission (currently between 10 and 15% of power is dissipated due to resistive loses, reducing this to zero would eliminate power loss and increase efficiency throughout the power grid)
• Superconducting magnetic storage (SMES - devices able to store DC electricity indefinitely, could see extensive use in solar cells).