When metals and semiconductors conduct, the motion of the electrons has to overcome the vibrational motion of the atoms in the crystal lattice. This lattice vibration, or phonon, leads to scattering of the electrons, or electrical resistance. A superconductor is a substance which conducts electricity without resistance.

A superconductor exhibits zero electrical resistance because the electrons near the Fermi level interact attractively and form pairs which cannot be scattered by the the lattice vibration. These electron pairs are known as Cooper Pairs, and they carry the current.

The Cooper pair electrons are separated in energy from the normal, unpaired, electrons by an energy gap of the order of kTc in size, where k is Boltzmann’s constant and Tc is the superconducting transition temperature.

The electron pairs are produced by a mechanism described by BCS theory:

The lattice is distorted by the attraction of the nuclei towards the first electron.

The first electron moves away, leaving a potential well which persists because the lattice does not relax as the nuclear motion is much slower than the electronic motion.

The second electron is attracted into the potential well created by the first electron, so the two electrons are, in effect, attracted towards each other.

The superconducting transition temperature, Tc, is given by the equation:

λ = the electron-phonon coupling constantω = the frequency of the lattice vibration that couples the electrons

V = strength of electron-phonon interaction

N(Ef) = the number of states at the Fermi level

Many superconducting compounds have maximum Tc values of only 30 K. For the zero resistance to be useful in building conducting materials, higher Tc values are required. Some compounds possess this, and are known as high temperature superconductors.

High Temperature Superconductors

Several materials are now known which have Tc values above 77 K, which is the boiling point of liquid nitrogen, which is a relatively inexpensive refrigerant.

The most widely studied include mixed copper oxides, such as YBa2Cu3O7. This has a structure based on the perovskite structure, but with some of the oxygen ions missing. The perovskite structure is adopted by compounds with the formula ABO3, and here the yttrium and barium ions take up the A positions, and the Cu ions take up the B positions.

The structure of the mixed copper oxides

The dots represent Cu ions, and the oxide ions are not shown. They have a square-planar and square-based pyramidal arrangement around the Cu ions, with the square-based pyramids sited either side of, and pointing away from, the Y ions.

In the perovskite structure, the B ions are all octahedrally coordinated by oxide ions, but in this compound, the Cu ions are four- or five-coordinate. The four-coordinate, square-planar, Cu ions are those in the top and bottom planes in the diagram. The five-coordinate, square-based pyramidal Cu ions are those in the middle planes in the diagram, and the pyramids are directed away from the central Y ion.

The copper in this compound occurs with mixed valency: if the oxidation states are, Y (+3), Ba (+2), and O(-2), then the oxidation state of Cu is +2.33. This is equivalent to two Cu2+ ions and one Cu3+ for each formula unit.