Metal-insulator junction

A phase transition based on the quantum properties of matter is called a metal-insulator transition . In particular, there are changes in the transport properties of a material, e.g. B. the electrical conductivity or the reflectivity , between values ​​that are typical for metals or for insulators .

Electric conductivity

One of the most important properties of metals is their electrical conductivity. Metals have a very high electrical conductivity, while insulators, in contrast, conduct electrical charges very poorly. Certain materials can change from one state to the other under specific conditions, with changes in pressure, temperature, density or degree of disorder. In the latter case one speaks of a metal-insulator junction of the Anderson type (see localization (physics) ), in the first three cases, however, of a Mott junction .

In the physical model, a metal is a material whose Fermi energy lies within a band at a temperature of 0  K , i.e. at absolute zero . As a result, this conduction band is not fully occupied. This generally results in a very high conductivity. In the case of an insulator, however, the Fermi energy lies in a band gap , whereby the states in the valence band are completely occupied, which completely prevents electrical conduction. At finite temperatures this distinction is generally ambiguous. Metals then have a lower electrical conductivity than a free electron gas . Nor is there a perfect insulator that conducts absolutely no electricity. The main reason for this are thermally excited electrons, which due to their kinetic energy can also occupy states above the Fermi energy. In the case of semiconductors that have a very small band gap, a strong increase in electrical conductivity can be generated by occupying the conduction band with thermally excited electrons. The distinction between metal and insulator is therefore not always clear and the transition between the two states is often continuous.

Mott effect

The Mott effect describes the transition from an insulator to a metal due to an increase in pressure. The simplest insulator is a hydrogen crystal , the atoms of which are arranged in hexagonal close packing and the atomic orbitals do not overlap. This grid forms an insulator if the grid constant is large enough. If you press this grid together, i.e. if you reduce the grid constant, this material will transform into a metal. The critical value is a density or a value of the lattice constant that corresponds to the Mott criterion:

${\displaystyle (n^{1/3}a_{0})_{_{c}}{\stackrel {!}{=}}0{,}2\quad {\rm {{\mbox{(Mott-Kriterium)}}\,\,,}}}$

where is the Bohr radius and n is the particle density of the system. The mechanism of this transition is that the band gap is narrowed and the conduction and valence bands eventually overlap. The Fermi energy is then within a band and the system is a metal, even at low temperatures. The fundamental finding of this thought experiment is that if the pressure is high enough, every insulator turns into a metal. ${\displaystyle a_{0}}$

Electron localization

The opposite case, that a metal, i.e. a conductor, becomes an insulator at 0 K, represents a phenomenon that is much more difficult to explain theoretically. The breakdown of electrical conductivity is explained by the localization of the unlocated electronic states in the metal. The theoretical interpretation is essentially based on the fact that the charge carriers in the insulator state repel each other so strongly that they cannot propagate. This localization comes about through interaction effects.

Various models can be used for the explanation. In the model of the Anderson transitions ( Philip Warren Anderson ) a localization of the electronic states occurs due to statistical disorder in the system. In the Mott-Hubbard transition ( Nevill Francis Mott , John Hubbard (physicist) ), strong electron-electron correlations freeze the local fluctuations in the electron concentration. With the electron-lattice coupling there is a further possibility with which a severe restriction of the freedom of movement of the electrons can be described.

In this way, one can physically understand why certain metal oxides, sulfides, and selenides, such as NiO , etc., are insulators.

Examples

An example of a temperature-driven metal-insulator junction was measured in phosphorus- doped silicon . At temperatures below 0.1 K and donor - concentrations of 3.6 × 10 ¹⁸  cm ^-3 , the highly conductive material to the insulator.

Another example is carbon , in which the metal-insulator transition is caused by a change in the spatial structure. While graphite shows metallic properties, diamond is an insulator. An interesting two-dimensional borderline case is graph , which is a single isolated graphite layer.

Individual evidence

1. ^ PP Edwards and CNR Rao (eds.): Metal-Insulator Transitions Revised . Taylor & Francis, Bristol 1995
2. ↑ ^{a b} Matter close to absolute zero of temperature. (No longer available online.) Welt der Physik, November 4, 2003, archived from the original on February 10, 2015 ; Retrieved February 25, 2011 . Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice.  
3. ↑ Sir Nevill Mott : Metal-Insulator Transitions . Taylor & Francis, Bristol, 2nd edition 1990
4. ^ TF Rosenbaum, K. Andres, GA Thomas and RN Bhatt. In: Physical Review Letters . Volume 45, 1980, p. 1723, doi: 10.1103 / PhysRevLett.45.1723

literature

• Ronald Redmer, Bastian Holst, Friedrich Hensel (eds.): Metal-to-Nonmetal Transitions , Springer, Berlin 2009, ISBN 978-3-642-03952-2
• Nils Blümer: Mott-Hubbard Metal-Insulator Transition and Optical Conductivity in High Dimensions . Shaker, Aachen 2002, ISBN 3-8322-2320-7 (English, online [PDF; accessed on May 19, 2009]).