Metal-insulator transition
Encyclopedia
Metal-insulator transitions are transitions from a metal
(material with good electrical conductivity
of electric charges) to an insulator (material where conductivity of charges is quickly suppressed). These transitions can be achieved by tuning various ambient parameters such as pressure
or, in case of a semiconductor
, doping
.
.
of solid state physics predicts the Fermi level
to lie in a band gap for insulators and in the conduction band for metals, which means metallic behavior is seen for compounds with partially filled bands. However, some compounds have been found which show insulating behavior even for partially filled bands. This is due to the electron-electron correlation, since electrons can't be seen as noninteracting. Mott considers a lattice model with just one electron per site. Without taking the interaction into account, each site could be occupied by two electrons, one with spin
up and one with spin down. Due to the interaction the electrons would then feel a strong Coulomb repulsion, which Mott argued splits the band in two: The lower band is then occupied by the first electron per site, the upper by the second. If each site is only occupied by a single electron the lower band is completely filled and the upper band completely empty, the system thus a so called Mott insulator
.
Metal
A metal , is an element, compound, or alloy that is a good conductor of both electricity and heat. Metals are usually malleable and shiny, that is they reflect most of incident light...
(material with good electrical conductivity
Electrical resistivity and conductivity
Electrical resistivity is a measure of how strongly a material opposes the flow of electric current. A low resistivity indicates a material that readily allows the movement of electric charge. The SI unit of electrical resistivity is the ohm metre...
of electric charges) to an insulator (material where conductivity of charges is quickly suppressed). These transitions can be achieved by tuning various ambient parameters such as pressure
Pressure
Pressure is the force per unit area applied in a direction perpendicular to the surface of an object. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure.- Definition :...
or, in case of a semiconductor
Semiconductor
A semiconductor is a material with electrical conductivity due to electron flow intermediate in magnitude between that of a conductor and an insulator. This means a conductivity roughly in the range of 103 to 10−8 siemens per centimeter...
, doping
Doping (semiconductor)
In semiconductor production, doping intentionally introduces impurities into an extremely pure semiconductor for the purpose of modulating its electrical properties. The impurities are dependent upon the type of semiconductor. Lightly and moderately doped semiconductors are referred to as extrinsic...
.
History
The basic distinction between metals and insulators was proposed by Bethe, Sommerfeld and Bloch in 1928/1929. It distinguished between conducting metals and nonconducting insulators. However, in 1937 de Boer and Verwey reported that many transition-metal oxides (such as NiO) with a partially filled d-band were poor conductors, often insulating. In the same year, the importance of the electron-electron correlation was stated by Peierls. Since then, these materials as well as others exhibiting a transition between a metal and an insulator have been extensively studied, e.g. by Sir Nevill Mott, after whom the insulating state is named Mott insulatorMott insulator
Mott insulators are a class of materials that should conduct electricity under conventional band theories, but are insulators when measured...
.
Theoretical description
The classical band structureElectronic band structure
In solid-state physics, the electronic band structure of a solid describes those ranges of energy an electron is "forbidden" or "allowed" to have. Band structure derives from the diffraction of the quantum mechanical electron waves in a periodic crystal lattice with a specific crystal system and...
of solid state physics predicts the Fermi level
Fermi level
The Fermi level is a hypothetical level of potential energy for an electron inside a crystalline solid. Occupying such a level would give an electron a potential energy \epsilon equal to its chemical potential \mu as they both appear in the Fermi-Dirac distribution function,which...
to lie in a band gap for insulators and in the conduction band for metals, which means metallic behavior is seen for compounds with partially filled bands. However, some compounds have been found which show insulating behavior even for partially filled bands. This is due to the electron-electron correlation, since electrons can't be seen as noninteracting. Mott considers a lattice model with just one electron per site. Without taking the interaction into account, each site could be occupied by two electrons, one with spin
Spin (physics)
In quantum mechanics and particle physics, spin is a fundamental characteristic property of elementary particles, composite particles , and atomic nuclei.It is worth noting that the intrinsic property of subatomic particles called spin and discussed in this article, is related in some small ways,...
up and one with spin down. Due to the interaction the electrons would then feel a strong Coulomb repulsion, which Mott argued splits the band in two: The lower band is then occupied by the first electron per site, the upper by the second. If each site is only occupied by a single electron the lower band is completely filled and the upper band completely empty, the system thus a so called Mott insulator
Mott insulator
Mott insulators are a class of materials that should conduct electricity under conventional band theories, but are insulators when measured...
.
Types of metal-insulator transitions
In general, one can distinguish between several types of transition:- Mott-Hubbard transition for materials that become Mott insulators. The metal-insulator transition (MIT) can in this case be achieved by varying the distance a between the atoms in the crystal. At zero temperature, the system is an antiferromagneticAntiferromagnetismIn materials that exhibit antiferromagnetism, the magnetic moments of atoms or molecules, usuallyrelated to the spins of electrons, align in a regular pattern with neighboring spins pointing in opposite directions. This is, like ferromagnetism and ferrimagnetism, a manifestation of ordered magnetism...
insulator for large a and a normal metal for small a. - In transition-metal compounds, the MIT can be achieved by tuning various parameters: In the case of undoped compounds due to rising temperature, rising pressure or varying composition (e.g.(V1-xTix)2O3). The transition in this case is of first order, which means that there is a discontinuous change in the number of free carriers and a discontinuous change of volume under pressure. Thus, in these cases, the driving force behind the transition is the increasing entropyEntropyEntropy is a thermodynamic property that can be used to determine the energy available for useful work in a thermodynamic process, such as in energy conversion devices, engines, or machines. Such devices can only be driven by convertible energy, and have a theoretical maximum efficiency when...
in the system when approaching the MIT. In the case of doped compounds the MIT can be achieved via changing the concentration of donorsElectron donorAn electron donor is a chemical entity that donates electrons to another compound. It is a reducing agent that, by virtue of its donating electrons, is itself oxidized in the process....
or acceptorsElectron acceptorAn electron acceptor is a chemical entity that accepts electrons transferred to it from another compound. It is an oxidizing agent that, by virtue of its accepting electrons, is itself reduced in the process....
. Doping a compound drastically changes its internal electronic structure, thus giving rise to or eliminating band gaps. - Disorder-induced MIT can also be achieved by doping the compound or generally spoken increasing the disorder in a given material. In this case, the states are Anderson localizedAnderson localizationIn condensed matter physics, Anderson localization, also known as strong localization, is the absence of diffusion of waves in a disordered medium. This phenomenon is named after the American physicist P. W...
, which prohibits conductivity. As long as the states at the Fermi level stay localized, the material is an insulator even if the Fermi level lies within a band. By increasing the disorder the mobility edge can be decreased. As soon as it drops below the Fermi level, if the Fermi level lies within a band, the material becomes a metal.