Metal–insulator transition

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.

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 insulator.

Theoretical description

The classical band structure 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 consideres 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.

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 antiferromagnetic 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.(V_1-xTi_x)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 entropy in the system when approaching the MIT. In the case of doped compounds the MIT can be achieved via changing the concentration of donors or acceptors. 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 localized, 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.

Further reading

• Mott, N. (1974). Metal-Insulator Transitions. Taylor & Francis Ltd. ISBN 0850660793. 
• Imada, M.; Fujimori, Tokura (1998). "Metal-insulator transitions". REV. MOD. PHYS 70 (4).  http://rmp.aps.org/abstract/RMP/v70/i4/p1039_1