User:Wslei97/Metal–insulator transition

Metal–insulator transitions (MITs) are transitions from a meta l, a material with good electrical conductivity of electric charges, to an insulator, a material where conductivity of charges is quickly suppressed. The intrinsic properties of such metals and insulators has to do with the size of the band gap between the valence and conduction bands, and the partial or full filling of these bands. Transitions between these states can be achieved by manipulating ambient parameters, such as pressure and temperature, or, in the case of a semiconductor, doping. Theoretically, all metals should become insulators at extremely high density, as predicted by the polarization catastrophe, which describes the dielectric properties of solids, and how at a certain critical concentration, excitation frequency in a solid is reduced to zero.

Elementary Mechanisms
Metal-insulator transitions(MIT) can be classified based on the origin of their transition. The most common MIT arises from intense electron-electron correlation as described by the Mott-Hubbard MIT.

In other occasions, the lattice itself through electron-phonon interactions can give rise to an MIT known as the Peierls MIT.

Insulator behavior in metals can also arise from the distortions and lattice defects, the transition of which is known as the Anderson MIT.

Polarization Catastrophe
The polarization catastrophe model describes the transition of a material from an insulator to a metal. This model considers the electrons in a solid to act as oscillators and the conditions for this transition to occur is determined by the number of oscillators per unit volume of the material. Since every oscillator has a frequency (ω0) we can describe the dielectric function of a solid as,

ε(ω) = 1+(Ne2/ε0m)/[ω02-(Ne2/3ε0m) -ω2-iω/tao]          (1)

where ε(ω) is the dielectric function, N is the number of oscillators per unit volume, ω0 is the fundamental oscillation frequency, m is the oscillator mass, and ω is the excitation frequency.

For a material to be a metal, the excitation frequency (ω) must be zero by definition, which then gives us the static dielectric constant,

εs = 1+(Ne2/ε0m)/[ω02-(Ne2/3ε0m)]           (2)

where εs is the static dielectric constant. If we rearrange equation (2) to isolate the number of oscillators per unit volume we get the critical concentration of oscillators (Nc) at which εs becomes infinite, indicating a metallic solid and the transition from an insulator to a metal.

Nc = 3ε0mω02/e2                      (3)

This expression creates a boundary that defines the transition of a material from an insulator to a metal. This phenomenon is known as the polarization catastrophe.

The polarization catastrophe model also theorizes that, with a high enough density, and thus a low enough molar volume, any solid could become metallic in character. Predicting whether a material will be metallic or insulating can be done by taking the ratio R/V, where R is the molar refractivity, sometimes represented by A, and V is the molar volume. In cases where R/V is less than 1, the material will have non-metallic, or insulating properties, while an R/V value greater than one yields metallic character.

Radio Frequency Switching
Radio Frequency (RF) switches are most commonly applicable to wireless communications systems. MIT materials, namely Vanadium dioxide (VO2), offer a number of advantages over comparable RF switching materials. Compared to conventional devices of the same size, VO2 based RF switches have low insertion loss, a high cut-off frequency, and fast switching speed. These advantages are attributed to the unique phase change of VO2, which occurs above room temperature.

Neuromorphic Computing
Resistive switching devices are directly applicable to neuromorphic computing. Some transition metal oxides (TMOs) which undergo MIT have the potential to provide a low energy consumption option for neuromorphic devices. As an example, La1-xSrxCoO3-δ (LSCO) is an MIT material with tunable resistivity as a result of changes in temperature, pressure, and Sr doping.