For the transition from insulator to metal, there have different transition mechanisms.
How to distinguish Anderson transition (Anderson insulator was induced by the disorder-induced localization of electrons) from Mott transition (Mott insulator was induced by the Coulomb repulsion between electrons. This transition can be controlled by the mechanisms of oxygen vacancy controlled electron filling), especially in 2 or 3-dimensions materials.
This is a very difficult question. It may be a Mott-Anderson Transition, which combines the two. Look at papers that show this theoretically. I am not sure if in a highly defective system you can make a distinction.
My understanding is that the Anderson localization or transition privilegis the role of disorder, without the influence of correlations (that is the electron-electron forces)
A Mott transition would mainly be due to the correlationns.
Dear Juan Weisz and Carlos Paz de Araujo
You are welcome.
The following is my understanding, if there has some mistake please provide some comments, thanks.
The mechanism of Mott transition can be based on Bandwidth controlled transition of Filling controlled transition. Anderson localization insulator can be result from the structure-disorder of defects-disorder. Here we just talk about how to distinguish defects-disorder Anderson insulator from Filling controlled Mott transition.
Take paper "Scientific reports, 3. 1704, 2013 (oxygen vacancy induced Filling controlled Mott transition in Pr0.7Ca0.3MnO3)" as an example. The initial state of Pr0.7Ca0.3MnO3 is a metal, the voltage induced oxygen vacancy can provide extra electrons, these electrons go to filling the Mn 3d orbit, and result in the chemical valence change of Mn and Pr0.7Ca0.3MnO3 transition into insulator. It is say Filling controlled Mott transition is related to chemical valence change of Mn which can be tested. If it was Anderson transition controlled by electrons localization near disorder oxygen vacancy defects, there will no chemical valence change of Mn. (The generation of oxygen vacancy maybe lead to a little change of lattice structure)
Besides, from the view of band structure. Mott transition from metal to insulator has an opened band gap at Fermi level. For Anderson transition from metal to insulator, in principle, there still has density of state at Fermi level without band gap, the difference is the density of state at Fermi level is localized.
Another question, if the oxygen vacancy mentioned above is disorder and can result in an Anderson insulator for Pr0.7Ca0.3MnO3. Then, how about when the oxygen vacancy is order/uniform distribution (for a low concentration of oxygen vacancy)? Is it a metal or insulator?
The transport of current through a material to distinguish metals and isolators
depends on both the mobility of carriers and their number (ie band filling)
Thus a small number of carriers (with long range coulomb effects) and low mobility
due to disorder is most certainly an insulator. In a metal with high density of carriers
Coulomb effects become short ranged.
Hello,
Anderson transition is a one body problem in which localization results from quantum interferences effects. The metal to insulator transition can occur at any fiilling (carrier density) , only the strength of the disorder controls the position of the mobility edge that separates extended from localized states.
The Anderson transition does not open a gap in the one particle spectrum.
However, the Mott transition is a many body feature, that occurs at specific band filling and controlled by the strength of the coulomb electron-electron interaction. At the metal to insulator transition, in contrast to Anderson transition a finite gap opens in the charge spectrum.
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