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When studying about metal-insulator transitions, I was wondering which material properties can give direct information about this phenomena. Also, what information can be derived from these properties. I cannot seem to find any good readings about this topic. One last thing: which type of materials are useful in experimentally studying the metal-insulator transitions and why is this the case ? Is there like a kind of way to accurately move through the transition ?

Thanks in advance !

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The metal to insulator transition is a characteristic of some materials that cannot be adequately described by a mean field theory like band theory. The reason that these materials may still behave like conventional band insulators while being gapless is due to strong correlation of electrons- meaning the energy penalty for a valence electron to occupy the same orbital angular momentum state as another electron is on the order of the hopping matrix element.

These materials are often oxides such as vanadium-oxide. More generally this is a characteristic of some metallic compounds with 3d and 4f electrons. This is largely due to the fact that electrons in these orbitals are relatively localized in space compared to other outer shells. As a result, the couloumbic repulsion when multiple electrons occupy a 3d or 4f state is relatively high.

So why would this phenomenon occur in an metal-oxide compound but not in 3d metals alone? There are a variety of factors for this, but the most trivial way to think about some simpler systems is by comparing the hopping matrix element to the energy penalty from correlation. The hopping matrix element, in a simplified picture, corresponds to how electrons may lower their energy by hopping from site to site. In typical 3d metals, the magnitude of the hopping matrix element is larger than the correlation energy, and therefore the material is well-described by band theory. On the other hand, for an material that may be a Mott insulator, the magnitude of the hopping matrix element would be less than the correlation energy. This prevents electrons from easily moving.

Perhaps the most physically intuitive (but not necessarily most accurate) way to think about why this may happen for an oxide is because the oxygen atoms effectively act as "spacers" that increase the distance between metal atoms in the solid. As a result, the wavefunctions involved in the hopping integral have lesser spatial overlap. This makes the hopping energy lesser than it would be in the pure metal, which may cause the magnitude to fall below the correlation energy penalty.

With this toy model in mind, it would then make sense that there could be an effective balance between the hopping energy and the correlation energy. The ratio of the two would determine whether or not your material will act as a metal or a gapless insulator. So it would make sense that you could have a phase transition when the correlation energy is the same in magnitude to the hopping energy.

So what could tip the balance? There are a variety of factors. Strain, temperature, electric field, and degree of doping have all been observed as parameters that may be varied to cause a metal-insulator transition.

I encourage you to read about the Hubbard model if you want a more detailed account of the model I described.

As an example of an experimental application of this, I encourage you to check out this (somewhat controversial) paper of using a metal-insulator transition in a field-effect transistor.

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