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Can anyone please explain the differences between Anderson and Mott insulator-metal transition? I found some information in the book named "The_Physics_of_Amorphous_Solids". enter image description here

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  • $\begingroup$ I gave my +1 long ago but just wanted to check how things are going now. Did you figure this out? Are you still working on it? $\endgroup$ Feb 6, 2023 at 20:39
  • $\begingroup$ Sorry, I havent been clear about those types of transitions. If you have some information, please share with us. $\endgroup$
    – Binh Thien
    Feb 10, 2023 at 11:05

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These transitions are not intuitive, so it not easy to explain. Simply, if you know the Bloch theorem well as a basis to describe approximately the solutions in a periodic system, you can understand that this theorem is based on a local periodic potential. Normally a Bloch state lead to the band theory where a partially occupied band is a conductor (there are delocalized states) and fully occupied bands is an insulator or a semiconductor (localized state).

Now the problem is the fact that the potential in solids is not a local periodic potential.

When the non-local electron-electron (e-e) interactions are dominant, the Bloch state is disturbed $\rightarrow $ We have a Mott transition the material with a partially occupied band become an insulator. When the potential is not strictly periodic, due to impurities (even if the e-e interaction can be neglected) the Bloch state is also disturbed $\rightarrow $ we have an Anderson transition.

For Bloch's theorem to remain valid, the electrons should have enough kinetic energy compared to the quantities affecting the periodicity of the potential (e-e interaction or impurities). Therefore a wide bandwidth $B$ (or hopping integral) is needed as in your image compared to $U$ or $W$ affecting the potential.

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