Mott insulators and electron-electron insulators

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SUMMARY

The discussion centers on Mott insulators, specifically the lattice model proposed by Sir Nevill Mott, which describes a system with one electron per site. The key point is that while the model initially disregards electron-electron interactions, it later emphasizes the significance of Coulomb repulsion, which leads to the formation of two distinct energy bands. The lower band is fully occupied by the single electron per site, while the upper band remains empty, thus characterizing the system as a Mott insulator. This phenomenon illustrates how strong electron interactions can drive a material from a metallic to an insulating state.

PREREQUISITES
  • Understanding of solid-state physics concepts, particularly band theory.
  • Familiarity with electron interactions and Coulomb repulsion.
  • Knowledge of lattice models in condensed matter physics.
  • Basic grasp of Mott insulator characteristics and their implications.
NEXT STEPS
  • Research the principles of Mott insulators and their role in condensed matter physics.
  • Explore the concept of Coulomb repulsion and its effects on electronic band structure.
  • Study lattice models and their applications in understanding electron behavior in solids.
  • Investigate the transition mechanisms from metallic to insulating states in materials.
USEFUL FOR

Physicists, materials scientists, and students interested in condensed matter physics, particularly those studying electronic properties of materials and the mechanisms behind Mott insulators.

Sagar Rawal
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I found this paragraph from one of wiki article, "Mott considers 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."

What I don't understood here is

At first it is said that Mott consider a lattice model without taking interaction into account but later mentioned that due to interaction electorns would feel strong columb repulsion? Isn't that contradicts the first statement?

It is first said that he considers just one electron per site but later said each site could be occupied by two electons, which again contradicts the first statement.

So anyone please explain me what I'm missing here or what really affects metals to become insulators or what is mott insulators?
 
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What it is saying that if you disregard the interaction you could have two electrons on each site, not that there is no interaction.
 

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