Mott insulators and electron-electron insulators

In summary: The interaction causes a strong Coulomb repulsion between the electrons, which splits the band into two - the lower band is occupied by one electron per site, and the upper band is occupied by the second electron. This results in a Mott insulator, where the lower band is completely filled and the upper band is completely empty. This is due to the strong interactions between the electrons, which prevents the electrons from freely moving and conducting electricity, making the material an insulator. In summary, Mott discovered that in a lattice model with just one electron per site, strong interactions between the electrons cause the band to split into a lower band, completely filled with one electron per site, and an upper band, completely empty. This results in a Mott
  • #1
Sagar Rawal
6
0
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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  • #2
What it is saying that if you disregard the interaction you could have two electrons on each site, not that there is no interaction.
 

1. What is a Mott insulator?

A Mott insulator is a type of material that does not conduct electricity at low temperatures, despite having a partially filled valence band. This is due to strong electron-electron interactions that prevent the movement of electrons.

2. What is the difference between a Mott insulator and an electron-electron insulator?

A Mott insulator specifically refers to a material where the electron-electron interactions are the dominant factor in inhibiting electron movement. On the other hand, an electron-electron insulator can also include materials where other factors, such as lattice vibrations, play a significant role in hindering electron conductivity.

3. How do Mott insulators and electron-electron insulators form?

Mott insulators and electron-electron insulators typically form in materials where the valence band is partially filled. This leads to a competition between the kinetic energy of the electrons, which promotes conductivity, and the potential energy of the electron-electron interactions, which hinder it. If the potential energy dominates, the material will become an insulator.

4. Can Mott insulators and electron-electron insulators be converted into conductors?

Yes, it is possible to convert Mott insulators and electron-electron insulators into conductors by altering external factors such as temperature, pressure, or doping the material with impurities. By changing these factors, the balance between kinetic and potential energy can be shifted, allowing for electron movement and conductivity.

5. What are some real-world applications of Mott insulators and electron-electron insulators?

Mott insulators and electron-electron insulators have potential uses in technologies such as high-temperature superconductivity, solid-state batteries, and quantum computing. They can also be used in the development of new materials with specific electronic properties for various applications in electronics and energy storage.

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