Tight binding (FCC structures)

In summary, tight binding is a method used to calculate the electronic structure of materials in the face-centered cubic (FCC) crystal structure. It is simpler than other electronic structure methods and takes into account interactions between atoms in the crystal lattice. However, it has limitations such as not accounting for long-range interactions and requiring a lot of parameterization. Tight binding is used in materials research to study the electronic properties of FCC materials, such as metals and semiconductors.
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I'm reading my lectures on TBM and I don't understand the following thing:

[tex]\omega(\overrightarrow k)=\omega_0-4t\cdot[\cos(k_xa/2)\cos(k_ya/2)+...][/tex]

It's related to FCC structures, in which the number of Nearest Neighbors [tex](Z)[/tex] of an atom is equal to 12. Basically the three dots at the end leave me puzzled. What are they supposed to mean? Any help appreciated.
 
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  • #2
I guess just the cyclic permutation of (k_x, k_y, k_z)
 

1. What is tight binding in FCC structures?

Tight binding is a method used to calculate the electronic structure of materials in the face-centered cubic (FCC) crystal structure. It takes into account the interactions between neighboring atoms in the crystal lattice to determine the energy levels and electronic properties of the material.

2. How does tight binding differ from other electronic structure methods?

Tight binding is a more simplistic method compared to other electronic structure methods, such as density functional theory (DFT). Instead of solving the full quantum mechanical equations, tight binding uses approximations and simplifications to make calculations faster and more manageable.

3. What are the limitations of tight binding in FCC structures?

One limitation of tight binding is that it does not account for long-range interactions between atoms, which can affect the electronic properties of materials. It also requires a lot of parameterization to accurately describe the interactions between atoms, which can be time-consuming and difficult.

4. How is tight binding used in materials research?

Tight binding is often used in materials research to study the electronic properties of materials in the FCC crystal structure. It can provide insights into the band structure, energy levels, and electronic properties of materials, which can be useful in designing new materials for various applications.

5. What are some examples of materials that use tight binding in FCC structures?

Some examples of materials that use tight binding in FCC structures include metals, such as copper and silver, as well as semiconductors, such as silicon and germanium. These materials have FCC crystal structures and their electronic properties can be accurately described using tight binding calculations.

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