What Do the Ellipses in the Tight Binding Model Equation Represent?

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SUMMARY

The ellipses in the Tight Binding Model (TBM) equation represent the continuation of terms resulting from the cyclic permutations of the wave vector components (k_x, k_y, k_z). In the context of Face-Centered Cubic (FCC) structures, where the number of nearest neighbors (Z) is 12, these ellipses indicate that additional cosine terms are included in the full expression of the energy dispersion relation. Understanding this notation is crucial for accurately interpreting the behavior of electrons in crystalline solids.

PREREQUISITES
  • Tight Binding Model (TBM) fundamentals
  • Understanding of Face-Centered Cubic (FCC) crystal structures
  • Basic knowledge of wave vector notation
  • Familiarity with energy dispersion relations in solid-state physics
NEXT STEPS
  • Study the derivation of the Tight Binding Model equations
  • Explore the implications of nearest neighbor interactions in FCC structures
  • Learn about the role of wave vectors in solid-state physics
  • Investigate the significance of cyclic permutations in mathematical expressions
USEFUL FOR

Students and researchers in solid-state physics, materials scientists, and anyone studying the electronic properties of crystalline materials.

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I'm reading my lectures on TBM and I don't understand the following thing:

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

It's related to FCC structures, in which the number of Nearest Neighbors (Z) 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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I guess just the cyclic permutation of (k_x, k_y, k_z)
 

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