Break points in band structure

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SUMMARY

Break points in band structure refer to the intersections of energy bands in the εnk vs. k plot, where ε represents energy and k represents the wave vector. When two bands intersect, the lower energy band is indexed as band 1 and the higher energy band as band 2, leading to discontinuities in the energy surface, particularly in Dirac cone structures. This phenomenon indicates critical points in the electronic properties of materials, as described in Jenö Sólyom and A. Piróth's "Fundamentals of the Physics of Solids Volume II".

PREREQUISITES
  • Understanding of band theory in solid-state physics
  • Familiarity with the concepts of energy bands and wave vectors
  • Knowledge of Dirac cone structures in materials science
  • Ability to interpret εnk plots and their significance
NEXT STEPS
  • Study the implications of band intersections on electronic properties
  • Research Dirac cone structures and their applications in materials
  • Learn about the mathematical representation of band structures
  • Explore advanced topics in solid-state physics related to band theory
USEFUL FOR

Physicists, materials scientists, and students studying solid-state physics, particularly those interested in electronic band structure and its implications in material properties.

chikou24i
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What do we mean by break points in band structure ? and what that sentence means : "if the band index were chosen in such a way that the energies are indexed in ascending order for any k then break points would appear in the εnk vs. k plot (with n fixed) wherever two lines intersect." ?
Reference: [Jenö_Sólyom,_A._Piróth]_Fundamentals_of_the_Physics of solids Volume II, page 85
 
sorry, I didn't understand what you have said.
 
chikou24i said:
sorry, I didn't understand what you have said.

Maybe I'm wrong, but I think that it's trying to describe what happens when 2 bands intersect. If 2 bands intersect, and you index band 1 has the "lower energy" band, and band 2 as the higher energy band

$$\epsilon_1(k)$$ would look like a surface with sharp edges (discontinuous) for dirac cone type structures. Maybe the dirac cone is a break point?

https://www.google.com/search?q=dir...=OcL_Vtm9POmpjgTwlbHwDw#imgrc=FS6VEyJMufMagM:
 
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