Brillouin Zone & K Point Explained

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SUMMARY

The Brillouin zone is a critical concept in solid state physics, defined as a unit cell in reciprocal space. It contains points of varying symmetry, typically denoted by capital letters. The K point, particularly relevant in the study of graphene, is where the conduction and valence bands intersect, resulting in a conical geometry around that point. This unique characteristic allows for low-energy electron excitations, leading to the effective massless behavior of electrons, which has sparked significant interest in graphene research.

PREREQUISITES
  • Understanding of solid state physics principles
  • Familiarity with reciprocal space concepts
  • Knowledge of band theory in materials science
  • Basic comprehension of graphene's electronic properties
NEXT STEPS
  • Study the Brillouin zone in detail using "Solid State Physics" by Mermin/Ashcroft
  • Explore the significance of K points in electronic band structure analysis
  • Investigate the implications of massless electrons in graphene
  • Learn about the geometric properties of conical intersections in band theory
USEFUL FOR

Students and researchers in solid state physics, materials scientists, and anyone interested in the electronic properties of graphene and related materials.

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what is Brillouin zone and K point?
 
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The Brillouin zone is a fundamental concept in solid state physics. I'd recommend to better consult an introductory book on that topic, e.g. Mermin/Ashcroft or Kittel. Basically, it is a unit cell in reciprocal space. There are points of different symmetry in that space/cell, which are usually named by capital letters. As you seem to be interested in graphene, the K point is the point where the conduction and the valence band touch. The geometry of the surfaces around that point is locally conical. As the bands touch there, an excitation of an electron costs arbitrarily low energy whence the electrons behave as if being effectively massless. Hence the large recent interest in that material.
 
DrDu said:
The Brillouin zone is a fundamental concept in solid state physics. I'd recommend to better consult an introductory book on that topic, e.g. Mermin/Ashcroft or Kittel. Basically, it is a unit cell in reciprocal space. There are points of different symmetry in that space/cell, which are usually named by capital letters. As you seem to be interested in graphene, the K point is the point where the conduction and the valence band touch. The geometry of the surfaces around that point is locally conical. As the bands touch there, an excitation of an electron costs arbitrarily low energy whence the electrons behave as if being effectively massless. Hence the large recent interest in that material.


oh! thank a lot!
 

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