Brillouin Zone & K Point Explained

In summary, the Brillouin zone is a unit cell in reciprocal space used in solid state physics. It contains points of different symmetry, typically named with capital letters. For those interested in graphene, the K point is where the conduction and valence bands meet, and the surfaces around it have a conical geometry. This allows for low energy electron excitation, making them behave as if they are effectively massless, which has sparked recent interest in the material.
  • #1
toex
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what is Brillouin zone and K point?
 
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  • #2
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.
 
  • #3
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!
 

1. What is a Brillouin Zone?

A Brillouin Zone is a concept in solid state physics that represents the allowed range of electron momentum in a crystal lattice. It is a geometric shape that is repeated throughout the crystal structure and contains all the possible states of the electrons in the lattice.

2. How is a Brillouin Zone determined?

A Brillouin Zone is determined by the reciprocal lattice vectors of a crystal. These vectors represent the spacing and orientation of the crystal lattice and are used to create the Brillouin Zone by connecting the midpoints of the reciprocal lattice vectors.

3. What is the significance of the Brillouin Zone?

The Brillouin Zone is significant because it helps us understand the properties and behavior of electrons in a crystal lattice. It also plays a vital role in determining the electronic band structure and conductivity of materials.

4. What are K points in the Brillouin Zone?

K points, or high symmetry points, are special points within the Brillouin Zone that have a high degree of symmetry. They are used as reference points for calculating the electronic band structure and are important in determining the properties of materials.

5. How are K points related to the electronic band structure?

The K points in the Brillouin Zone are used as reference points for calculating the electronic band structure. They represent the points where the energy levels of electrons are at their highest or lowest, and provide insight into the electronic properties of materials.

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