Why is the valence band maxima at k = 0?

In summary, there are two types of materials, direct and indirect. In direct materials, both the valence band maxima and conduction band minima are located at k = 0. In indirect materials, only the valence band maxima is at k = 0 while the conduction band minima is at a non-zero value of k. The assumption is often made that the valence band maxima is always at k = 0, but this is not always the case. In lead sulfide, for example, the valence band maxima is at the L point. Graphene and graphite are also examples of materials where the valence band maxima is not at k = 0.
  • #1
nmbr28albert
13
3
In general, materials are either direct or indirect materials. For direct materials, both the valence band maxima and the conduction band minima are at k = 0. For indirect materials, only the valence band maxima is at k = 0 and the conduction band minima is at some other non-zero value of k. In all the books I've read, it seems to always be assumed that the valence band maxima is at k = 0. Is this true, and if so why?
 
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  • #3
I have always seen the same, I think it's arbitrary defined like this.
 
  • #4
After some digging, I found that it actually isn't true that the valence band maxima is always at k = 0. In lead sulfide for example, the valence band maximum is at the L point.
 
  • #5
Graphene and gaphite also come to my mind.
 

1. What is the valence band maxima at k = 0?

The valence band maxima at k=0 refers to the highest energy level or band in the valence band, which is the outermost electron shell of an atom. It is the point where the energy of electrons is at its maximum and they are most tightly bound to the atom.

2. Why is the valence band maxima at k = 0 important?

The valence band maxima at k=0 is important because it determines the electronic and optical properties of a material. It is also a key factor in understanding the conductivity and bandgap of a material, which are important in various applications such as in electronics and semiconductors.

3. How is the valence band maxima at k = 0 calculated?

The valence band maxima at k=0 is calculated using quantum mechanics and the band structure of a material. The energy levels of electrons at different points in the material's momentum space are analyzed to determine the location of the valence band maxima at k=0.

4. What factors can affect the valence band maxima at k = 0?

The valence band maxima at k=0 can be affected by various factors such as the atomic structure and composition of the material, temperature, and external forces such as applied electric fields. It can also be influenced by the presence of impurities or defects in the material.

5. How does the valence band maxima at k = 0 relate to other band structures?

The valence band maxima at k=0 is a key factor in understanding the overall band structure of a material. It is often compared to the conduction band maxima, which is the highest energy level in the conduction band. The difference between the two helps determine the bandgap of a material and its ability to conduct electricity.

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