Can I get Bandgap of 3D material with 1D Hamiltonian

In summary, the speaker is asking if it is possible to get the bandgap of a 3d material by using the average potential (U(x)) obtained from the first principal result. However, another person responds that this is not possible as a one-dimensional chain is a different physical system from a 3d bulk material, and there may be significant approximations involved in the process.
  • #1
Arya_
7
0
Hi All,

Greetings!

I have a 3d material and I use result from first principal for getting the potential (U(x,y,z)). I then find average U(x) from U(x,y,z). Now if I write one dimensional Hamiltonian in X direction and use this value of U(x), can I get bandgap of the original 3d material (I am not interested to see the bandstructure, bandgap is what I need)

Thanks,
_Arya
 
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  • #2
No. Why do you think this should be possible? A one-dimensional chain of something is a completely different physical system than a 3d bulk material. (And that is not even considering the /massive/ approximations in what I can only guess you are doing)
 

1. What is a Bandgap?

A bandgap is the energy difference between the top of the valence band and the bottom of the conduction band in a material. It is a crucial characteristic of a material's electronic structure and determines its conductivity and optical properties.

2. Can I get a Bandgap in a 3D material using a 1D Hamiltonian?

Yes, it is possible to calculate the bandgap of a 3D material using a 1D Hamiltonian. However, this approach may not accurately capture all the electronic properties of the material, as it simplifies the system to only one dimension.

3. What is a 1D Hamiltonian?

A 1D Hamiltonian is a mathematical model that describes the behavior of a one-dimensional system. It takes into account the energy levels and interactions of particles within the system and is commonly used in quantum mechanics to study the electronic properties of materials.

4. How accurate is the bandgap calculation using a 1D Hamiltonian?

The accuracy of the bandgap calculation using a 1D Hamiltonian depends on the specific material and the assumptions made in the model. In some cases, it can provide a good estimate, but in others, it may not accurately capture the full electronic structure of the material.

5. Are there any limitations to using a 1D Hamiltonian to calculate bandgap in 3D materials?

Yes, there are limitations to using a 1D Hamiltonian for bandgap calculations in 3D materials. It neglects the interactions between particles in the other two dimensions, which can significantly affect the electronic properties of the material. Additionally, it may not accurately represent the material's behavior under certain conditions, such as high temperatures or extreme pressures.

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