Tight binding supercell help

In summary: Your Name]In summary, constructing the tight binding Hamiltonian for a GaAs supercell involves considering the atomic orbitals of the atoms in the supercell, calculating the overlap integrals between these orbitals, and using the tight binding Hamiltonian equation to construct the matrix. It is recommended to consult with a supervisor or experienced colleague and use additional resources for guidance.
  • #1
josecherukara
3
0
Hi

I am trying to construct the tight binding Hamiltonian for 2X1X1 GaAs supercell in SP3S* model and to study band folding. I am a newcomer to this field so kindly reply me how and where to start

I know that there would be 20 orbitals in the supercell unit cell, 10 in the first primitive cell and 10 in the next primitive cell. I don't know how these orbitals couple each other. I thought they won't couple to get the Hamiltonian in block diagonal form which is not true. Please help me to proceed
Thankingly
Jose Mathew
 
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  • #2
Hi Jose,

Thank you for reaching out and sharing your project with us. I am happy to assist you in constructing the tight binding Hamiltonian for your GaAs supercell.

First, let's start with the basics. The tight binding model is a method used to calculate the electronic structure of a material by considering the overlap of atomic orbitals and their energies. In your case, you are working with a 2X1X1 supercell, which means you have two primitive cells stacked in the x-direction and one in the y and z-directions.

To construct the tight binding Hamiltonian, you will need to consider the atomic orbitals of the atoms in your supercell. In GaAs, there are four valence electrons, two from Ga and two from As. These electrons will occupy the s and p orbitals, and each orbital will have a different energy level. You can refer to a periodic table to determine the specific energy levels for each orbital.

Next, you will need to consider the overlap of these orbitals between neighboring atoms. This will depend on the distance between the atoms, and you can use the Slater-Koster method to calculate the overlap integrals. The overlap integrals will determine how the orbitals couple with each other.

Once you have all the necessary information, you can use the tight binding Hamiltonian equation to construct the matrix for your supercell. This matrix will be in block diagonal form, with each block representing the orbitals in each primitive cell.

I understand that this may seem overwhelming, especially if you are new to this field. I recommend consulting with your supervisor or a colleague who has experience with tight binding models to guide you through the process. Additionally, there are many resources available online, such as textbooks and research papers, that can provide you with more detailed information and examples.

I hope this helps you get started on your project. Please feel free to reach out with any further questions or concerns. Good luck!
 

1. What is a tight binding supercell?

A tight binding supercell is a computational model used to study the electronic structure of a solid material. It combines the concepts of tight binding theory and supercell approximation to simulate the behavior of electrons in a crystal lattice.

2. How does a tight binding supercell differ from other methods?

Unlike first-principles methods, which require a large amount of computational resources, tight binding supercell calculations are less computationally demanding. They also do not rely on any empirical parameters, making them more accurate than semi-empirical methods.

3. What are the advantages of using a tight binding supercell?

One of the main advantages of using a tight binding supercell is its ability to accurately predict the electronic structure of materials, even those that are difficult to study experimentally. It is also useful for studying the effects of defects and impurities on the electronic properties of a material.

4. How is a tight binding supercell constructed?

A tight binding supercell is constructed by replicating a unit cell of a crystal lattice multiple times in all three dimensions. This creates a larger system with periodic boundary conditions, allowing for the simulation of an infinite crystal. The tight binding parameters are then calculated based on the electronic structure of the isolated unit cell.

5. What are some limitations of tight binding supercell calculations?

While tight binding supercell calculations are useful for studying the electronic properties of materials, they are limited in their ability to accurately predict the structural properties of a material. They also do not account for the effects of temperature or phonons, which can have a significant impact on the behavior of electrons in a crystal lattice.

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