How to determine band structure (E(k)) of a one dimensional crystal?

In summary, the person is new to the physics forum and is impressed by the knowledge of others. They are looking for help with determining the band structure for a one-dimensional crystal with two atoms spaced a/2 units apart. They mention that they are using tight-binding with one orbital per atom and only nearest neighbor hopping. They are seeking ideas and help from others on the forum.
  • #1
Wicked85
5
0
Hi!
I'm new to the physics forum but I've read a little bit and I'm impressed with the knowledge a lot of people have here. I've tried searching for any topic on my question without any luck.

My question is simply what the algorithm is to determine the band structure for a one dimensional crystal (I'm supposed to do it by hand), this seems fairly easy but I just don't know where to start!

Any help would be GREATLY appreciated! :)
Thanks!
Simon
 
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  • #2
I should add that it's two atoms in the chrystal, A & B spaced a/2 units apart.
 
  • #3
Are you doing tight-binding with one orbital per atom and only nearest neighbor hopping?
 
  • #4
Yes, that's correct. Any ideas? :)
 

1. How is the band structure of a one dimensional crystal determined?

The band structure of a one dimensional crystal is determined by plotting the energy (E) of the electrons in the crystal against the crystal's wave vector (k). This plot is known as the E(k) plot.

2. What information can be obtained from the band structure of a one dimensional crystal?

The band structure of a one dimensional crystal provides information about the energy levels of the electrons in the crystal and their corresponding wave vectors. It also shows the energy gaps or bands in which the electrons can exist, and the allowed and forbidden energy states.

3. How is the E(k) plot obtained for a one dimensional crystal?

The E(k) plot can be obtained by solving the Schrodinger equation for the one dimensional crystal, using the Bloch theorem which takes into account the periodic nature of the crystal lattice. This involves calculating the energy eigenvalues and eigenfunctions for the crystal's Hamiltonian matrix.

4. What factors affect the band structure of a one dimensional crystal?

The band structure of a one dimensional crystal is affected by various factors such as the crystal's composition and lattice structure, the number of atoms in the unit cell, the strength of the bonds between atoms, and the presence of any external electric or magnetic fields.

5. Why is the band structure of a one dimensional crystal important?

The band structure of a one dimensional crystal is important because it provides a fundamental understanding of the electronic properties of the crystal. It helps in predicting the crystal's electrical conductivity, optical properties, and its response to external stimuli. It also plays a crucial role in designing and developing electronic and optical devices based on one dimensional crystals.

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