Coupling to an electric field in a tight binding model

In summary, the expert explains that one needs to replace the hopping parameter with an exponent of the line integral of the vector potential along the hopping path, and then find the current by calculating the derivative of the Hamiltonian with respect to the vector potential.
  • #1
Qturtle
11
0
Hi
i'm looking for some references (prefer books) or explanations as to how one couple electrons so an EM field in a second quantized formalism tight binding model.
from what i know, one need to replace the hopping parameter with the same parameter multiplied by an exponent of the line integral of the vector potential along the hopping path. this is called the peierls substitution. after that in order to find the current - one need to calculate the derivative of the Hamiltonian with respect to the vector potential.
Can someone refer me to a book where this formalism is explained, or maybe explain here? i actually need this for a work I'm doing. I know that this is the method to couple to an EM field and finding the resulted current but i don't really understand why.

thank you very much!
 
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  • #2
Qturtle said:
Hi
i'm looking for some references (prefer books) or explanations as to how one couple electrons so an EM field in a second quantized formalism tight binding model.
from what i know, one need to replace the hopping parameter with the same parameter multiplied by an exponent of the line integral of the vector potential along the hopping path. this is called the peierls substitution. after that in order to find the current - one need to calculate the derivative of the Hamiltonian with respect to the vector potential.
Can someone refer me to a book where this formalism is explained, or maybe explain here? i actually need this for a work I'm doing. I know that this is the method to couple to an EM field and finding the resulted current but i don't really understand why.

thank you very much!
Not a book, but this article is the reference of the expert:
http://www.wsi.tum.de/Portals/0/Media/Publications/76e71959-883d-474a-b8a0-7569651515fb/PRB51_4940_95.pdf
and this I find also helpful:
http://docs.lib.purdue.edu/cgi/viewcontent.cgi?article=1509&context=nanopub
 
Last edited:
  • #3
Thanks DrDu
i'm actually looking for a good derivation of the peierls substitution (Eq. 9 and rf. 16 in the first paper)
I wasn't able to find the original paper of peierls though ):
 
  • #4
Don't equation 9 and 10 of Vogl and Graf suffice as a derivation?
 
  • #5
It is if you understand why an exponent of a line integral of A(x) can transform a function of p to a function of p-eA(x)
 
  • #6
Equation 9 is an exact relation for any function of p and x. Just use ##p=\frac{\hbar}{i} \partial_\vec{r}##.
 
  • #7
yes I can see now that this is more general. Thanks
 

1. What is a tight binding model?

A tight binding model is a simplified approach to studying the electronic structure of materials. It considers the interactions between electrons in a solid to be localized to a specific set of atoms, rather than treating each electron as a delocalized wave. This simplification allows for easier calculations of electronic properties.

2. How does coupling to an electric field affect a tight binding model?

Coupling to an electric field means that the motion of electrons in the tight binding model will be influenced by the presence of an external electric field. This can lead to changes in the electronic properties of the material, such as band structure and conductivity.

3. What factors determine the strength of coupling to an electric field in a tight binding model?

The strength of coupling to an electric field in a tight binding model depends on the strength of the electric field itself, the electronic structure of the material, and the strength of the electron-electron interactions in the material.

4. Can coupling to an electric field be used to control the electronic properties of a material?

Yes, coupling to an electric field can be a powerful tool for controlling the electronic properties of a material. By varying the strength and direction of the electric field, researchers can manipulate the band structure, conductivity, and other electronic properties of the material.

5. How is coupling to an electric field experimentally measured in a tight binding model?

Coupling to an electric field can be experimentally measured in a tight binding model through various techniques such as spectroscopy, transport measurements, and scanning tunneling microscopy. These methods allow researchers to directly observe the effects of an electric field on the electronic properties of the material.

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