How to Plot a 2D band structure?

In summary, the conversation is about someone who has just learned how to get a tight-binding dispersion for graphene and is now trying to figure out how to plot it. They mention using the path K-Gamma-M-K and using the function surf in Matlab. They also mention using meshgrid for a 3D plot. The conversation ends with them expressing their gratitude for the help they received.
  • #1
stranhuz
2
0
Dear forum people,

I just learned how to get a tight-binding dispersion for graphene:

[itex] E = +- \sqrt{1+4\cos((\sqrt{3}a/2) k_x)\cos((a/2) k_y)+4\cos^2((a/2) k_y)} [/itex]

But i can not figure out how can I plot that. I want to plot that in the following path: [itex] K \rightarrow \Gamma \rightarrow M \rightarrow K[/itex].

I think k_y = 0 in the line [itex]\Gamma M[/itex] and I should plot(E,k_x); k_x = constant in the line MK and I should plot(E,k_y); but I don't know how the plot() is look like for [itex]K \Gamma[/itex], where both k_x and k_y are not constant.

For nanotube, I was able to do that becouse we just had k, so I just made "plot(E,k,'b')". Here in graphene, we have both [itex] k_x, k_y[/itex].

I would be appreciated if could some one give me a hand on my problem.

Best wishes for all.
 
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  • #2
The curve connecting the two points is a straight line, hence both k_x and k_y can be written as linear functions of a common parameter s ranging from 0 to 1.
Specifically if k_0 ist the coordinate vector of the first point and k_1 of the last, then the line is
k_0 +s*(k_1-k_0) and you can plot the energy as a function of the scalar parameter s.
 
  • #3
I guess you are using Matlab.

You can using the function surf to get the E-K diagram. Syntax would be surf(kx,ky,Ek)

The output would look like this
http://en.wikipedia.org/wiki/File:GrapheneE2.png
 
  • #4
How to Plot a 2D band structure? [Solved]

Dear DrDu and Wolfgang2b,

Thank you very much. Your answer was very useful. It worked pretty fine. Now I'm able to plot the 2D and 3D for graphene on matlab.

For 3D plot, I had to use meshgrid(), in order to create the matrix KX an KY, then use surf(KX,KY,Ek). It worked fine. The plot was very nice.

Best wishes and Thank you again.
 

1. How do I obtain the energy values for a 2D band structure plot?

To obtain the energy values for a 2D band structure plot, you will need to use the band structure data from your electronic structure calculation. This data can be obtained from software packages such as VASP or Quantum ESPRESSO. Once you have the band structure data, you can plot the energy values using a software tool such as Matplotlib or gnuplot.

2. What is the significance of the band structure plot in materials science?

The band structure plot is a graphical representation of the electronic energy levels in a material. It is significant in materials science because it provides insight into the electronic properties of a material, such as its conductivity, optical properties, and magnetic properties. It also helps in understanding the behavior of electrons in a material, which is crucial in designing new materials with specific properties.

3. How do I interpret the information presented in a 2D band structure plot?

In a 2D band structure plot, the horizontal axis represents the crystal momentum (k) and the vertical axis represents the energy levels. The bands in the plot represent the allowed energy levels for electrons in the material. The width of the bands represents the energy range that is allowed for electrons at a particular crystal momentum. The gaps between the bands indicate energy levels that are not allowed for electrons. The slope of the bands also provides information about the effective mass of the electrons in the material.

4. Can I plot the 2D band structure for any material?

Yes, you can plot the 2D band structure for any material as long as you have the band structure data from an electronic structure calculation. However, the accuracy of the plot may vary depending on the quality of the data and the software used for plotting. It is also essential to consider the symmetry of the material since it can affect the shape and behavior of the bands in the plot.

5. Are there any limitations to plotting a 2D band structure?

One of the limitations of plotting a 2D band structure is that it only provides information about the electronic properties of a material at a specific point in the Brillouin zone. To obtain a more comprehensive understanding of the electronic properties, it is necessary to plot the band structure at different points in the Brillouin zone. Additionally, the accuracy of the plot may also be affected by the accuracy of the electronic structure calculation and the assumptions made during the plotting process.

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