Plotting Silicene Band Structure in Γ→M→K→Γ Path using Correct Equation

In summary, the speaker is using a tight binding model to plot the band structure of silicene in the path Γ→M→K→Γ using lattice vectors and silicon atom positions. They have provided code for the calculations but have requested further clarification on the material and Hamiltonian model used.
  • #1
anahita
39
0
I want to plot band structure silicene in the following path: Γ→M→K→Γ
Do the following equation for the above path is correct:
close all
clear all
clc
aa=2.28;
a=3.86;
a1=(a/2)*[sqrt(3),-1,0];
a2=(a/2)*[sqrt(3),1,0];
b1y=-(2*pi)/a;
b1x=(2*pi)/(sqrt(3)*a);
b2x=b1x;
b2y=-b1y;
%K-point
pKx = (1/3)*b1x+(2/3)*b2x;
pKy = (1/3)*b1y+(2/3)*b2y;
%M-point
pMx = b2x/2;
pMy = b2y/(2);
%Gamma point
pGx = 0;
pGy = 0;
xxx =(0:0.05:1)';
%K-G
xx =xxx;
yy = xx;
xx = -(pKx - pGx)*xx + pKx;
yy = -(pKy -pGy)*yy + pKy;
%G-M
xx1 = xxx;
yy1 = xx1;
xx1 = -(pGx - pMx)*xx1 + pGx;
yy1 = -(pGy-pMy)*yy1 + pGy;
%M-k
xx2 = xxx;
yy2 = xx2;
xx2 = -(pMx - pKx)*xx2 + pMx;
yy2 = -(pMy -pKy)*yy2 + pMy;

xx = [transp(xx2),transp(xx),transp(xx1)];
yy =[transp(yy2),transp(yy),transp(yy1)];

for ope=1:length(xx),
k = [xx(ope),yy(ope),0]
end
 
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  • #2
anahita said:
I want to plot band structure silicene in the following path: Γ→M→K→Γ
Please first explain the model you are using and specify your algorithm (before giving the code). There are many unclear items in your post. Is your material sheet or ribbon? What is the Hamiltonian model you have used? What are the basis?
 
  • #3
I'm using tight binding model. I wants to plotting band structure silicene in path : Γ→M→K→Γ.
lattice vectors:
a1=a/2*[sqrt(3),-1,0]
a2=a/2*[sqrt(3),1,0]
silicon atoms are positions at (0,0,0) and (a/sqrt(3),0,0.45).
 

1. What is silicene and why is it important to study its band structure?

Silicene is a two-dimensional allotrope of silicon, similar to graphene but made of silicon atoms. It is important to study its band structure because it has potential applications in nanoelectronics and optoelectronics due to its unique electronic properties.

2. What does the Γ→M→K→Γ path represent in the context of silicene band structure?

The Γ→M→K→Γ path represents the high symmetry points in the Brillouin zone of the silicene crystal. These points are important in determining the electronic properties and behavior of the material.

3. What is the correct equation for plotting the silicene band structure in the Γ→M→K→Γ path?

The correct equation for plotting the silicene band structure in the Γ→M→K→Γ path is the tight-binding model, which takes into account the interactions between neighboring silicon atoms and their energy levels.

4. How is the band structure of silicene different from that of graphene?

The band structure of silicene differs from that of graphene due to the presence of spin-orbit coupling, which breaks the symmetry between the two spin states. This results in a band gap in the silicene band structure, unlike in graphene where the bands intersect at the Dirac point.

5. How can studying the silicene band structure in the Γ→M→K→Γ path help in the development of new technologies?

Studying the silicene band structure in the Γ→M→K→Γ path can provide valuable insights into the electronic properties of this material, which can then be utilized in the development of new technologies such as flexible electronics, sensors, and quantum devices.

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