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

Click For Summary
SUMMARY

The discussion focuses on plotting the band structure of silicene along the path Γ→M→K→Γ using a tight binding model. The user provides specific lattice vectors and equations necessary for calculating the k-points in the Brillouin zone. Key parameters include a lattice constant of 3.86 Å and a bond length of 2.28 Å. The provided MATLAB code outlines the steps to compute the k-points and prepare for plotting the band structure.

PREREQUISITES
  • Understanding of tight binding models in solid-state physics
  • Familiarity with MATLAB programming for numerical computations
  • Knowledge of band structure concepts and Brillouin zone paths
  • Basic understanding of lattice vectors and k-point calculations
NEXT STEPS
  • Learn how to implement the tight binding model in MATLAB for different materials
  • Research the significance of k-points in band structure calculations
  • Explore advanced plotting techniques for visualizing band structures in MATLAB
  • Study the effects of varying lattice constants on band structure properties
USEFUL FOR

Researchers and students in condensed matter physics, materials science, and computational physics, particularly those interested in the electronic properties of 2D materials like silicene.

anahita
Messages
27
Reaction score
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
 
Physics news on Phys.org
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?
 
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).