# Band structure silicene

• A
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

## Answers and Replies

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).