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super_cell_3D_graph.m
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super_cell_3D_graph.m
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clc;
clear;
%n=1
% eigenvector1=[ 0.40675,-0.01097];
% eigenvector2=[0.27679, 0.06658];
% eigenvector3=[-0.35016,-0.07603];
% eigenvector4=[0.24530,-0.05126];
% eigenvector5=[-0.21638, 0.37472];
% eigenvector6=[-0.38793,-0.12720];
% eigenvector7=[0.13743, 0.05263];
% eigenvector8=[-0.43143,-0.02241];
%n=2
% eigenvector1=[ 0.61184, 0.00000];
% eigenvector2=[0.01321,-0.01577];
% eigenvector3=[0.00330, 0.00496];
% eigenvector4=[0.43288, 0.00000];
% eigenvector5=[0.16706,-0.18675];
% eigenvector6=[0.23439, 0.08745];
% eigenvector7=[0.31740, 0.07764];
% eigenvector8=[0.45351, 0.00000];
%n=3
% eigenvector1=[ 0.39865, 0.01291];
% eigenvector2=[-0.10592,-0.43757];
% eigenvector3=[0.10967, 0.03476];
% eigenvector4=[-0.07810, 0.23798];
% eigenvector5=[-0.21630,-0.37484];
% eigenvector6=[-0.07715, 0.33159];
% eigenvector7=[-0.34332,-0.19770];
% eigenvector8=[-0.30120,-0.10671];
%n=4
eigenvector1=[ 0.08748,-0.16745];
eigenvector2=[0.04215,-0.39644];
eigenvector3=[0.38092, 0.18797];
eigenvector4=[-0.21632, 0.37471];
eigenvector5=[0.07816, 0.23797];
eigenvector6=[0.13073,-0.38546];
eigenvector7=[0.36389, 0.21275];
eigenvector8=[-0.14652,-0.10090];
%n=5
% eigenvector1=[0.41863,-0.00185];
% eigenvector2=[-0.14442, 0.33944];
% eigenvector3=[0.24709, 0.05119];
% eigenvector4=[-0.16689,-0.18672];
% eigenvector5=[0.43279, 0.00000];
% eigenvector6=[-0.00366,-0.37932];
% eigenvector7=[-0.42887,-0.01025];
% eigenvector8=[-0.17432, 0.12905];
%n=6
% eigenvector1=[ 0.10700, 0.17765];
% eigenvector2=[-0.03470, 0.23175];
% eigenvector3=[0.51545,-0.10705];
% eigenvector4=[-0.21632,-0.37472];
% eigenvector5=[-0.24516,-0.05125];
% eigenvector6=[-0.01612, 0.30600];
% eigenvector7=[0.45222, 0.00000];
% eigenvector8=[-0.22936, 0.15488];
%n=7
% eigenvector1=[ -0.01091,-0.00081];
% eigenvector2=[0.27097,-0.08232];
% eigenvector3=[0.54283, 0.00000];
% eigenvector4=[0.24514,-0.05125];
% eigenvector5=[-0.21636, 0.37467];
% eigenvector6=[-0.26822, 0.03972];
% eigenvector7=[-0.36132,-0.08254];
% eigenvector8=[0.39799,-0.07634];
%n=8
% eigenvector1=[ -0.21629,-0.01181];
% eigenvector2=[0.53452, 0.00000];
% eigenvector3=[0.18937,-0.08101];
% eigenvector4=[0.43270,-0.00000];
% eigenvector5=[0.16697,-0.18665];
% eigenvector6=[0.42174, 0.00000];
% eigenvector7=[-0.09360,-0.04777];
% eigenvector8=[-0.41993, 0.09873];
data1=importdata("k=( 0.849, 0.000, 0.000)_1BS.dat");
data2=importdata("k=( 0.849, 0.000, 0.000)_2BS.dat");
data3=importdata("k=( 0.849, 0.000, 0.000)_3BS.dat");
data4=importdata("k=( 0.849, 0.000, 0.000)_4BS.dat");
data5=importdata("k=( 0.849, 0.000, 0.000)_5BS.dat");
data6=importdata("k=( 0.849, 0.000, 0.000)_6BS.dat");
data7=importdata("k=( 0.849, 0.000, 0.000)_7BS.dat");
data8=importdata("k=( 0.849, 0.000, 0.000)_8BS.dat");
isovalue_AbsSqr=0.45*0.0047;
tolerance_AbsSqr=0.0018;
isovalue_AbsReIm=0.4*0.0685;
tolerance_AbsReIm=0.013;
%n=4 part
flag1=0;
for i=1:+1:length(data1.data(:,1))
if data1.data(i,1)<1.9 && data1.data(i,1)>-1.76 && data1.data(i,2)>1.38 && data1.data(i,2)<7.17 && data1.data(i,3)<12.5 && data1.data(i,3)>9
flag1=flag1+1;
psi1(1,flag1)=(eigenvector1(1)+eigenvector1(2)*1i)*(data1.data(i,4)+data1.data(i,5)*1i)+ ...
(eigenvector2(1)+eigenvector2(2)*1i)*(data2.data(i,4)+data2.data(i,5)*1i)+ ...
(eigenvector3(1)+eigenvector3(2)*1i)*(data3.data(i,4)+data3.data(i,5)*1i)+ ...
(eigenvector4(1)+eigenvector4(2)*1i)*(data4.data(i,4)+data4.data(i,5)*1i)+ ...
(eigenvector5(1)+eigenvector5(2)*1i)*(data5.data(i,4)+data5.data(i,5)*1i)+ ...
(eigenvector6(1)+eigenvector6(2)*1i)*(data6.data(i,4)+data6.data(i,5)*1i)+ ...
(eigenvector7(1)+eigenvector7(2)*1i)*(data7.data(i,4)+data7.data(i,5)*1i)+ ...
(eigenvector8(1)+eigenvector8(2)*1i)*(data8.data(i,4)+data8.data(i,5)*1i);
x1(1,flag1)=data1.data(i,1);
y1(1,flag1)=data1.data(i,2);
z1(1,flag1)=data1.data(i,3);
else
flag1=flag1+0;
end
end
figure(1)
for i=1:+1:flag1
if abs(real(psi1(1,i)))<(isovalue_AbsReIm+tolerance_AbsReIm) && abs(real(psi1(1,i)))>(isovalue_AbsReIm-tolerance_AbsReIm)
if real(psi1(1,i))>0
plot3(x1(1,i),y1(1,i),z1(1,i),'r.','MarkerSize',15);hold on;
elseif real(psi1(1,i))<0
plot3(x1(1,i),y1(1,i),z1(1,i),'b.','MarkerSize',15);hold on;
end
end
end
plot_carbon_atoms
xlabel('x(Å)');
ylabel('y(Å)');
zlabel('z(Å)');
title('(n=4)Re(Ψ) at K point');
axis([-4 4 0 8])
grid on
figure(2)
for i=1:+1:flag1
if abs(imag(psi1(1,i)))<(isovalue_AbsReIm+tolerance_AbsReIm) && abs(imag(psi1(1,i)))>(isovalue_AbsReIm-tolerance_AbsReIm)
if imag(psi1(1,i))>0
plot3(x1(1,i),y1(1,i),z1(1,i),'r.','MarkerSize',15);hold on;
elseif imag(psi1(1,i))<0
plot3(x1(1,i),y1(1,i),z1(1,i),'b.','MarkerSize',15);hold on;
end
end
end
plot_carbon_atoms
xlabel('x(Å)');
ylabel('y(Å)');
zlabel('z(Å)');
title('(n=4)Im(Ψ) at K point');
axis([-4 4 0 8])
grid on
figure(3)
for i=1:+1:flag1
if (sqrt(real(psi1(1,i))^2+imag(psi1(1,i))^2))^2<(isovalue_AbsSqr+tolerance_AbsSqr) && (sqrt(real(psi1(1,i))^2+imag(psi1(1,i))^2))^2>(isovalue_AbsSqr-tolerance_AbsSqr)
if sqrt(real(psi1(1,i))^2+imag(psi1(1,i))^2)>0
plot3(x1(1,i),y1(1,i),z1(1,i),'r.','MarkerSize',15);hold on;
elseif sqrt(real(psi1(1,i))^2+imag(psi1(1,i))^2)<0
plot3(x1(1,i),y1(1,i),z1(1,i),'b.','MarkerSize',15);hold on;
end
end
end
plot_carbon_atoms
xlabel('x(Å)');
ylabel('y(Å)');
zlabel('z(Å)');
title('(n=4)|Ψ|^2 at K point');
axis([-4 4 0 8])
grid on
function plot_carbon_atoms
a0=2.4669;
a1=a0*[0.5,sqrt(3)/2,0];
a2=a0*[-0.5,sqrt(3)/2,0];
%the carbon atoms in the unit cell
X1(1)=(a1(1)+a2(1))/3;
Y1(1)=(a1(2)+a2(2))/3;
X1(2)=(a1(1)+a2(1))/3*2;
Y1(2)=(a1(2)+a2(2))/3*2;
Z1(1)=10.25;
Z1(2)=10.25;
X2(1)=a1(1)/3+4*a2(1)/3;
Y2(1)=a1(2)/3+4*a2(2)/3;
X2(2)=2*a1(1)/3+5*a2(1)/3;
Y2(2)=2*a1(2)/3+5*a2(2)/3;
Z2(1)=10.25;
Z2(2)=10.25;
X3(1)=4*a1(1)/3+a2(1)/3;
Y3(1)=4*a1(2)/3+a2(2)/3;
X3(2)=5*a1(1)/3+2*a2(1)/3;
Y3(2)=5*a1(2)/3+2*a2(2)/3;
Z3(1)=10.25;
Z3(2)=10.25;
X4(1)=4*a1(1)/3+4*a2(1)/3;
Y4(1)=4*a1(2)/3+4*a2(2)/3;
X4(2)=5*a1(1)/3+5*a2(1)/3;
Y4(2)=5*a1(2)/3+5*a2(2)/3;
Z4(1)=10.25;
Z4(2)=10.25;
plot3(X1,Y1,Z1,'k.','Markersize',80);hold on;
plot3(X2,Y2,Z2,'k.','Markersize',80);hold on;
plot3(X3,Y3,Z3,'k.','Markersize',80);hold on;
plot3(X4,Y4,Z4,'k.','Markersize',80);hold on;
end