ConradAveraging said:
Could you elaborate a little more? Is your question about the physics of tight binding calculations or about implementing tight binding calculations in MATLAB?
implementing tight binding calculation in matlab.
matlab cose in the following path: Γ→K→M→Γ is:
Nk=20;
t=-2.550;
for ik=1:Nk+1
k_x=2*pi*(ik-1)/Nk*0;
k_y=2*pi*(ik-1)/Nk*0.667;
H=zeros(2);
H(1,2)=t*(exp(-1i*k_x/sqrt(3))+exp(1i/(2*sqrt(3))*((k_x+sqrt(3)*k_y)))+exp(1i/(2*sqrt(3))*(k_x-sqrt(3)*k_y)));
H(2,1)=t*(exp(1i*k_x/sqrt(3))+exp(-1i/(2*sqrt(3))*((k_x+sqrt(3)*k_y)))+exp(-1i/(2*sqrt(3))*(k_x-sqrt(3)*k_y)));
[V,D]=eig(H)
E_1(ik)=D(1,1)
E_2(ik)=D(2,2)
end
plot(E_1)
hold on
plot(E_2)
Nk=20;
t=-2.550;
for ik=21:Nk+10
k_x=2*pi*(ik-1)/Nk*0;
k_y=2*pi*(ik-1)/Nk*-0.667;
H=zeros(2);
H(1,2)=t*(exp(-1i*k_x/sqrt(3))+exp(1i/(2*sqrt(3))*((k_x+sqrt(3)*k_y)))+exp(1i/(2*sqrt(3))*(k_x-sqrt(3)*k_y)));
H(2,1)=t*(exp(1i*k_x/sqrt(3))+exp(-1i/(2*sqrt(3))*((k_x+sqrt(3)*k_y)))+exp(-1i/(2*sqrt(3))*(k_x-sqrt(3)*k_y)));
[V,D]=eig(H)
E_1(ik)=D(1,1)
E_2(ik)=D(2,2)
end
plot(E_1)
hold on
plot(E_2)
Nk=20;
t=-2.550;
for ik=31:Nk+20
k_x=2*pi*(ik-1)/Nk*0.557;
k_y=2*pi*(ik-1)/Nk*0;
H=zeros(2);
H(1,2)=t*(exp(-1i*k_x/sqrt(3))+exp(1i/(2*sqrt(3))*((k_x+sqrt(3)*k_y)))+exp(1i/(2*sqrt(3))*(k_x-sqrt(3)*k_y)));
H(2,1)=t*(exp(1i*k_x/sqrt(3))+exp(-1i/(2*sqrt(3))*((k_x+sqrt(3)*k_y)))+exp(-1i/(2*sqrt(3))*(k_x-sqrt(3)*k_y)));
[V,D]=eig(H)
E_1(ik)=D(1,1)
E_2(ik)=D(2,2)
end
plot(E_1)
hold on
plot(E_2)
but in the following path: K→Γ→M→K not true.
Nk is The number of points between two points K and Γ.