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kp_8bands_Kane_Bastard_f.m
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kp_8bands_Kane_Bastard_f.m
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function[E]=kp_8bands_Kane_Bastard_f(k_list, Eg, EP, Dso)
% Gerard Bastard
% "Wave mechanics applied to semiconductor heterostructures" (1992)
% page 43
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%% Constants %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
h=6.62606896E-34; %% Planck constant [J.s]
hbar=h/(2*pi);
e=1.602176487E-19; %% electron charge [Coulomb]
m0=9.10938188E-31; %% electron mass [kg]
H0=hbar^2/(2*m0) ;
Dso = Dso*e;
Eg = Eg*e;
EP = EP*e;
P = sqrt(EP*hbar^2/(2*m0)) ;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%% Building of the Hamiltonien %%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%k+ = 1/sqrt(2)*( kx + 1i*ky )
%k- = 1/sqrt(2)*( kx - 1i*ky )
for i=1:length(k_list(:,1))
kx=k_list(i,1);
ky=k_list(i,2);
kz=k_list(i,3);
k=sqrt(kx.^2 + ky.^2 + kz.^2);
kpp = sqrt(1/2)*( kx + 1i*ky );
kmm = sqrt(1/2)*( kx - 1i*ky );
%%%%%%%%%%%%%%%%%%%%%% Bastard filling method %%%%%%%%%%%%%%%%%%%%%%%%%%%%%
H=zeros(8,8);
Hdiag = [ Eg+H0*k^2 H0*k^2 H0*k^2 H0*k^2-Dso Eg+H0*k^2 H0*k^2 H0*k^2 H0*k^2-Dso ];
% Ec LH HH SO EC LH HH SO
H=[
0 -sqrt(2/3)*P*kz P*kpp sqrt(1/3)*P*kz 0 -sqrt(1/3)*P*kmm 0 -sqrt(2/3)*P*kmm % EC
0 0 0 0 sqrt(1/3)*P*kmm 0 0 0 % LH
0 0 0 0 0 0 0 0 % HH
0 0 0 0 sqrt(2/3)*P*kmm 0 0 0 % SO
0 0 0 0 0 -sqrt(2/3)*P*kz P*kmm sqrt(1/3)*P*kz % EC
0 0 0 0 0 0 0 0 % LH
0 0 0 0 0 0 0 0 % HH
0 0 0 0 0 0 0 0 % SO
];
H=H'+H+diag(Hdiag);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
E(:,i) = eig(H)/e;
end
end