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kp_8bands_Kane_Fishman_f.m
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function[E]=kp_8bands_Kane_Fishman_f(k_list, Eg, EP, Dso)
% Guy Fishman
% "Semi-Conducteurs: les Bases de la Theorie k.p " (2010)
% 3.3.2/ L’hamiltonien à l’intérieur de {G6 ; G8 ; G7} ou hamiltonien de Kane
% page 152
% https://www.amazon.fr/Semi-Conducteurs-Bases-Theorie-K-P-Fishman/dp/2730214976/ref=sr_1_fkmr1_1?ie=UTF8&qid=1548234034&sr=8-1-fkmr1&keywords=guy+fishman+kp
% https://www.abebooks.fr/semi-conducteurs-bases-th%C3%A9orie-k.p-Fishman-ECOLE/30091636895/bd
% https://www.decitre.fr/livres/semi-conducteurs-les-bases-de-la-theorie-k-p-9782730214971.html
% https://www.unitheque.com/Livre/ecole_polytechnique/Semi_conducteurs_les_bases_de_la_theorie_K.p-35055.html
% https://www.eyrolles.com/Sciences/Livre/semi-conducteurs-les-bases-de-la-theorie-k-p-9782730214971/
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%% 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+ = kx + 1i*ky
%k- = 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 = kx + 1i*ky;
kmm = kx - 1i*ky;
%%%%%%%%%%%%%%%%%%%%%% Fishman filling method %%%%%%%%%%%%%%%%%%%%%%%%%%%%%
H=zeros(8,8);
Hdiag = H0*k^2*ones(1,8) + [ Eg Eg 0 0 0 0 -Dso -Dso ];
% Ec EC HH LH LH HH SO SO
H=[
0 0 -sqrt(1/2)*P*kpp sqrt(2/3)*P*kz sqrt(1/6)*P*kmm 0 sqrt(1/3)*P*kz sqrt(1/3)*P*kmm % EC
0 0 0 -sqrt(1/6)*P*kpp sqrt(2/3)*P*kz sqrt(1/2)*P*kmm sqrt(1/3)*P*kpp -sqrt(1/3)*P*kz % EC
0 0 0 0 0 0 0 0 % HH
0 0 0 0 0 0 0 0 % LH
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
0 0 0 0 0 0 0 0 % SO
];
H=H'+H+diag(Hdiag);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
E(:,i) = eig(H)/e;
end
end