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kp_4bands_Luttinger_Fishman_f.m
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kp_4bands_Luttinger_Fishman_f.m
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function[E]=kp_4bands_Luttinger_Fishman_f(k_list, g1, g2, g3)
% Guy Fishman
% "Semi-Conducteurs: les Bases de la Theorie k.p " (2010)
% 3.3.5/ L’hamiltonien projeté sur G8 : l’hamiltonien H4 de Luttinger-Kohn
% page 175
% 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; %% charge de l electron [Coulomb]
m0=9.10938188E-31; %% electron mass [kg]
H0=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);
AA = H0*g2*( 2*kz^2 - kx.^2 - ky.^2 );
BB = H0*2*sqrt(3)*g3*kz*(kx - 1i*ky) ;
CC = H0*sqrt(3)*(g2*(kx^2-ky^2)-2i*g3*kx*ky);
Hdiag= -g1*H0*k^2*[1 1 1 1];
% HH LH LH HH
H=[
AA BB CC 0 % HH
BB' -AA 0 CC % LH
CC' 0 -AA -BB % LH
0 CC' -BB' AA % HH
];
H = H + diag(Hdiag);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
E(:,i) = eig(H)/e;
end
end