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kp_4bands_Luttinger_Rosencher_f.m
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kp_4bands_Luttinger_Rosencher_f.m
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function[E]=kp_4bands_Luttinger_Rosencher_f(k_list, g1, g2, g3)
% Emmanuel Rosencher
% "Optoelectronics"
% Complement to Chapter 5C: "Kane’s k · p method", page 239
% https://www.cambridge.org/core/books/optoelectronics/86B6621671230A798D5BFBE24266EE3F
% https://www.amazon.fr/Optoelectronics-Emmanuel-Rosencher/dp/0521778131
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%% 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+ = 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);
Hh = -H0*(g1+g2)*(kx^2+ky^2) -H0*(g1-2*g2)*kz^2;
Hl = -H0*(g1-g2)*(kx^2+ky^2) -H0*(g1+2*g2)*kz^2;
b = H0*2*sqrt(3)*g3*(kx-1i*ky)*kz;
c = H0* sqrt(3)* (g2*(kx^2-ky^2)-2i*g3*kx*ky);
% HH LH LH HH
H=[
Hh c b 0 % HH
c' Hl 0 -b % LH
b' 0 Hl c % LH
0 -b' c' Hh % HH
];
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
E(:,i) = eig(H)/e;
end
end