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kp_8bands_Kane_DKK_f.m
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kp_8bands_Kane_DKK_f.m
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function[E]=kp_8bands_Kane_DKK_f(k_list, Eg, EP, Dso)
% DKK model: Dresselhaus, Kip and Kittel
% Calin Galeriu
% PhD thesis: "k.p Theory of semiconductor nanostructures" (2005)
% Chapter 3, page 26
% Download:
% https://web.wpi.edu/Pubs/ETD/Available/etd-120905-095359/unrestricted/cgaleriu.pdf
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%% 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 %%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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);
Hdiag = H0*k^2 + [Eg -Dso/3 -Dso/3 -Dso/3 ];
H4=[
0 1i*P*kx 1i*P*ky 1i*P*kz
0 0 0 0
0 0 0 0
0 0 0 0
];
HH4 = H4' + H4 + diag(Hdiag);
Hso=[
0 0 0 0 0 0 0 0
0 0 1 0 0 0 0 1i
0 -1 0 0 0 0 0 1
0 0 0 0 0 -1i -1 0
0 0 0 0 0 0 0 0
0 0 0 -1i 0 0 -1 0
0 0 0 1 0 1 0 0
0 1i -1 0 0 0 0 0
];
H=[HH4 zeros(4,4) ; zeros(4,4) HH4] + Hso*Dso/(3i);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
E(:,i) = eig(H)/e ;
end
end