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kp_6bands_Luttinger_DKK_strain_f.m
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kp_6bands_Luttinger_DKK_strain_f.m
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function[E]=kp_6bands_Luttinger_DKK_strain_f(k_list, Dso, g123, av, bv, dv, exx, ezz)
% 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
% Stefan Birner (Nextnano)
% PhD thesis: "Modeling of semiconductor nanostructures and semiconductor-electrolyte interfaces" (2011)
% Chapter3, page 36: "Multi-band k.p envelope function approximation"
% Download:
% https://mediatum.ub.tum.de/doc/1084806/1084806.pdf
% https://www.nextnano.com/downloads/publications/PhD_thesis_Stefan_Birner_TUM_2011_WSIBook.pdf
% Thomas B. Bahder,
% "Eight-band k.p model of strained zinc-blende crystals", PRB 41, 11992 (1990)
% https://journals.aps.org/prb/abstract/10.1103/PhysRevB.41.11992
% https://www.researchgate.net/publication/235532200_Eight-band_k_p_model_of_strained_zinc-blende_crystals
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%% 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;
g1=g123(1);
g2=g123(2);
g3=g123(3);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
eyy = exx;
exy = 0; eyx=0;
ezx = 0; exz=0;
eyz = 0; ezy=0;
ee = exx+eyy+ezz;
av = abs(av)*e;
bv = abs(bv)*e;
dv = abs(dv)*e;
l = av-2*bv;
m = av+bv;
n = sqrt(3)*dv;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
L = H0*(-1-g1-4*g2);
M = H0*(-1-g1+2*g2);
N = -H0*6*g3;
B = H0*0;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%% 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 -Dso/3*ones(1,6);
HR=[
L*kx^2+M*(ky^2+kz^2) N*kx*ky N*kx*kz
N*kx*ky L*ky^2+M*(kx^2+kz^2) N*ky*kz
N*kx*kz N*ky*kz L*kz^2+M*(kx^2+ky^2)
];
Hso=[
0 1 0 0 0 1i
-1 0 0 0 0 1
0 0 0 -1i -1 0
0 0 -1i 0 -1 0
0 0 1 1 0 0
1i -1 0 0 0 0
];
Hs=[
l*exx+m*(eyy+ezz) n*exy n*exz
n*exy l*eyy+m*(exx+ezz) n*eyz
n*exz n*eyz l*ezz+m*(exx+eyy)
];
H = diag(Hdiag) + Hso*Dso/(3i) + [HR zeros(3,3) ; zeros(3,3) HR] + [Hs zeros(3,3) ; zeros(3,3) Hs];
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
E(:,i) = eig(H)/e ;
end
end