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kp_6bands_Luttinger_strain_f.m
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kp_6bands_Luttinger_strain_f.m
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function[E]=kp_6bands_Luttinger_strain_f(k_list, Dso, g123, av, bv, dv, exx, ezz);
% Calvin Yi-Ping Chao and Shun Lien Chuang
% PHYSICAL REVIEW B VOLUME 46, NUMBER 7, (1992)
% "Spin-orbit-coupling effects on the valence-band structure of strained semiconductor quantum wells"
% Warren James Elder
% PhD thesis: "Semi-empirical modelling of SiGe hetero-structures" (2012)
% Chapter3: "The k.p method" page 68
% https://spiral.imperial.ac.uk:8443/handle/10044/1/9816
% Maxi Scheinert
% PhD thesis: "Optical Pumping: A Possible Approach towards a SiGe Quantum Cascade Laser"
% page 18
% https://core.ac.uk/download/pdf/20642119.pdf
% https://www.e-helvetica.nb.admin.ch/directAccess?callnumber=rero-004-104096
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%% 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) ;
Dso=Dso*e;
g1=g123(1);
g2=g123(2);
g3=g123(3);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
eyy = exx;
exy = 0;
ezx = 0;
eyz = 0;
ee = exx+eyy+ezz;
av = abs(av)*e;
bv = abs(bv)*e;
dv = abs(dv)*e;
Pe = av * ee;
Qe = -bv * (exx-ezz);
Re = sqrt(3)/2 * bv*(exx-eyy) - 1i*dv*exy;
Se = -dv * (ezx - 1i*eyz);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%% 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);
Pk = -H0 * g1 * k^2;
Qk = -H0 * g2 *(kx^2 + ky^2 - 2*kz^2);
Rk = H0 * sqrt(3) * (g2*(kx^2-ky^2) - 2i*g3*kx*ky );
Sk = H0 *2*sqrt(3) * g3*(kx-1i*ky)*kz;
P = Pk + Pe;
Q = Qk + Qe;
R = Rk + Re;
S = Sk + Se;
Hdiag = [ P+Q P-Q P-Q P+Q -Dso+P -Dso+P ];
% HH LH LH HH SO SO
H=[
0 -S R 0 -sqrt(1/2)*S sqrt(2) *R % HH
0 0 0 R -sqrt(2) *Q sqrt(3/2)*S % LH
0 0 0 S sqrt(3/2)*S' sqrt(2) *Q % LH
0 0 0 0 -sqrt(2) *R' -sqrt(1/2)*S' % HH
0 0 0 0 0 0 % SO
0 0 0 0 0 0 % SO
];
H=H'+H+diag(Hdiag);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
E(:,i) = eig(H)/e;
end
end