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kp_8bands_Luttinger_Fishman_strain_f.m
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kp_8bands_Luttinger_Fishman_strain_f.m
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function[E]=kp_8bands_Luttinger_Fishman_strain_f(k_list, Eg, EP, Dso, F, g123, ac, av, bv, dv, exx, ezz)
% Guy Fishman
% "Semi-Conducteurs: les Bases de la Theorie k.p " (2010)
% 3.3.4 L’hamiltonien projeté sur {G6 ; G8 ; G7} : l’hamiltonien H8 de Pidgeon-Brown
% page 169
% 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) ;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Dso = Dso*e;
Eg = Eg*e;
EP = EP*e;
P = sqrt(EP*hbar^2/(2*m0)) ;
% gc= 1+2*F + EP*(Eg+2*Dso/3) / (Eg*(Eg+Dso)) ; % =1/mc electron in CB eff mass
% renormalization of the paramter from 6x6kp to 8x8kp
% gc=gc-EP/3*( 2/Eg + 1/(Eg+Dso) );
gc = 1+2*F;
g1 = g123(1)-EP/(3*Eg);
g2 = g123(2)-EP/(6*Eg);
g3 = g123(3)-EP/(6*Eg);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Fishman is using the Pidgeon Brown Hamiltonian...
% It uses 3 additionnal parameters
% If we set thoses parameter = Luttinger parameters, the results are exactly
% the same as for the other models like Pistol or DKK
%gD1=gD1-EP/(3*(Eg+Dso));
%gD2=gD2-EP/12*(1/Eg+1/(Eg+Dso));
%gD3=gD3-EP/12*(1/Eg+1/(Eg+Dso));
gD1=g1;
gD2=g2;
gD3=g3;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
eyy = exx;
exy = 0; eyx=0;
ezx = 0; exz=0;
eyz = 0; ezy=0;
ee = exx+eyy+ezz;
ac = -abs(ac)*e;
av = +abs(av)*e;
bv = +abs(bv)*e;
dv = +abs(dv)*e;
Hs=[
ac*ee 0 0 0 0 0 0 0
0 ac*ee 0 0 0 0 0 0
0 0 av*ee-bv*(exx-ezz) 0 0 0 0 0
0 0 0 av*ee+bv*(exx-ezz) 0 0 sqrt(2)*bv*(exx-ezz) 0
0 0 0 0 av*ee+bv*(exx-ezz) 0 0 -sqrt(2)*bv*(exx-ezz)
0 0 0 0 0 av*ee-bv*(exx-ezz) 0 0
0 0 0 sqrt(2)*bv*(exx-ezz) 0 0 av*ee 0
0 0 0 0 -sqrt(2)*bv*(exx-ezz) 0 0 av*ee
];
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%% 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);
kpp = kx + 1i*ky;
kmm = kx - 1i*ky;
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);
AA_D = H0*gD2*( 2*kz^2 - kx.^2 - ky.^2 );
BB_D = H0*2*sqrt(3)*gD3*kz*(kx - 1i*ky) ;
CC_D = H0*sqrt(3)*(gD2*(kx^2-ky^2)-2i*gD3*kx*ky);
Hdiag = -H0*k^2*[-gc -gc g1 g1 g1 g1 gD1 gD1] + [ +Eg +Eg +AA -AA -AA +AA -Dso -Dso ];
% Ec- Ec+ HH+ LH+ LH- HH- SO+ SO-
H=[
0 0 -sqrt(1/2)*P*kpp sqrt(2/3)*P*kz sqrt(1/6)*P*kmm 0 sqrt(1/3)*P*kz sqrt(1/3)*P*kmm % Ec+
0 0 0 -sqrt(1/6)*P*kpp sqrt(2/3)*P*kz sqrt(1/2)*P*kmm sqrt(1/3)*P*kpp -sqrt(1/3)*P*kz % Ec-
0 0 0 BB CC 0 sqrt(1/2)*BB_D sqrt(2) *CC_D % HH+
0 0 0 0 0 CC -sqrt(2) *AA_D -sqrt(3/2)*BB_D % LH+
0 0 0 0 0 -BB -sqrt(3/2)*BB_D' sqrt(2) *AA_D % LH-
0 0 0 0 0 0 -sqrt(2) *CC_D' sqrt(1/2)*BB_D' % HH-
0 0 0 0 0 0 0 0 % SO+
0 0 0 0 0 0 0 0 % SO-
];
H=H'+H+diag(Hdiag);
H=H+Hs;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
E(:,i) = eig(H)/e;
end
end