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kp_8bands_Luttinger_Pistol_f.m
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kp_8bands_Luttinger_Pistol_f.m
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function[E]=kp_8bands_Luttinger_Pistol_f(k_list, Eg, EP, Dso, F, g1, g2, g3)
% Craig E. Pryor and M. E. Pistol
% "Atomistic k.p theory", Journal of Applied Physics 118, 225702 (2015);
% https://doi.org/10.1063/1.4936170
% https://www.researchgate.net/publication/273067732_Atomistic_kp_theory
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%% 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;
P0 = sqrt(EP*hbar^2/(2*m0)) ; % Here I use "P0" instead of "P" because it uses "P" inside the H for something else
% 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 = g1-EP/(3*Eg);
g2 = g2-EP/(6*Eg);
g3 = g3-EP/(6*Eg);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%% 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;
B = 0;
A = Eg + gc*H0 * k^2;
U = sqrt(1/3) * P0 * kz;
V = sqrt(1/6) * P0 * kmm;
W = 1i*sqrt(1/3)*B * kx*ky;
T = sqrt(1/6)*B * kz*kpp;
P = -g1*H0 * k^2;
Q = -g2*H0 *(kx^2 + ky^2 - 2*kz^2);
R = -H0 * sqrt(3) * (g2*(kx^2-ky^2) - 2i*g3*kx*ky );
S = H0 *2*sqrt(3) * g3*(kx-1i*ky)*kz;
Hdiag = [A A P-Q P+Q P+Q P-Q -Dso+P -Dso+P];
% Ec Ec LH HH HH LH SO SO
H=[
0 0 T'+V' 0 -sqrt(3)*(T-V) sqrt(2)*(W-U) (W-U) sqrt(2)*(T'+V') % Ec
0 0 sqrt(2)*(W-U) -sqrt(3)*(T'+V') 0 (T-V) -sqrt(2)*(T-V) W'+U % Ec
0 0 0 -S' R 0 sqrt(3/2)*S sqrt(2) *Q % LH
0 0 0 0 0 R -sqrt(2) *R sqrt(1/2)*S % HH
0 0 0 0 0 S' sqrt(1/2)*S' sqrt(2) *R' % HH
0 0 0 0 0 0 -sqrt(2) *Q sqrt(3/2)*S' % LH
0 0 0 0 0 0 0 0 % SO
0 0 0 0 0 0 0 0 % SO
];
H=H'+H+diag(Hdiag);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
E(:,i) = eig(H)/e;
end
end