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kp_8bands_Luttinger_Pistol1_strain_f.m
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kp_8bands_Luttinger_Pistol1_strain_f.m
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function[E]=kp_8bands_Luttinger_Pistol1_strain_f(k_list, Eg, EP, Dso, F, g123, ac, av, bv, dv, exx, ezz)
% 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
% 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
% Guy Fishman
% "Semi-Conducteurs: les Bases de la Theorie k.p " (2010)
% 4.5.4 L’hamiltonien de Bir-Pikus
% 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;
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 = g123(1)-EP/(3*Eg);
g2 = g123(2)-EP/(6*Eg);
g3 = g123(3)-EP/(6*Eg);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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 0 -sqrt(2)*bv*(exx-ezz)
0 0 0 0 av*ee+bv*(exx-ezz) 0 sqrt(2)*bv*(exx-ezz) 0
0 0 0 0 0 av*ee-bv*(exx-ezz) 0 0
0 0 0 0 sqrt(2)*bv*(exx-ezz) 0 av*ee 0
0 0 0 -sqrt(2)*bv*(exx-ezz) 0 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;
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;
% Ec- Ec+ HH+ LH+ LH- HH- SO- SO+
Hdiag = [A A P+Q P-Q P-Q P+Q -Dso+P -Dso+P];
H=[
0 0 0 T'+V' sqrt(2)*(W-U) -sqrt(3)*(T-V) (W-U) sqrt(2)*(T'+V') % Ec-
0 0 -sqrt(3)*(T'+V') sqrt(2)*(W-U) (T-V) 0 -sqrt(2)*(T-V) W'+U % Ec+
0 0 0 -S R 0 -sqrt(2) *R sqrt(1/2)*S % HH+
0 0 0 0 0 R sqrt(3/2)*S sqrt(2) *Q % LH+
0 0 0 0 0 S -sqrt(2) *Q sqrt(3/2)*S' % LH-
0 0 0 0 0 0 sqrt(1/2)*S' sqrt(2) *R' % 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