-
Notifications
You must be signed in to change notification settings - Fork 7
/
kp_6bands_Luttinger_Fishman_f.m
78 lines (58 loc) · 3 KB
/
kp_6bands_Luttinger_Fishman_f.m
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
function[E]=kp_6bands_Luttinger_Fishman_f(k_list, Dso, g1, g2, g3, gD1, gD2, gD3)
% Guy Fishman
% "Semi-Conducteurs: les Bases de la Theorie k.p " (2010)
% 3.3.6/ L’hamiltonien projeté sur {G8 ; G7} : l’hamiltonien 6 × 6 de Luttinger-Kohn ou hamiltonien H6
% page 179
% 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;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 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=g1;
gD2=g2;
gD3=g3;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%% 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);
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*[g1 g1 g1 g1 gD1 gD1] +[ +AA -AA -AA +AA -Dso -Dso ];
% HH LH LH HH SO SO
H=[
0 BB CC 0 sqrt(1/2)*BB_D sqrt(2) *CC_D % HH
0 0 0 CC -sqrt(2) *AA_D -sqrt(3/2)*BB_D % LH
0 0 0 -BB -sqrt(3/2)*BB_D' sqrt(2) *AA_D % LH
0 0 0 0 -sqrt(2) *CC_D' sqrt(1/2)*BB_D' % 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