-
Notifications
You must be signed in to change notification settings - Fork 1
/
kp_8bands_Luttinger_Pistol2_strain_f.m
129 lines (100 loc) · 4.42 KB
/
kp_8bands_Luttinger_Pistol2_strain_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
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
function[E]=kp_8bands_Luttinger_Pistol2_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
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%% 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);
B = 0;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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;
Ae = ac * ee;
Pe = av * ee;
Qe = -bv * (exx-ezz);
Re = sqrt(3)/2 * bv*(exx-eyy) - 1i*dv*exy;
Se = -dv * (ezx - 1i*eyz);
We = 1i*sqrt(1/3)*B*exy;
Te = sqrt(1/6)*B*(exz + 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);
kpp = kx + 1i*ky;
kmm = kx - 1i*ky;
Ak = Eg + gc*H0 * k^2;
Uk = sqrt(1/3) * P0 * kz;
Vk = sqrt(1/6) * P0 * kmm;
Wk = 1i*sqrt(1/3)*B * kx*ky;
Tk = sqrt(1/6)*B * kz*kpp;
Pk = -g1*H0 * k^2;
Qk = -g2*H0 *(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;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Here are the 2 terms that make it slightly different from Pistl-1 and Fishman Hamiltonian
% Removing those 2 terms gives exactly the same results
Ue = sqrt(1/3) * P0 *(ezx*kx + ezy*ky + ezz*kz);
Ve = sqrt(1/6) * P0 * ( (exx-1i*eyx)*kx + (exy-1i*eyy)*ky + (exz-1i*eyz)*kz );
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
A = Ak + Ae;
P = Pk + Pe;
Q = Qk + Qe;
R = Rk + Re;
S = Sk + Se;
U = Uk;% + Ue;
T = Tk + Te;
V = Vk;% + Ve;
W = Wk + We;
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